Auswahl Schwarzes Brett Aktion im Forum Suche Kontakt Für Mitglieder Mathematisch für Anfänger Wer ist Online | |
| Autor |
 Streichholzgraphen 4-regulär und 4/n-regulär (n>4) und 2/5 |
|
Slash
Aktiv 
Dabei seit: 23.03.2005
Mitteilungen: 7758
Aus: Cuxhaven-Sahlenburg
 |      Beitrag No.1880, vom Themenstarter, eingetragen 2020-01-12
|
Ich habe, wie man auch dem Code entnehmen kann, den Graphen symmetrisch aufgebaut. Linkes unteres Viertel, an P13 und P19 gespiegelt, dann P37 eingesetzt. Wenn ich jetzt zuerst P35,P37 bzw. P17,P37 (Kante nicht gezeichnet!) auf 1 bringe und dann P18,P19 gibt es genau zwei Möglichkeiten von denen keine funktioniert. Sind die beiden Rauten an P37 groß wird der Graph "aufgebläht" mit 60 Grad Winkeln, sind die Rauten schmal verschwinden sie weil P17 und P18, sowie P35 und P36 zusammenfallen.
37 Knoten, 3×Grad 2, 3×Grad 3, 30×Grad 4, 1×Grad 5, 0? Überschneidungen
70 Kanten, minimal 0.99999999796318217449, maximal 1.00000000000000133227
einzustellende Kanten, Abstände und Winkel:
|P35-P37|=0.99999999796318217449
|P18-P19|=0.99999999898158853373
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>4-regulärer Graph</Bildtext>
%<Ausrichten von="13" nach="37"/>
%<Winkel size="18" color="blue" id="blue_angle" value="59.998171739876376"/>
%<Winkel size="18" color="green" id="green_angle" value="0.0018281927627456828"/>
%<Winkel size="18" color="orange" id="orange_angle" value="50.09058415159389"/>
%<Feinjustieren Anzahl="2"/>
%<Rechenweg>
%P[1]=[199.99999996225333,-60.6264089832257];
%P[2]=[253.58572859643078,-91.56300388649035]; D=ab(1,2); A(2,1); L(3,1,2); L(4,3,2); L(5,4,2);
%M(6,1,3,blue_angle,2,green_angle,2);
%N(14,3,4); N(15,10,8); N(16,6,14); N(17,16,14); N(18,15,16); N(19,12,15);
%A(18,19);
%A(13,19,ab(13,19,[1,19],"gespiegelt"));
%N(37,36,18);
%RA(35,37);
%RA(18,19);
%
%</Rechenweg>
%</Streichholzgraph>
%Ende der Eingabe.
% Streichholzgraphen mit pgfplots, TikZ/pgf
% v3.1a
%\documentclass[margin=5mm, tikz]{standalone}
%\usetikzlibrary{angles, quotes, babel}
\usetikzlibrary{spy}%<- Neu
\tikzset{SpyStyle/.style={
spy using outlines={rectangle, magnification=3, width=7.5cm, height=3cm, connect spies}
}}%<- Neu
%\usepackage{pgfplots}
%\usepgfplotslibrary{patchplots}
%\pgfplotsset{compat=1.13}
% Eingaben ===========================
\def\DefaultTextposition{south} % south west % etc.
\def\AusnahmeTextposition{north}
\def\AusnahmeListe{8,29}
% Möglichst eingeben:
\xdef\BeliebigesVorhandenesKoordinatenpaar{{3.46413352268023189140,3.99999999745406631391}} % 0,0
\colorlet{Kantenfarbe}{gray}
\colorlet{Punktfarbe}{red}
\def\Beschriftung{\punktnummer} % \punktnummer oder {} leer
\pgfplotsset{
x=12mm, y=12mm, % Maßstab
% width=20cm, height=5cm, % oder Bildmaße
}
\tikzset{font=\scriptsize} % Schrift Punktnummern und Winkel
% ===========================
%Unterprogramm, das Mehrfachplatzierung (je nach Pfadanzahl)
% von Punktbezeichnungen verhindert =======
\xdef\LstPN{0}
\newif\ifDupe
\pgfplotsset{avoid dupes/.code={\Dupefalse
\xdef\anker{\DefaultTextposition} % Default
\foreach \X in \LstPN
{\pgfmathtruncatemacro{\itest}{ifthenelse(\X==\punktnummer,1,0)}
\ifnum\itest=1
\global\Dupetrue
\breakforeach
\fi}
\ifDupe
% auskommentieren:
\typeout{\punktnummer\space ist\space ein\space Duplikat!}%
\xdef\punktnummer{} %löscht mehrfache Nummern
%\pgfkeysalso{/tikz/opacity=1} % macht mehrfache Nummern unsichtbar
\else
\xdef\LstPN{\LstPN,\punktnummer}
\typeout{\punktnummer\space ist\space neu\space mit\space urprgl.\space Anker=\anker}
\foreach \X in \LstExcept
{\ifnum\X=\punktnummer
%\pgfkeysalso{/tikz/anchor=-90}
\xdef\anker{\AusnahmeTextposition}
\fi}
\typeout{\punktnummer\space ist\space neu\space mit\space Anker=\anker}
\fi}}
% ============
\begin{document}
\xdef\LstExcept{\AusnahmeListe}
% Für Zeichnung der Winkel
\pgfdeclarelayer{bg} % declare background layer
\pgfsetlayers{bg,main} % set the order of the layers (main is the standard
% Aliaswerte für Aliasplot (Winkelplot)
\pgfmathsetmacro{\xAlias}{\BeliebigesVorhandenesKoordinatenpaar[0]}
\pgfmathsetmacro{\yAlias}{\BeliebigesVorhandenesKoordinatenpaar[1]}
%\xAlias, \yAlias
\begin{tikzpicture}[SpyStyle]
% Punkte und Kanten ========================
\begin{axis}[hide axis,
colormap={kantenfarbe}{color=(Kantenfarbe) color=(Kantenfarbe)},
thick, % Kanten
]
\addplot+[mark size=1.125pt,
mark options={Punktfarbe},
table/row sep=newline,
patch, % Plot-Typ
patch type=polygon,
vertex count=2, % damit nur Kanten, keine Flächen, gezeichnet werden
%
% Angabe der Verbindungskanten =====================
patch table with point meta={
Startpkt Endpkt colordata \\
1 1 \\
2 1 \\
3 1 \\
3 2 \\
4 3 \\
4 2 \\
5 4 \\
5 2 \\
6 1 \\
7 1 \\
7 6 \\
8 7 \\
8 6 \\
9 7 \\
9 8 \\
10 9 \\
11 9 \\
11 10 \\
12 11 \\
12 10 \\
13 11 \\
13 12 \\
13 30 \\
13 31 \\
14 3 \\
14 4 \\
15 10 \\
15 8 \\
16 6 \\
16 14 \\
17 16 \\
17 14 \\
18 15 \\
18 16 \\
19 12 \\
19 15 \\
19 31 \\
19 33 \\
20 20 \\
21 20 \\
22 20 \\
22 21 \\
23 21 \\
23 22 \\
24 21 \\
24 23 \\
25 20 \\
26 20 \\
26 25 \\
27 25 \\
27 26 \\
28 26 \\
28 27 \\
29 28 \\
30 28 \\
30 29 \\
31 29 \\
31 30 \\
32 22 \\
32 23 \\
33 27 \\
33 29 \\
34 25 \\
34 32 \\
35 32 \\
35 34 \\
35 37 \\
36 33 \\
36 34 \\
36 19 \\
37 36 \\
37 18 \\
},
%
% Beschriftung
visualization depends on={value \thisrowno{0} \as \punktnummer},
every node near coord/.append style={
/pgfplots/avoid dupes,% Methode für Mehrfachplatzierung anwenden
},
nodes near coords={\Beschriftung},
nodes near coords style={
anchor=\anker,
text=black,
%font=\scriptsize,
name=p-\punktnummer, % Punkte bennennen
path picture={% Jedem Punkt als Koordinate zuordnen:
\coordinate[] (P\punktnummer) at (p-\punktnummer.\anker);}
},
]
% Koordinatentabelle
table[header=true, x index=1, y index=2, row sep=\\] {
Nr x y \\
0 0 0 \\% 0 Aliaspunkt
1 1.73206676133524650751 0.99997236471520989376 \\
2 2.59810014259226695899 0.49998618235760483586 \\
3 2.59808418742664182233 1.49998618223032109675 \\
4 3.46411756868366227380 0.99999999987271626090 \\
5 3.46413352384928696637 0.00000000000000000000 \\
6 1.73208271532836000084 1.99997236458794502845 \\
7 0.86604933465757927280 1.49998618121490534527 \\
8 0.86606528865069276613 2.49998618108764025791 \\
9 0.00003190797991197527 1.99999999771460124087 \\
10 0.86604933465915800994 2.50001381421156265716 \\
11 0.00001595398995598764 2.99999999758733615352 \\
12 0.86603338066920210192 3.50001381408429734776 \\
13 0.00000000000000000000 3.99999999746007173229 \\
14 3.46410161351803624896 1.99999999974543274384 \\
15 1.73208271533009372511 2.99999999758433411046 \\
16 2.59808418625251968948 2.50001381522698107318 \\
17 3.46411756633548373330 2.99999999961818630823 \\
18 2.59810014142134315662 3.50001381509969711203 \\
19 1.73206676134013726198 3.99999999745706880105 \\
20 1.73206676134564752090 7.00002763019892881857 \\
21 2.59810014260440258482 7.50001381255353027910 \\
22 2.59808418743530999961 6.50001381268081424025 \\
23 3.46411756869406239900 6.99999999503541747714 \\
24 3.46413352386315542830 7.99999999490813351599 \\
25 1.73208271533529378772 6.00002763032619323980 \\
26 0.86604933466624656191 6.50001381370223363376 \\
27 0.86606528865589349486 5.50001381382949983134 \\
28 0.00003190798684619460 5.99999999720554111349 \\
29 0.86604933466435829459 5.49998618070557832027 \\
30 0.00001595399342309730 4.99999999733280642289 \\
31 0.86603338067093560415 4.49998618083284274149 \\
32 3.46410161352496936971 5.99999999516270055011 \\
33 1.73208271533356072958 4.99999999732980349165 \\
34 2.59808418625771997412 5.49998617968415359769 \\
35 3.46411756633895162594 4.99999999528994631959 \\
36 2.59810014142307643681 4.49998617981143844702 \\
37 3.46413352268023189140 3.99999999745406631391 \\
};
% ===================================
% Zeichnung der Dreiecke =====================
\addplot[no marks, % Aliasplot
nodes near coords={},% Aliasplot
visualization depends on={value \thisrowno{0} \as \PunktI},
visualization depends on={value \thisrowno{1} \as \PunktII},
visualization depends on={value \thisrowno{2} \as \PunktIII},
nodes near coords style={anchor=center,%Letzer Feinschliff für Aliaswerte
path picture={%\pgftransformreset
% Winkel zeichnen
\begin{pgfonlayer}{bg} % "select the background layer" für die Winkel
\fill[black!10] (p-\PunktI) -- (p-\PunktII) -- (p-\PunktIII) ;
\end{pgfonlayer}
}},%
]
table[header=true, x expr =\xAlias, y expr=\yAlias]{% Hier möglichst vorhandene Koordinaten eintragen
Punkt1 Punkt2 Punkt3
};
% Zeichnung der Winkel =====================
\addplot[no marks, % Aliasplot
nodes near coords={},% Aliasplot
visualization depends on={value \thisrowno{0} \as \PunktI},
visualization depends on={value \thisrowno{1} \as \Scheitel},
visualization depends on={value \thisrowno{2} \as \PunktII},
visualization depends on={value \thisrowno{3} \as \Winkelradius},
visualization depends on={value \thisrowno{4} \as \Winkelfarbe},
visualization depends on={value \thisrowno{5} \as \Winkelname},
visualization depends on={value \thisrowno{6} \as \WinkelExzentrizitaet},
nodes near coords style={anchor=center,%Letzer Feinschliff für Aliaswerte
path picture={%\pgftransformreset
% Winkel zeichnen
\begin{pgfonlayer}{bg} % "select the background layer" für die Winkel
\draw pic [angle radius=\Winkelradius cm,%
fill=\Winkelfarbe!40, draw=\Winkelfarbe,%<- Winkel färben / zeichnen
%-latex, %<- Winkel mit Pfeil
"$\Winkelname$", angle eccentricity =\WinkelExzentrizitaet,
text=\Winkelfarbe%
] {angle = P\PunktI--P\Scheitel--P\PunktII};
\end{pgfonlayer}
}},%
]
table[header=true, x expr =\xAlias, y expr=\yAlias]{% Hier möglichst vorhandene Koordinaten eintragen
Punkt1 Scheitel Punkt2 Winkelradius[cm] Winkelfarbe Winkelname WinkelExz
3 1 6 0.5 Blue {} 1.5 \\
8 9 10 0.5 Green {} 1.5 \\
};
\end{axis}
% Annotationen
%\node[above=3mm, align=center, font=\tiny] at (P11) {Wichtiger \\ Punkt};
%\draw[purple, very thick] (P8) -- (P10) node[near start, below, align=center, font=\tiny]{Wichtige \\ Kante};
%\begin{pgfonlayer}{bg}
%\fill[yellow] (P12) -- (P13) -- (P14) -- cycle;
%\end{pgfonlayer}
%\foreach \n in \AusnahmeListe
%\draw[cyan] (P\n) circle (3pt)
%\if\n4 node[anchor=north west, font=\tiny, align=left]{Default-\\position \\ ge{\"a}ndert} \else\fi ;
%\spy [red] on (P5) in node at (2.5,-1.25);
%einzustellende Kanten, Abstände und Winkel:
\draw[green,very thick] (P35) -- (P37);
\draw[green,very thick] (P18) -- (P19);
%nicht passende Kanten:
\end{tikzpicture}
\end{document}
</math>](/matheplanet/nuke/html/latexrender/pictures/83b16987fa3b655a4667d37094b4da1d.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>4-regulärer Graph</Bildtext>
%<Ausrichten von=\"13\" nach=\"37\"/>
%<Winkel size=\"18\" color=\"blue\" id=\"blue_angle\" value=\"59.998171739876376\"/>
%<Winkel size=\"18\" color=\"green\" id=\"green_angle\" value=\"0.0018281927627456828\"/>
%<Winkel size=\"18\" color=\"orange\" id=\"orange_angle\" value=\"50.09058415159389\"/>
%<Feinjustieren Anzahl=\"2\"/>
%<Rechenweg>
%P[1]=[199.99999996225333,-60.6264089832257];
%P[2]=[253.58572859643078,-91.56300388649035]; D=ab(1,2); A(2,1); L(3,1,2); L(4,3,2); L(5,4,2);
%M(6,1,3,blue_angle,2,green_angle,2);
%N(14,3,4); N(15,10,8); N(16,6,14); N(17,16,14); N(18,15,16); N(19,12,15);
%A(18,19);
%A(13,19,ab(13,19,[1,19],\"gespiegelt\"));
%N(37,36,18);
%RA(35,37);
%RA(18,19);
%
%</Rechenweg>
%</Streichholzgraph>
%Ende der Eingabe.
% Streichholzgraphen mit pgfplots, TikZ/pgf
% v3.1a
%\documentclass[margin=5mm, tikz]{standalone}
%\usetikzlibrary{angles, quotes, babel}
\usetikzlibrary{spy}%<- Neu
\tikzset{SpyStyle/.style={
spy using outlines={rectangle, magnification=3, width=7.5cm, height=3cm, connect spies}
}}%<- Neu
%\usepackage{pgfplots}
%\usepgfplotslibrary{patchplots}
%\pgfplotsset{compat=1.13}
% Eingaben ===========================
\def\DefaultTextposition{south} % south west % etc.
\def\AusnahmeTextposition{north}
\def\AusnahmeListe{8,29}
% Möglichst eingeben:
\xdef\BeliebigesVorhandenesKoordinatenpaar{{3.46413352268023189140,3.99999999745406631391}} % 0,0
\colorlet{Kantenfarbe}{gray}
\colorlet{Punktfarbe}{red}
\def\Beschriftung{\punktnummer} % \punktnummer oder {} leer
\pgfplotsset{
x=12mm, y=12mm, % Maßstab
% width=20cm, height=5cm, % oder Bildmaße
}
\tikzset{font=\scriptsize} % Schrift Punktnummern und Winkel
% ===========================
%Unterprogramm, das Mehrfachplatzierung (je nach Pfadanzahl)
% von Punktbezeichnungen verhindert =======
\xdef\LstPN{0}
\newif\ifDupe
\pgfplotsset{avoid dupes/.code={\Dupefalse
\xdef\anker{\DefaultTextposition} % Default
\foreach \X in \LstPN
{\pgfmathtruncatemacro{\itest}{ifthenelse(\X==\punktnummer,1,0)}
\ifnum\itest=1
\global\Dupetrue
\breakforeach
\fi}
\ifDupe
% auskommentieren:
\typeout{\punktnummer\space ist\space ein\space Duplikat!}%
\xdef\punktnummer{} %löscht mehrfache Nummern
%\pgfkeysalso{/tikz/opacity=1} % macht mehrfache Nummern unsichtbar
\else
\xdef\LstPN{\LstPN,\punktnummer}
\typeout{\punktnummer\space ist\space neu\space mit\space urprgl.\space Anker=\anker}
\foreach \X in \LstExcept
{\ifnum\X=\punktnummer
%\pgfkeysalso{/tikz/anchor=-90}
\xdef\anker{\AusnahmeTextposition}
\fi}
\typeout{\punktnummer\space ist\space neu\space mit\space Anker=\anker}
\fi}}
% ============
\begin{document}
\xdef\LstExcept{\AusnahmeListe}
% Für Zeichnung der Winkel
\pgfdeclarelayer{bg} % declare background layer
\pgfsetlayers{bg,main} % set the order of the layers (main is the standard
% Aliaswerte für Aliasplot (Winkelplot)
\pgfmathsetmacro{\xAlias}{\BeliebigesVorhandenesKoordinatenpaar[0]}
\pgfmathsetmacro{\yAlias}{\BeliebigesVorhandenesKoordinatenpaar[1]}
%\xAlias, \yAlias
\begin{tikzpicture}[SpyStyle]
% Punkte und Kanten ========================
\begin{axis}[hide axis,
colormap={kantenfarbe}{color=(Kantenfarbe) color=(Kantenfarbe)},
thick, % Kanten
]
\addplot+[mark size=1.125pt,
mark options={Punktfarbe},
table/row sep=newline,
patch, % Plot-Typ
patch type=polygon,
vertex count=2, % damit nur Kanten, keine Flächen, gezeichnet werden
%
% Angabe der Verbindungskanten =====================
patch table with point meta={
Startpkt Endpkt colordata \\
1 1 \\
2 1 \\
3 1 \\
3 2 \\
4 3 \\
4 2 \\
5 4 \\
5 2 \\
6 1 \\
7 1 \\
7 6 \\
8 7 \\
8 6 \\
9 7 \\
9 8 \\
10 9 \\
11 9 \\
11 10 \\
12 11 \\
12 10 \\
13 11 \\
13 12 \\
13 30 \\
13 31 \\
14 3 \\
14 4 \\
15 10 \\
15 8 \\
16 6 \\
16 14 \\
17 16 \\
17 14 \\
18 15 \\
18 16 \\
19 12 \\
19 15 \\
19 31 \\
19 33 \\
20 20 \\
21 20 \\
22 20 \\
22 21 \\
23 21 \\
23 22 \\
24 21 \\
24 23 \\
25 20 \\
26 20 \\
26 25 \\
27 25 \\
27 26 \\
28 26 \\
28 27 \\
29 28 \\
30 28 \\
30 29 \\
31 29 \\
31 30 \\
32 22 \\
32 23 \\
33 27 \\
33 29 \\
34 25 \\
34 32 \\
35 32 \\
35 34 \\
35 37 \\
36 33 \\
36 34 \\
36 19 \\
37 36 \\
37 18 \\
},
%
% Beschriftung
visualization depends on={value \thisrowno{0} \as \punktnummer},
every node near coord/.append style={
/pgfplots/avoid dupes,% Methode für Mehrfachplatzierung anwenden
},
nodes near coords={\Beschriftung},
nodes near coords style={
anchor=\anker,
text=black,
%font=\scriptsize,
name=p-\punktnummer, % Punkte bennennen
path picture={% Jedem Punkt als Koordinate zuordnen:
\coordinate[] (P\punktnummer) at (p-\punktnummer.\anker);}
},
]
% Koordinatentabelle
table[header=true, x index=1, y index=2, row sep=\\] {
Nr x y \\
0 0 0 \\% 0 Aliaspunkt
1 1.73206676133524650751 0.99997236471520989376 \\
2 2.59810014259226695899 0.49998618235760483586 \\
3 2.59808418742664182233 1.49998618223032109675 \\
4 3.46411756868366227380 0.99999999987271626090 \\
5 3.46413352384928696637 0.00000000000000000000 \\
6 1.73208271532836000084 1.99997236458794502845 \\
7 0.86604933465757927280 1.49998618121490534527 \\
8 0.86606528865069276613 2.49998618108764025791 \\
9 0.00003190797991197527 1.99999999771460124087 \\
10 0.86604933465915800994 2.50001381421156265716 \\
11 0.00001595398995598764 2.99999999758733615352 \\
12 0.86603338066920210192 3.50001381408429734776 \\
13 0.00000000000000000000 3.99999999746007173229 \\
14 3.46410161351803624896 1.99999999974543274384 \\
15 1.73208271533009372511 2.99999999758433411046 \\
16 2.59808418625251968948 2.50001381522698107318 \\
17 3.46411756633548373330 2.99999999961818630823 \\
18 2.59810014142134315662 3.50001381509969711203 \\
19 1.73206676134013726198 3.99999999745706880105 \\
20 1.73206676134564752090 7.00002763019892881857 \\
21 2.59810014260440258482 7.50001381255353027910 \\
22 2.59808418743530999961 6.50001381268081424025 \\
23 3.46411756869406239900 6.99999999503541747714 \\
24 3.46413352386315542830 7.99999999490813351599 \\
25 1.73208271533529378772 6.00002763032619323980 \\
26 0.86604933466624656191 6.50001381370223363376 \\
27 0.86606528865589349486 5.50001381382949983134 \\
28 0.00003190798684619460 5.99999999720554111349 \\
29 0.86604933466435829459 5.49998618070557832027 \\
30 0.00001595399342309730 4.99999999733280642289 \\
31 0.86603338067093560415 4.49998618083284274149 \\
32 3.46410161352496936971 5.99999999516270055011 \\
33 1.73208271533356072958 4.99999999732980349165 \\
34 2.59808418625771997412 5.49998617968415359769 \\
35 3.46411756633895162594 4.99999999528994631959 \\
36 2.59810014142307643681 4.49998617981143844702 \\
37 3.46413352268023189140 3.99999999745406631391 \\
};
% ===================================
% Zeichnung der Dreiecke =====================
\addplot[no marks, % Aliasplot
nodes near coords={},% Aliasplot
visualization depends on={value \thisrowno{0} \as \PunktI},
visualization depends on={value \thisrowno{1} \as \PunktII},
visualization depends on={value \thisrowno{2} \as \PunktIII},
nodes near coords style={anchor=center,%Letzer Feinschliff für Aliaswerte
path picture={%\pgftransformreset
% Winkel zeichnen
\begin{pgfonlayer}{bg} % \"select the background layer\" für die Winkel
\fill[black!10] (p-\PunktI) -- (p-\PunktII) -- (p-\PunktIII) ;
\end{pgfonlayer}
}},%
]
table[header=true, x expr =\xAlias, y expr=\yAlias]{% Hier möglichst vorhandene Koordinaten eintragen
Punkt1 Punkt2 Punkt3
};
% Zeichnung der Winkel =====================
\addplot[no marks, % Aliasplot
nodes near coords={},% Aliasplot
visualization depends on={value \thisrowno{0} \as \PunktI},
visualization depends on={value \thisrowno{1} \as \Scheitel},
visualization depends on={value \thisrowno{2} \as \PunktII},
visualization depends on={value \thisrowno{3} \as \Winkelradius},
visualization depends on={value \thisrowno{4} \as \Winkelfarbe},
visualization depends on={value \thisrowno{5} \as \Winkelname},
visualization depends on={value \thisrowno{6} \as \WinkelExzentrizitaet},
nodes near coords style={anchor=center,%Letzer Feinschliff für Aliaswerte
path picture={%\pgftransformreset
% Winkel zeichnen
\begin{pgfonlayer}{bg} % \"select the background layer\" für die Winkel
\draw pic [angle radius=\Winkelradius cm,%
fill=\Winkelfarbe!40, draw=\Winkelfarbe,%<- Winkel färben / zeichnen
%-latex, %<- Winkel mit Pfeil
\"$\Winkelname$\", angle eccentricity =\WinkelExzentrizitaet,
text=\Winkelfarbe%
] {angle = P\PunktI--P\Scheitel--P\PunktII};
\end{pgfonlayer}
}},%
]
table[header=true, x expr =\xAlias, y expr=\yAlias]{% Hier möglichst vorhandene Koordinaten eintragen
Punkt1 Scheitel Punkt2 Winkelradius[cm] Winkelfarbe Winkelname WinkelExz
3 1 6 0.5 Blue {} 1.5 \\
8 9 10 0.5 Green {} 1.5 \\
};
\end{axis}
% Annotationen
%\node[above=3mm, align=center, font=\tiny] at (P11) {Wichtiger \\ Punkt};
%\draw[purple, very thick] (P8) -- (P10) node[near start, below, align=center, font=\tiny]{Wichtige \\ Kante};
%\begin{pgfonlayer}{bg}
%\fill[yellow] (P12) -- (P13) -- (P14) -- cycle;
%\end{pgfonlayer}
%\foreach \n in \AusnahmeListe
%\draw[cyan] (P\n) circle (3pt)
%\if\n4 node[anchor=north west, font=\tiny, align=left]{Default-\\position \\ ge{\\"a}ndert} \else\fi ;
%\spy [red] on (P5) in node at (2.5,-1.25);
%einzustellende Kanten, Abstände und Winkel:
\draw[green,very thick] (P35) -- (P37);
\draw[green,very thick] (P18) -- (P19);
%nicht passende Kanten:
\end{tikzpicture}
\end{document}")
37 Knoten, 3×Grad 2, 3×Grad 3, 30×Grad 4, 1×Grad 5, 8? Überschneidungen
70 Kanten, minimal 0.99999999999999888978, maximal 1.00000000000000288658
einzustellende Kanten, Abstände und Winkel:
|P35-P37|=1.00000000000000088818
|P18-P19|=1.00000000000000288658
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>4-regulärer Graph</Bildtext>
%<Ausrichten von="13" nach="37"/>
%<Winkel size="18" color="blue" id="blue_angle" value="29.56986755338101"/>
%<Winkel size="18" color="green" id="green_angle" value="7.078610995879132"/>
%<Winkel size="18" color="orange" id="orange_angle" value="50.09058415159389"/>
%<Feinjustieren Anzahl="2"/>
%<Rechenweg>
%P[1]=[192.03544850833785,-114.13476613030267];
%P[2]=[269.0322607989641,-118.31712787460212]; D=ab(1,2); A(2,1); L(3,1,2); L(4,3,2); L(5,4,2);
%M(6,1,3,blue_angle,2,green_angle,2);
%N(14,3,4); N(15,10,8); N(16,6,14); N(17,16,14); N(18,15,16); N(19,12,15);
%A(18,19);
%A(13,19,ab(13,19,[1,19],"gespiegelt"));
%N(37,36,18);
%RA(35,37);
%RA(18,19);
%
%</Rechenweg>
%</Streichholzgraph>
%Ende der Eingabe.
% Streichholzgraphen mit pgfplots, TikZ/pgf
% v3.1a
%\documentclass[margin=5mm, tikz]{standalone}
%\usetikzlibrary{angles, quotes, babel}
\usetikzlibrary{spy}%<- Neu
\tikzset{SpyStyle/.style={
spy using outlines={rectangle, magnification=3, width=7.5cm, height=3cm, connect spies}
}}%<- Neu
%\usepackage{pgfplots}
%\usepgfplotslibrary{patchplots}
%\pgfplotsset{compat=1.13}
% Eingaben ===========================
\def\DefaultTextposition{south} % south west % etc.
\def\AusnahmeTextposition{north}
\def\AusnahmeListe{8,16,18,29,33,35}
% Möglichst eingeben:
\xdef\BeliebigesVorhandenesKoordinatenpaar{{3.58096098925905748089,3.20968054257941037832}} % 0,0
\colorlet{Kantenfarbe}{gray}
\colorlet{Punktfarbe}{red}
\def\Beschriftung{\punktnummer} % \punktnummer oder {} leer
\pgfplotsset{
x=12mm, y=12mm, % Maßstab
% width=20cm, height=5cm, % oder Bildmaße
}
\tikzset{font=\scriptsize} % Schrift Punktnummern und Winkel
% ===========================
%Unterprogramm, das Mehrfachplatzierung (je nach Pfadanzahl)
% von Punktbezeichnungen verhindert =======
\xdef\LstPN{0}
\newif\ifDupe
\pgfplotsset{avoid dupes/.code={\Dupefalse
\xdef\anker{\DefaultTextposition} % Default
\foreach \X in \LstPN
{\pgfmathtruncatemacro{\itest}{ifthenelse(\X==\punktnummer,1,0)}
\ifnum\itest=1
\global\Dupetrue
\breakforeach
\fi}
\ifDupe
% auskommentieren:
\typeout{\punktnummer\space ist\space ein\space Duplikat!}%
\xdef\punktnummer{} %löscht mehrfache Nummern
%\pgfkeysalso{/tikz/opacity=1} % macht mehrfache Nummern unsichtbar
\else
\xdef\LstPN{\LstPN,\punktnummer}
\typeout{\punktnummer\space ist\space neu\space mit\space urprgl.\space Anker=\anker}
\foreach \X in \LstExcept
{\ifnum\X=\punktnummer
%\pgfkeysalso{/tikz/anchor=-90}
\xdef\anker{\AusnahmeTextposition}
\fi}
\typeout{\punktnummer\space ist\space neu\space mit\space Anker=\anker}
\fi}}
% ============
\begin{document}
\xdef\LstExcept{\AusnahmeListe}
% Für Zeichnung der Winkel
\pgfdeclarelayer{bg} % declare background layer
\pgfsetlayers{bg,main} % set the order of the layers (main is the standard
% Aliaswerte für Aliasplot (Winkelplot)
\pgfmathsetmacro{\xAlias}{\BeliebigesVorhandenesKoordinatenpaar[0]}
\pgfmathsetmacro{\yAlias}{\BeliebigesVorhandenesKoordinatenpaar[1]}
%\xAlias, \yAlias
\begin{tikzpicture}[SpyStyle]
% Punkte und Kanten ========================
\begin{axis}[hide axis,
colormap={kantenfarbe}{color=(Kantenfarbe) color=(Kantenfarbe)},
thick, % Kanten
]
\addplot+[mark size=1.125pt,
mark options={Punktfarbe},
table/row sep=newline,
patch, % Plot-Typ
patch type=polygon,
vertex count=2, % damit nur Kanten, keine Flächen, gezeichnet werden
%
% Angabe der Verbindungskanten =====================
patch table with point meta={
Startpkt Endpkt colordata \\
1 1 \\
2 1 \\
3 1 \\
3 2 \\
4 3 \\
4 2 \\
5 4 \\
5 2 \\
6 1 \\
7 1 \\
7 6 \\
8 7 \\
8 6 \\
9 7 \\
9 8 \\
10 9 \\
11 9 \\
11 10 \\
12 11 \\
12 10 \\
13 11 \\
13 12 \\
13 30 \\
13 31 \\
14 3 \\
14 4 \\
15 10 \\
15 8 \\
16 6 \\
16 14 \\
17 16 \\
17 14 \\
18 15 \\
18 16 \\
19 12 \\
19 15 \\
19 31 \\
19 33 \\
20 20 \\
21 20 \\
22 20 \\
22 21 \\
23 21 \\
23 22 \\
24 21 \\
24 23 \\
25 20 \\
26 20 \\
26 25 \\
27 25 \\
27 26 \\
28 26 \\
28 27 \\
29 28 \\
30 28 \\
30 29 \\
31 29 \\
31 30 \\
32 22 \\
32 23 \\
33 27 \\
33 29 \\
34 25 \\
34 32 \\
35 32 \\
35 34 \\
35 37 \\
36 33 \\
36 34 \\
36 19 \\
37 36 \\
37 18 \\
},
%
% Beschriftung
visualization depends on={value \thisrowno{0} \as \punktnummer},
every node near coord/.append style={
/pgfplots/avoid dupes,% Methode für Mehrfachplatzierung anwenden
},
nodes near coords={\Beschriftung},
nodes near coords style={
anchor=\anker,
text=black,
%font=\scriptsize,
name=p-\punktnummer, % Punkte bennennen
path picture={% Jedem Punkt als Koordinate zuordnen:
\coordinate[] (P\punktnummer) at (p-\punktnummer.\anker);}
},
]
% Koordinatentabelle
table[header=true, x index=1, y index=2, row sep=\\] {
Nr x y \\
0 0 0 \\% 0 Aliaspunkt
1 1.79048049462953273725 0.10847735592002018257 \\
2 2.78900849414339191412 0.05423867796001000108 \\
3 2.33671656736751387484 0.94610863090907304507 \\
4 3.33524456688137371785 0.89186995294906323828 \\
5 3.78753649365725175713 0.00000000000000000000 \\
6 1.85221375055123615994 1.10657003954880295282 \\
7 0.95697350323647412118 0.66098626562093287795 \\
8 1.01870675915817776591 1.65907894924971555106 \\
9 0.12346651184341590757 1.21349517532184547619 \\
10 0.95697350323647234482 1.76600408502276184919 \\
11 0.06173325592170791215 2.21158785895062770521 \\
12 0.89524024731476437022 2.76409676865154452230 \\
13 0.00000000000000000000 3.20968054257941037832 \\
14 2.88295264010549567857 1.78373990589812603247 \\
15 1.85221375055123660403 2.21158785895062770521 \\
16 1.93532274310601715150 2.10311050303060698141 \\
17 2.68572074194429122329 2.76409676865154674275 \\
18 2.68572074194429477600 2.76409676865154141367 \\
19 1.79048049462952874045 3.20968054257941037832 \\
20 1.79048049462953295929 6.31088372923880136511 \\
21 2.78900849414339369048 6.36512240719881017270 \\
22 2.33671656736751431893 5.47325245424974760056 \\
23 3.33524456688137460603 5.52749113220975818450 \\
24 3.78753649365725175713 6.41936108515882164482 \\
25 1.85221375055123615994 5.31279104561001869200 \\
26 0.95697350323647456527 5.75837481953788810074 \\
27 1.01870675915817821000 4.76028213590910542763 \\
28 0.12346651184341544960 5.20586590983697572455 \\
29 0.95697350323647234482 4.65335700013605890746 \\
30 0.06173325592170772480 4.20777322620819305143 \\
31 0.89524024731476437022 3.65526431650727623435 \\
32 2.88295264010549656675 4.63562117926069561236 \\
33 1.85221375055123727016 4.20777322620819305143 \\
34 1.93532274310601715150 4.31625058212821333115 \\
35 2.68572074194429122329 3.65526431650727490208 \\
36 2.68572074194429477600 3.65526431650727934297 \\
37 3.58096098925905748089 3.20968054257941037832 \\
38 3.89 0 0 \\
};
% ===================================
% Zeichnung der Dreiecke =====================
\addplot[no marks, % Aliasplot
nodes near coords={},% Aliasplot
visualization depends on={value \thisrowno{0} \as \PunktI},
visualization depends on={value \thisrowno{1} \as \PunktII},
visualization depends on={value \thisrowno{2} \as \PunktIII},
nodes near coords style={anchor=center,%Letzer Feinschliff für Aliaswerte
path picture={%\pgftransformreset
% Winkel zeichnen
\begin{pgfonlayer}{bg} % "select the background layer" für die Winkel
\fill[black!10] (p-\PunktI) -- (p-\PunktII) -- (p-\PunktIII) ;
\end{pgfonlayer}
}},%
]
table[header=true, x expr =\xAlias, y expr=\yAlias]{% Hier möglichst vorhandene Koordinaten eintragen
Punkt1 Punkt2 Punkt3
};
% Zeichnung der Winkel =====================
\addplot[no marks, % Aliasplot
nodes near coords={},% Aliasplot
visualization depends on={value \thisrowno{0} \as \PunktI},
visualization depends on={value \thisrowno{1} \as \Scheitel},
visualization depends on={value \thisrowno{2} \as \PunktII},
visualization depends on={value \thisrowno{3} \as \Winkelradius},
visualization depends on={value \thisrowno{4} \as \Winkelfarbe},
visualization depends on={value \thisrowno{5} \as \Winkelname},
visualization depends on={value \thisrowno{6} \as \WinkelExzentrizitaet},
nodes near coords style={anchor=center,%Letzer Feinschliff für Aliaswerte
path picture={%\pgftransformreset
% Winkel zeichnen
\begin{pgfonlayer}{bg} % "select the background layer" für die Winkel
\draw pic [angle radius=\Winkelradius cm,%
fill=\Winkelfarbe!40, draw=\Winkelfarbe,%<- Winkel färben / zeichnen
%-latex, %<- Winkel mit Pfeil
"$\Winkelname$", angle eccentricity =\WinkelExzentrizitaet,
text=\Winkelfarbe%
] {angle = P\PunktI--P\Scheitel--P\PunktII};
\end{pgfonlayer}
}},%
]
table[header=true, x expr =\xAlias, y expr=\yAlias]{% Hier möglichst vorhandene Koordinaten eintragen
Punkt1 Scheitel Punkt2 Winkelradius[cm] Winkelfarbe Winkelname WinkelExz
3 1 6 0.5 Blue {} 1.5 \\
8 9 10 0.5 Green {} 1.5 \\
};
\end{axis}
% Annotationen
%\node[above=3mm, align=center, font=\tiny] at (P11) {Wichtiger \\ Punkt};
%\draw[purple, very thick] (P8) -- (P10) node[near start, below, align=center, font=\tiny]{Wichtige \\ Kante};
%\begin{pgfonlayer}{bg}
%\fill[yellow] (P12) -- (P13) -- (P14) -- cycle;
%\end{pgfonlayer}
%\foreach \n in \AusnahmeListe
%\draw[cyan] (P\n) circle (3pt)
%\if\n4 node[anchor=north west, font=\tiny, align=left]{Default-\\position \\ ge{\"a}ndert} \else\fi ;
%\spy [red] on (P5) in node at (2.5,-1.25);
%einzustellende Kanten, Abstände und Winkel:
\draw[green,very thick] (P35) -- (P37);
\draw[green,very thick] (P18) -- (P19);
%nicht passende Kanten:
\end{tikzpicture}
\end{document}
</math>](/matheplanet/nuke/html/latexrender/pictures/14c2b1a1a14da2297cf97895b499bf21.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>4-regulärer Graph</Bildtext>
%<Ausrichten von=\"13\" nach=\"37\"/>
%<Winkel size=\"18\" color=\"blue\" id=\"blue_angle\" value=\"29.56986755338101\"/>
%<Winkel size=\"18\" color=\"green\" id=\"green_angle\" value=\"7.078610995879132\"/>
%<Winkel size=\"18\" color=\"orange\" id=\"orange_angle\" value=\"50.09058415159389\"/>
%<Feinjustieren Anzahl=\"2\"/>
%<Rechenweg>
%P[1]=[192.03544850833785,-114.13476613030267];
%P[2]=[269.0322607989641,-118.31712787460212]; D=ab(1,2); A(2,1); L(3,1,2); L(4,3,2); L(5,4,2);
%M(6,1,3,blue_angle,2,green_angle,2);
%N(14,3,4); N(15,10,8); N(16,6,14); N(17,16,14); N(18,15,16); N(19,12,15);
%A(18,19);
%A(13,19,ab(13,19,[1,19],\"gespiegelt\"));
%N(37,36,18);
%RA(35,37);
%RA(18,19);
%
%</Rechenweg>
%</Streichholzgraph>
%Ende der Eingabe.
% Streichholzgraphen mit pgfplots, TikZ/pgf
% v3.1a
%\documentclass[margin=5mm, tikz]{standalone}
%\usetikzlibrary{angles, quotes, babel}
\usetikzlibrary{spy}%<- Neu
\tikzset{SpyStyle/.style={
spy using outlines={rectangle, magnification=3, width=7.5cm, height=3cm, connect spies}
}}%<- Neu
%\usepackage{pgfplots}
%\usepgfplotslibrary{patchplots}
%\pgfplotsset{compat=1.13}
% Eingaben ===========================
\def\DefaultTextposition{south} % south west % etc.
\def\AusnahmeTextposition{north}
\def\AusnahmeListe{8,16,18,29,33,35}
% Möglichst eingeben:
\xdef\BeliebigesVorhandenesKoordinatenpaar{{3.58096098925905748089,3.20968054257941037832}} % 0,0
\colorlet{Kantenfarbe}{gray}
\colorlet{Punktfarbe}{red}
\def\Beschriftung{\punktnummer} % \punktnummer oder {} leer
\pgfplotsset{
x=12mm, y=12mm, % Maßstab
% width=20cm, height=5cm, % oder Bildmaße
}
\tikzset{font=\scriptsize} % Schrift Punktnummern und Winkel
% ===========================
%Unterprogramm, das Mehrfachplatzierung (je nach Pfadanzahl)
% von Punktbezeichnungen verhindert =======
\xdef\LstPN{0}
\newif\ifDupe
\pgfplotsset{avoid dupes/.code={\Dupefalse
\xdef\anker{\DefaultTextposition} % Default
\foreach \X in \LstPN
{\pgfmathtruncatemacro{\itest}{ifthenelse(\X==\punktnummer,1,0)}
\ifnum\itest=1
\global\Dupetrue
\breakforeach
\fi}
\ifDupe
% auskommentieren:
\typeout{\punktnummer\space ist\space ein\space Duplikat!}%
\xdef\punktnummer{} %löscht mehrfache Nummern
%\pgfkeysalso{/tikz/opacity=1} % macht mehrfache Nummern unsichtbar
\else
\xdef\LstPN{\LstPN,\punktnummer}
\typeout{\punktnummer\space ist\space neu\space mit\space urprgl.\space Anker=\anker}
\foreach \X in \LstExcept
{\ifnum\X=\punktnummer
%\pgfkeysalso{/tikz/anchor=-90}
\xdef\anker{\AusnahmeTextposition}
\fi}
\typeout{\punktnummer\space ist\space neu\space mit\space Anker=\anker}
\fi}}
% ============
\begin{document}
\xdef\LstExcept{\AusnahmeListe}
% Für Zeichnung der Winkel
\pgfdeclarelayer{bg} % declare background layer
\pgfsetlayers{bg,main} % set the order of the layers (main is the standard
% Aliaswerte für Aliasplot (Winkelplot)
\pgfmathsetmacro{\xAlias}{\BeliebigesVorhandenesKoordinatenpaar[0]}
\pgfmathsetmacro{\yAlias}{\BeliebigesVorhandenesKoordinatenpaar[1]}
%\xAlias, \yAlias
\begin{tikzpicture}[SpyStyle]
% Punkte und Kanten ========================
\begin{axis}[hide axis,
colormap={kantenfarbe}{color=(Kantenfarbe) color=(Kantenfarbe)},
thick, % Kanten
]
\addplot+[mark size=1.125pt,
mark options={Punktfarbe},
table/row sep=newline,
patch, % Plot-Typ
patch type=polygon,
vertex count=2, % damit nur Kanten, keine Flächen, gezeichnet werden
%
% Angabe der Verbindungskanten =====================
patch table with point meta={
Startpkt Endpkt colordata \\
1 1 \\
2 1 \\
3 1 \\
3 2 \\
4 3 \\
4 2 \\
5 4 \\
5 2 \\
6 1 \\
7 1 \\
7 6 \\
8 7 \\
8 6 \\
9 7 \\
9 8 \\
10 9 \\
11 9 \\
11 10 \\
12 11 \\
12 10 \\
13 11 \\
13 12 \\
13 30 \\
13 31 \\
14 3 \\
14 4 \\
15 10 \\
15 8 \\
16 6 \\
16 14 \\
17 16 \\
17 14 \\
18 15 \\
18 16 \\
19 12 \\
19 15 \\
19 31 \\
19 33 \\
20 20 \\
21 20 \\
22 20 \\
22 21 \\
23 21 \\
23 22 \\
24 21 \\
24 23 \\
25 20 \\
26 20 \\
26 25 \\
27 25 \\
27 26 \\
28 26 \\
28 27 \\
29 28 \\
30 28 \\
30 29 \\
31 29 \\
31 30 \\
32 22 \\
32 23 \\
33 27 \\
33 29 \\
34 25 \\
34 32 \\
35 32 \\
35 34 \\
35 37 \\
36 33 \\
36 34 \\
36 19 \\
37 36 \\
37 18 \\
},
%
% Beschriftung
visualization depends on={value \thisrowno{0} \as \punktnummer},
every node near coord/.append style={
/pgfplots/avoid dupes,% Methode für Mehrfachplatzierung anwenden
},
nodes near coords={\Beschriftung},
nodes near coords style={
anchor=\anker,
text=black,
%font=\scriptsize,
name=p-\punktnummer, % Punkte bennennen
path picture={% Jedem Punkt als Koordinate zuordnen:
\coordinate[] (P\punktnummer) at (p-\punktnummer.\anker);}
},
]
% Koordinatentabelle
table[header=true, x index=1, y index=2, row sep=\\] {
Nr x y \\
0 0 0 \\% 0 Aliaspunkt
1 1.79048049462953273725 0.10847735592002018257 \\
2 2.78900849414339191412 0.05423867796001000108 \\
3 2.33671656736751387484 0.94610863090907304507 \\
4 3.33524456688137371785 0.89186995294906323828 \\
5 3.78753649365725175713 0.00000000000000000000 \\
6 1.85221375055123615994 1.10657003954880295282 \\
7 0.95697350323647412118 0.66098626562093287795 \\
8 1.01870675915817776591 1.65907894924971555106 \\
9 0.12346651184341590757 1.21349517532184547619 \\
10 0.95697350323647234482 1.76600408502276184919 \\
11 0.06173325592170791215 2.21158785895062770521 \\
12 0.89524024731476437022 2.76409676865154452230 \\
13 0.00000000000000000000 3.20968054257941037832 \\
14 2.88295264010549567857 1.78373990589812603247 \\
15 1.85221375055123660403 2.21158785895062770521 \\
16 1.93532274310601715150 2.10311050303060698141 \\
17 2.68572074194429122329 2.76409676865154674275 \\
18 2.68572074194429477600 2.76409676865154141367 \\
19 1.79048049462952874045 3.20968054257941037832 \\
20 1.79048049462953295929 6.31088372923880136511 \\
21 2.78900849414339369048 6.36512240719881017270 \\
22 2.33671656736751431893 5.47325245424974760056 \\
23 3.33524456688137460603 5.52749113220975818450 \\
24 3.78753649365725175713 6.41936108515882164482 \\
25 1.85221375055123615994 5.31279104561001869200 \\
26 0.95697350323647456527 5.75837481953788810074 \\
27 1.01870675915817821000 4.76028213590910542763 \\
28 0.12346651184341544960 5.20586590983697572455 \\
29 0.95697350323647234482 4.65335700013605890746 \\
30 0.06173325592170772480 4.20777322620819305143 \\
31 0.89524024731476437022 3.65526431650727623435 \\
32 2.88295264010549656675 4.63562117926069561236 \\
33 1.85221375055123727016 4.20777322620819305143 \\
34 1.93532274310601715150 4.31625058212821333115 \\
35 2.68572074194429122329 3.65526431650727490208 \\
36 2.68572074194429477600 3.65526431650727934297 \\
37 3.58096098925905748089 3.20968054257941037832 \\
38 3.89 0 0 \\
};
% ===================================
% Zeichnung der Dreiecke =====================
\addplot[no marks, % Aliasplot
nodes near coords={},% Aliasplot
visualization depends on={value \thisrowno{0} \as \PunktI},
visualization depends on={value \thisrowno{1} \as \PunktII},
visualization depends on={value \thisrowno{2} \as \PunktIII},
nodes near coords style={anchor=center,%Letzer Feinschliff für Aliaswerte
path picture={%\pgftransformreset
% Winkel zeichnen
\begin{pgfonlayer}{bg} % \"select the background layer\" für die Winkel
\fill[black!10] (p-\PunktI) -- (p-\PunktII) -- (p-\PunktIII) ;
\end{pgfonlayer}
}},%
]
table[header=true, x expr =\xAlias, y expr=\yAlias]{% Hier möglichst vorhandene Koordinaten eintragen
Punkt1 Punkt2 Punkt3
};
% Zeichnung der Winkel =====================
\addplot[no marks, % Aliasplot
nodes near coords={},% Aliasplot
visualization depends on={value \thisrowno{0} \as \PunktI},
visualization depends on={value \thisrowno{1} \as \Scheitel},
visualization depends on={value \thisrowno{2} \as \PunktII},
visualization depends on={value \thisrowno{3} \as \Winkelradius},
visualization depends on={value \thisrowno{4} \as \Winkelfarbe},
visualization depends on={value \thisrowno{5} \as \Winkelname},
visualization depends on={value \thisrowno{6} \as \WinkelExzentrizitaet},
nodes near coords style={anchor=center,%Letzer Feinschliff für Aliaswerte
path picture={%\pgftransformreset
% Winkel zeichnen
\begin{pgfonlayer}{bg} % \"select the background layer\" für die Winkel
\draw pic [angle radius=\Winkelradius cm,%
fill=\Winkelfarbe!40, draw=\Winkelfarbe,%<- Winkel färben / zeichnen
%-latex, %<- Winkel mit Pfeil
\"$\Winkelname$\", angle eccentricity =\WinkelExzentrizitaet,
text=\Winkelfarbe%
] {angle = P\PunktI--P\Scheitel--P\PunktII};
\end{pgfonlayer}
}},%
]
table[header=true, x expr =\xAlias, y expr=\yAlias]{% Hier möglichst vorhandene Koordinaten eintragen
Punkt1 Scheitel Punkt2 Winkelradius[cm] Winkelfarbe Winkelname WinkelExz
3 1 6 0.5 Blue {} 1.5 \\
8 9 10 0.5 Green {} 1.5 \\
};
\end{axis}
% Annotationen
%\node[above=3mm, align=center, font=\tiny] at (P11) {Wichtiger \\ Punkt};
%\draw[purple, very thick] (P8) -- (P10) node[near start, below, align=center, font=\tiny]{Wichtige \\ Kante};
%\begin{pgfonlayer}{bg}
%\fill[yellow] (P12) -- (P13) -- (P14) -- cycle;
%\end{pgfonlayer}
%\foreach \n in \AusnahmeListe
%\draw[cyan] (P\n) circle (3pt)
%\if\n4 node[anchor=north west, font=\tiny, align=left]{Default-\\position \\ ge{\\"a}ndert} \else\fi ;
%\spy [red] on (P5) in node at (2.5,-1.25);
%einzustellende Kanten, Abstände und Winkel:
\draw[green,very thick] (P35) -- (P37);
\draw[green,very thick] (P18) -- (P19);
%nicht passende Kanten:
\end{tikzpicture}
\end{document}")
-----------------
Bound to be disappointing so why wait?
|
 Profil
 Quote
 Link |
haribo
Senior 
Dabei seit: 25.10.2012
Mitteilungen: 2298
 | Beitrag No.1881, eingetragen 2020-01-12
|
oh mann ist dass komplex im detail,
also nochmal ausführlich meine herleitung dargestellt
ich hab eine konstruktion die immer in einem 60° winkel passt, aber elastisch mit nur einem einzigen winkel, ihre länge verändern kann wie ein stossdämpfer von ~3,5 bis 3,99, passt dabei immer noch immer in 60°!
diese konstruktion passe ich in der länge auf einen erweiterten kite an, welcher erstaunlicherweise (wiso eigentlich?) auch in einen 60° winkel passt
danach halbiere ich den stossdämpfer und setze also 60+30=90° zusammen und kann eine linie des kites umlegen,(die weisse), meine idee oder frage ist jetzt: "wird dies gebilde im 90° winkel beweglicher durch dieses umlegen, immerhin wird der kite ja damit aufgebrochen?"
die konstruktion ist soweit absolut stringent und hat mit der grünen länge und vier mal gespiegelt grad 4/6, hat also soweit ab anfang nur vier zu lange strecken (die grünen 1.07er)... noch ohne irgendetwas hinzuziehen
slash ich bewundere deine inzwischen erlernten hinzieh fähigkeiten sehr, aber diesmal meinte ich wohl schon meinen aufbau, also im detail irgend wie etwas anderes als du draus gemacht hast
also kann man, wenn man erstmal die grünen falschen längen weglässt, den ganzen graphen über den kite-rest bewegen oder nicht ? ( z.B. über den winkel bei 6)
änderung: die vier blauen waren nur für die geometrische konstruktion gedacht, und sollen für die beweglichkeitsfrage entfernt werden, ich will ja keinen 4/5/6er graphen untersuchen
|
Profil
Quote
Link |
StefanVogel
Senior
Dabei seit: 26.11.2005
Mitteilungen: 3446
Aus: Raun
|  Beitrag No.1882, eingetragen 2020-01-12
|
Die beiden untersten (und obersten) blauen Linien sind im letzten Graph gegenüber #1867 rechts hinzugekommen und führen zu vier Knoten von Grad 5.
Zuerst der untere linke Teilgraph vom letzten Graph, er soll im 90° Winkel liegen und um das einzustellen werden alle beweglichen Winkel verbraucht.
21 Knoten, 2×Grad 2, 5×Grad 3, 13×Grad 4, 1×Grad 5, 0 Überschneidungen
38 Kanten, minimal 0.99999999999999966693, maximal 1.00000000001218536383
einzustellende Kanten, Abstände und Winkel:
|P20-P21|=1.00000000001218536383
∠(P19-P20,P5-P7)=89.99999999990558308127°
∠(P19-P9,P5-P7)=90.00000000007770495358°
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1881 unten</Bildtext>
%<Ausrichten von="19" nach="20"/>
%<Winkel size="18" color="green" id="gruenerWinkel" value="75.5224878142018"/>
%<Winkel size="18" color="blue" id="blauerWinkel" value="104.47751218561983"/>
%<Feinjustieren Anzahl="2,2"/>
%<Rechenweg>
%P[1]=[-18.11479523711481,-11.925524469941678]; P[2]=[31.542078892652935,-17.77316088651216]; D=ab(1,2); A(2,1,Bew(1)); L(3,1,2); L(4,3,2); L(5,4,2); L(6,3,4); M(7,6,4,blauerWinkel); L(8,6,7); L(9,8,7); L(10,6,8); N(11,1,10); L(12,1,11); L(13,12,11); L(14,12,13); M(15,13,11,gruenerWinkel); N(16,14,15); L(17,14,16); L(18,17,16); L(19,17,18); N(20,18,15); N(21,15,9); RA(20,21); RK([5,7],[19,20,9],90);
%</Rechenweg>
%
%<Knopf id="Stopp_alleWinkel" color="grey"/>
%
%<Knopf id="Start_blauerWinkel" color="blue"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#blauerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_blauerWinkel.click+0s" end="Stopp_alleWinkel.click+0s"/>
%
%<Knopf id="Start_gruenerWinkel" color="green"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#gruenerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_gruenerWinkel.click+0s" end="Stopp_alleWinkel.click+0s"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LimeGreen}{rgb}{0.20,0.80,0.20}
\definecolor{Violet}{rgb}{0.93,0.51,0.93}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.85122958680809945875/0.23390545666281925552,
2/2.84436706940345462868/0.11695272833140960000,
3/2.44908236188267780520/1.03551138187521774014,
4/3.44221984447803297513/0.91855865354380805687,
5/3.83750455199880979862/0.00000000000000000000,
6/3.04693513695725615165/1.83711730708761633579,
7/3.83750455200284568136/2.44948974277889908180,
8/2.91188975859404752811/2.82795672181774193632,
9/3.70245917363963750191/3.44032915750902468233,
10/2.12132034354845799839/2.21558428612645963440,
11/1.98627496517827872857/1.22474487139463938945,
12/1.06066017176452787041/0.84627789236098616144,
13/1.19570555013470714023/1.83711730709280618434,
14/0.27009075672095617104/1.45865032805915295633,
15/1.98627496517598878256/2.44948974278965048157,
16/1.06066017176823335078/2.07102276374825722272,
17/0.13504537836047808552/2.44948974278965048157,
18/0.92561479340775498770/3.06186217847875497000,
19/0.00000000000000000000/3.44032915752014822885,
20/1.85122958681551041948/3.44032915752014822885,
21/2.77684438023188207012/3.06186217846763097938}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
6/293.28/397.76/0.4/Blue,
13/322.24/397.76/0.4/Green}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
2/1,
3/1, 3/2,
4/3, 4/2,
5/4, 5/2,
6/3, 6/4,
7/6,
8/6, 8/7,
9/8, 9/7,
10/6, 10/8,
11/1, 11/10,
12/1, 12/11,
13/12, 13/11,
14/12, 14/13,
15/13,
16/14, 16/15,
17/14, 17/16,
18/17, 18/16,
19/17, 19/18,
20/18, 20/15, 20/21,
21/15, 21/9}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,21}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[LimeGreen,very thick] (p-20) -- (p-21);
%\draw[Violet,very thick] (p-5) -- (p-7);
%\draw[Violet,very thick] (p-5) -- (p-7);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
6/293.28/397.76/0.4/Blue,
13/322.24/397.76/0.4/Green}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/292,
2/263,
3/83,
4/83,
5/323,
6/308,
7/8,
8/188,
9/68,
10/188,
11/52,
12/292,
13/52,
14/172,
15/248,
16/8,
17/188,
18/8,
19/128,
20/128,
21/8}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/fc952925a89cf974cdb0d80648010c0b.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1881 unten</Bildtext>
%<Ausrichten von=\"19\" nach=\"20\"/>
%<Winkel size=\"18\" color=\"green\" id=\"gruenerWinkel\" value=\"75.5224878142018\"/>
%<Winkel size=\"18\" color=\"blue\" id=\"blauerWinkel\" value=\"104.47751218561983\"/>
%<Feinjustieren Anzahl=\"2,2\"/>
%<Rechenweg>
%P[1]=[-18.11479523711481,-11.925524469941678]; P[2]=[31.542078892652935,-17.77316088651216]; D=ab(1,2); A(2,1,Bew(1)); L(3,1,2); L(4,3,2); L(5,4,2); L(6,3,4); M(7,6,4,blauerWinkel); L(8,6,7); L(9,8,7); L(10,6,8); N(11,1,10); L(12,1,11); L(13,12,11); L(14,12,13); M(15,13,11,gruenerWinkel); N(16,14,15); L(17,14,16); L(18,17,16); L(19,17,18); N(20,18,15); N(21,15,9); RA(20,21); RK([5,7],[19,20,9],90);
%</Rechenweg>
%
%<Knopf id=\"Stopp_alleWinkel\" color=\"grey\"/>
%
%<Knopf id=\"Start_blauerWinkel\" color=\"blue\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#blauerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_blauerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0s\"/>
%
%<Knopf id=\"Start_gruenerWinkel\" color=\"green\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#gruenerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_gruenerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0s\"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LimeGreen}{rgb}{0.20,0.80,0.20}
\definecolor{Violet}{rgb}{0.93,0.51,0.93}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.85122958680809945875/0.23390545666281925552,
2/2.84436706940345462868/0.11695272833140960000,
3/2.44908236188267780520/1.03551138187521774014,
4/3.44221984447803297513/0.91855865354380805687,
5/3.83750455199880979862/0.00000000000000000000,
6/3.04693513695725615165/1.83711730708761633579,
7/3.83750455200284568136/2.44948974277889908180,
8/2.91188975859404752811/2.82795672181774193632,
9/3.70245917363963750191/3.44032915750902468233,
10/2.12132034354845799839/2.21558428612645963440,
11/1.98627496517827872857/1.22474487139463938945,
12/1.06066017176452787041/0.84627789236098616144,
13/1.19570555013470714023/1.83711730709280618434,
14/0.27009075672095617104/1.45865032805915295633,
15/1.98627496517598878256/2.44948974278965048157,
16/1.06066017176823335078/2.07102276374825722272,
17/0.13504537836047808552/2.44948974278965048157,
18/0.92561479340775498770/3.06186217847875497000,
19/0.00000000000000000000/3.44032915752014822885,
20/1.85122958681551041948/3.44032915752014822885,
21/2.77684438023188207012/3.06186217846763097938}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
6/293.28/397.76/0.4/Blue,
13/322.24/397.76/0.4/Green}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
2/1,
3/1, 3/2,
4/3, 4/2,
5/4, 5/2,
6/3, 6/4,
7/6,
8/6, 8/7,
9/8, 9/7,
10/6, 10/8,
11/1, 11/10,
12/1, 12/11,
13/12, 13/11,
14/12, 14/13,
15/13,
16/14, 16/15,
17/14, 17/16,
18/17, 18/16,
19/17, 19/18,
20/18, 20/15, 20/21,
21/15, 21/9}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,21}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[LimeGreen,very thick] (p-20) -- (p-21);
%\draw[Violet,very thick] (p-5) -- (p-7);
%\draw[Violet,very thick] (p-5) -- (p-7);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
6/293.28/397.76/0.4/Blue,
13/322.24/397.76/0.4/Green}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/292,
2/263,
3/83,
4/83,
5/323,
6/308,
7/8,
8/188,
9/68,
10/188,
11/52,
12/292,
13/52,
14/172,
15/248,
16/8,
17/188,
18/8,
19/128,
20/128,
21/8}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
Der Graph ist nicht beweglich, wenn die Punkte 19,20,9,7,5 im 90°-Winkel verbleiben sollen. Der Winkel ∠(P19-P9,P5-P7)=90° muss sogar extra bewiesen werden, weil er nicht separat einstellbar ist. Der Graph im Ganzen (Button "Kaleidoskop"):
74 Knoten, 8×Grad 3, 56×Grad 4, 4×Grad 5, 6×Grad 6, 0 Überschneidungen
152 Kanten, minimal 0.99999999999999777955, maximal 1.00000000002292543932
einzustellende Kanten, Abstände und Winkel:
|P20-P21|=1.00000000001218536383
∠(P19-P20,P5-P7)=89.99999999990558308127°
∠(P19-P9,P5-P7)=90.00000000007770495358°
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1881 unten</Bildtext>
%<Ausrichten von="19" nach="20"/>
%<Winkel size="18" color="green" id="gruenerWinkel" value="75.5224878142018"/>
%<Winkel size="18" color="blue" id="blauerWinkel" value="104.47751218561983"/>
%<Feinjustieren Anzahl="2,2"/>
%<Rechenweg>
%P[1]=[-18.11479523711481,-11.925524469941678]; P[2]=[31.542078892652935,-17.77316088651216]; D=ab(1,2); A(2,1,Bew(1)); L(3,1,2); L(4,3,2); L(5,4,2); L(6,3,4); M(7,6,4,blauerWinkel); L(8,6,7); L(9,8,7); L(10,6,8); N(11,1,10); L(12,1,11); L(13,12,11); L(14,12,13); M(15,13,11,gruenerWinkel); N(16,14,15); L(17,14,16); L(18,17,16); L(19,17,18); N(20,18,15); N(21,15,9); RA(20,21); RK([5,7],[19,20,9],90);
%</Rechenweg>
%
%<Knopf id="Stopp_alleWinkel" color="grey"/>
%
%<Knopf id="Start_blauerWinkel" color="blue"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#blauerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_blauerWinkel.click+0s" end="Stopp_alleWinkel.click+0s"/>
%
%<Knopf id="Start_gruenerWinkel" color="green"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#gruenerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_gruenerWinkel.click+0s" end="Stopp_alleWinkel.click+0s"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LimeGreen}{rgb}{0.20,0.80,0.20}
\definecolor{Violet}{rgb}{0.93,0.51,0.93}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.85122958680809945875/0.23390545666281925552,
2/2.84436706940345462868/0.11695272833140960000,
3/2.44908236188267780520/1.03551138187521774014,
4/3.44221984447803297513/0.91855865354380805687,
5/3.83750455199880979862/0.00000000000000000000,
6/3.04693513695725615165/1.83711730708761633579,
7/3.83750455200284568136/2.44948974277889908180,
8/2.91188975859404752811/2.82795672181774193632,
9/3.70245917363963750191/3.44032915750902468233,
10/2.12132034354845799839/2.21558428612645963440,
11/1.98627496517827872857/1.22474487139463938945,
12/1.06066017176452787041/0.84627789236098616144,
13/1.19570555013470714023/1.83711730709280618434,
14/0.27009075672095617104/1.45865032805915295633,
15/1.98627496517598878256/2.44948974278965048157,
16/1.06066017176823335078/2.07102276374825722272,
17/0.13504537836047808552/2.44948974278965048157,
18/0.92561479340775498770/3.06186217847875497000,
19/0.00000000000000000000/3.44032915752014822885,
20/1.85122958681551041948/3.44032915752014822885,
21/2.77684438023188207012/3.06186217846763097938,
22/1.85122958680809945875/6.64675285837747864548,
23/2.84436706940345596095/6.76370558670888666342,
24/2.44908236188267780520/5.84514693316507738530,
25/3.44221984447803341922/5.96209966149648629141,
26/3.83750455199880935453/6.88065831504029734589,
27/3.04693513695725615165/5.04354100795268056601,
28/3.83750455200284568136/4.43116857226139604364,
29/2.91188975859404752811/4.05270159322255452139,
30/2.12132034354845799839/4.66507402891383726740,
31/1.98627496517827917266/5.65591344364565529190,
32/1.06066017176452809245/6.03438042267930985219,
33/1.19570555013470669614/5.04354100794749005132,
34/0.27009075672095617104/5.42200798698114372343,
35/1.98627496517598900461/4.43116857225064553205,
36/1.06066017176823335078/4.80963555129203879090,
37/0.13504537836047808552/4.43116857225064553205,
38/0.92561479340775498770/3.81879613656154148771,
39/2.77684438023188207012/3.81879613657266459015,
40/5.82377951719029063327/6.64675285838402452043,
41/4.83064203459455043799/6.76370558671216048907,
42/5.22592674211835372944/5.84514693316965505687,
43/4.23278925952261353416/5.96209966149779280187,
44/4.62807396704641771379/5.04354100795528825785,
45/4.76311934541289172529/4.05270159322560896697,
46/3.97254993036931969286/3.44032915753171719686,
47/5.55368876045646331363/4.66507402891949496393,
48/5.68873413882337697345/5.65591344365175974218,
49/6.61434893223588193933/6.03438042268846075444,
50/6.47930355386896827952/5.04354100795619864073,
51/7.40491834728146969269/5.42200798699290320570,
52/5.68873413882970258015/4.43116857225674820597,
53/6.61434893223621056535/4.80963555130119058134,
54/7.53996372564521344373/4.43116857226285176807,
55/6.74939431059995431639/3.81879613657114003189,
56/7.67500910400895808294/3.44032915753279544546,
57/5.82377951719344633119/3.44032915752669499199,
58/4.89816472377582723396/3.81879613657616401312,
59/5.82377951721142217423/0.23390545666936704561,
60/4.83064203461645380600/0.11695272833468434159,
61/5.22592674213420149698/1.03551138187979541172,
62/4.23278925953923401693/0.91855865354511323506,
63/4.62807396705698526063/1.83711730709022447172,
64/4.76311934541692760803/2.82795672182079371737,
65/5.55368876046453596729/2.21558428613211688685,
66/5.68873413883797862667/1.22474487140074161928,
67/6.61434893225297670938/0.84627789237013906209,
68/6.47930355387953316182/1.83711730710151388557,
69/7.40491834729453213271/1.45865032807091044020,
70/5.68873413883623513243/2.44948974279575271140,
71/6.61434893224523623445/2.07102276375741034542,
72/7.53996372565174510783/2.44948974280185272079,
73/6.74939431060245009775/3.06186217848835173783,
74/4.89816472377832390350/3.06186217847112995827}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
6/293.28/397.76/0.4/Blue,
13/322.24/397.76/0.4/Green}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Punkte als \fill[red] (p-1) circle (1.125pt)
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[LimeGreen,very thick] (p-20) -- (p-21);
%\draw[Violet,very thick] (p-5) -- (p-7);
%\draw[Violet,very thick] (p-5) -- (p-7);
%Kanten als \draw[line width=0] (p-1) -- (p-2);
\foreach \i/\j in {
2/1,
3/1, 3/2,
4/3, 4/2,
5/4, 5/2, 5/62, 5/60,
6/3, 6/4,
7/6, 7/63, 7/64, 7/46,
8/6, 8/7,
9/8, 9/7, 9/29, 9/28, 9/39,
10/6, 10/8,
11/1, 11/10,
12/1, 12/11,
13/12, 13/11,
14/12, 14/13,
15/13,
16/14, 16/15,
17/14, 17/16,
18/17, 18/16,
19/17, 19/18, 19/37, 19/38,
20/18, 20/15, 20/21, 20/35, 20/38, 20/39,
21/15, 21/9,
23/22,
24/22, 24/23,
25/23, 25/24,
26/23, 26/25, 26/41, 26/43,
27/24, 27/25,
28/27, 28/44,
29/27, 29/28,
30/27, 30/29,
31/22, 31/30,
32/22, 32/31,
33/31, 33/32,
34/32, 34/33,
35/33,
36/34, 36/35,
37/34, 37/36,
38/36, 38/37,
39/35,
41/40,
42/40, 42/41,
43/41, 43/42,
44/42, 44/43,
45/44, 45/28,
46/28, 46/45, 46/64, 46/74,
47/44, 47/45,
48/40, 48/47,
49/40, 49/48,
50/48, 50/49,
51/49, 51/50,
52/50,
53/51, 53/52,
54/51, 54/53,
55/53, 55/54,
56/54, 56/55, 56/72, 56/73,
57/52, 57/55, 57/58, 57/70, 57/73, 57/74,
58/46, 58/52,
60/59,
61/59, 61/60,
62/60, 62/61,
63/61, 63/62,
64/63,
65/63, 65/64,
66/59, 66/65,
67/59, 67/66,
68/66, 68/67,
69/67, 69/68,
70/68,
71/69, 71/70,
72/69, 72/71,
73/71, 73/72,
74/70}
\draw[line width=0] (p-\i) -- (p-\j);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
6/293.28/397.76/0.4/Blue,
13/322.24/397.76/0.4/Green}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/292,
2/263,
3/83,
4/83,
5/217,
6/308,
7/172,
8/188,
9/292,
10/188,
11/52,
12/292,
13/52,
14/172,
15/248,
16/8,
17/188,
18/8,
19/128,
20/128,
21/8,
22/68,
23/97,
24/157,
25/277,
26/143,
27/112,
28/188,
29/292,
30/172,
31/308,
32/68,
33/308,
34/112,
35/112,
36/352,
37/112,
38/352,
39/352,
40/112,
41/23,
42/323,
43/143,
44/68,
45/8,
46/112,
47/8,
48/172,
49/352,
50/232,
51/68,
52/68,
53/188,
54/8,
55/248,
56/308,
57/308,
58/188,
59/337,
60/337,
61/97,
62/217,
63/97,
64/112,
65/352,
66/188,
67/8,
68/68,
69/8,
70/292,
71/172,
72/352,
73/172,
74/172}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/8cee8f7fd119750f2495ade9c9264ccd.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1881 unten</Bildtext>
%<Ausrichten von=\"19\" nach=\"20\"/>
%<Winkel size=\"18\" color=\"green\" id=\"gruenerWinkel\" value=\"75.5224878142018\"/>
%<Winkel size=\"18\" color=\"blue\" id=\"blauerWinkel\" value=\"104.47751218561983\"/>
%<Feinjustieren Anzahl=\"2,2\"/>
%<Rechenweg>
%P[1]=[-18.11479523711481,-11.925524469941678]; P[2]=[31.542078892652935,-17.77316088651216]; D=ab(1,2); A(2,1,Bew(1)); L(3,1,2); L(4,3,2); L(5,4,2); L(6,3,4); M(7,6,4,blauerWinkel); L(8,6,7); L(9,8,7); L(10,6,8); N(11,1,10); L(12,1,11); L(13,12,11); L(14,12,13); M(15,13,11,gruenerWinkel); N(16,14,15); L(17,14,16); L(18,17,16); L(19,17,18); N(20,18,15); N(21,15,9); RA(20,21); RK([5,7],[19,20,9],90);
%</Rechenweg>
%
%<Knopf id=\"Stopp_alleWinkel\" color=\"grey\"/>
%
%<Knopf id=\"Start_blauerWinkel\" color=\"blue\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#blauerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_blauerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0s\"/>
%
%<Knopf id=\"Start_gruenerWinkel\" color=\"green\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#gruenerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_gruenerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0s\"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LimeGreen}{rgb}{0.20,0.80,0.20}
\definecolor{Violet}{rgb}{0.93,0.51,0.93}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.85122958680809945875/0.23390545666281925552,
2/2.84436706940345462868/0.11695272833140960000,
3/2.44908236188267780520/1.03551138187521774014,
4/3.44221984447803297513/0.91855865354380805687,
5/3.83750455199880979862/0.00000000000000000000,
6/3.04693513695725615165/1.83711730708761633579,
7/3.83750455200284568136/2.44948974277889908180,
8/2.91188975859404752811/2.82795672181774193632,
9/3.70245917363963750191/3.44032915750902468233,
10/2.12132034354845799839/2.21558428612645963440,
11/1.98627496517827872857/1.22474487139463938945,
12/1.06066017176452787041/0.84627789236098616144,
13/1.19570555013470714023/1.83711730709280618434,
14/0.27009075672095617104/1.45865032805915295633,
15/1.98627496517598878256/2.44948974278965048157,
16/1.06066017176823335078/2.07102276374825722272,
17/0.13504537836047808552/2.44948974278965048157,
18/0.92561479340775498770/3.06186217847875497000,
19/0.00000000000000000000/3.44032915752014822885,
20/1.85122958681551041948/3.44032915752014822885,
21/2.77684438023188207012/3.06186217846763097938,
22/1.85122958680809945875/6.64675285837747864548,
23/2.84436706940345596095/6.76370558670888666342,
24/2.44908236188267780520/5.84514693316507738530,
25/3.44221984447803341922/5.96209966149648629141,
26/3.83750455199880935453/6.88065831504029734589,
27/3.04693513695725615165/5.04354100795268056601,
28/3.83750455200284568136/4.43116857226139604364,
29/2.91188975859404752811/4.05270159322255452139,
30/2.12132034354845799839/4.66507402891383726740,
31/1.98627496517827917266/5.65591344364565529190,
32/1.06066017176452809245/6.03438042267930985219,
33/1.19570555013470669614/5.04354100794749005132,
34/0.27009075672095617104/5.42200798698114372343,
35/1.98627496517598900461/4.43116857225064553205,
36/1.06066017176823335078/4.80963555129203879090,
37/0.13504537836047808552/4.43116857225064553205,
38/0.92561479340775498770/3.81879613656154148771,
39/2.77684438023188207012/3.81879613657266459015,
40/5.82377951719029063327/6.64675285838402452043,
41/4.83064203459455043799/6.76370558671216048907,
42/5.22592674211835372944/5.84514693316965505687,
43/4.23278925952261353416/5.96209966149779280187,
44/4.62807396704641771379/5.04354100795528825785,
45/4.76311934541289172529/4.05270159322560896697,
46/3.97254993036931969286/3.44032915753171719686,
47/5.55368876045646331363/4.66507402891949496393,
48/5.68873413882337697345/5.65591344365175974218,
49/6.61434893223588193933/6.03438042268846075444,
50/6.47930355386896827952/5.04354100795619864073,
51/7.40491834728146969269/5.42200798699290320570,
52/5.68873413882970258015/4.43116857225674820597,
53/6.61434893223621056535/4.80963555130119058134,
54/7.53996372564521344373/4.43116857226285176807,
55/6.74939431059995431639/3.81879613657114003189,
56/7.67500910400895808294/3.44032915753279544546,
57/5.82377951719344633119/3.44032915752669499199,
58/4.89816472377582723396/3.81879613657616401312,
59/5.82377951721142217423/0.23390545666936704561,
60/4.83064203461645380600/0.11695272833468434159,
61/5.22592674213420149698/1.03551138187979541172,
62/4.23278925953923401693/0.91855865354511323506,
63/4.62807396705698526063/1.83711730709022447172,
64/4.76311934541692760803/2.82795672182079371737,
65/5.55368876046453596729/2.21558428613211688685,
66/5.68873413883797862667/1.22474487140074161928,
67/6.61434893225297670938/0.84627789237013906209,
68/6.47930355387953316182/1.83711730710151388557,
69/7.40491834729453213271/1.45865032807091044020,
70/5.68873413883623513243/2.44948974279575271140,
71/6.61434893224523623445/2.07102276375741034542,
72/7.53996372565174510783/2.44948974280185272079,
73/6.74939431060245009775/3.06186217848835173783,
74/4.89816472377832390350/3.06186217847112995827}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
6/293.28/397.76/0.4/Blue,
13/322.24/397.76/0.4/Green}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Punkte als \fill[red] (p-1) circle (1.125pt)
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[LimeGreen,very thick] (p-20) -- (p-21);
%\draw[Violet,very thick] (p-5) -- (p-7);
%\draw[Violet,very thick] (p-5) -- (p-7);
%Kanten als \draw[line width=0] (p-1) -- (p-2);
\foreach \i/\j in {
2/1,
3/1, 3/2,
4/3, 4/2,
5/4, 5/2, 5/62, 5/60,
6/3, 6/4,
7/6, 7/63, 7/64, 7/46,
8/6, 8/7,
9/8, 9/7, 9/29, 9/28, 9/39,
10/6, 10/8,
11/1, 11/10,
12/1, 12/11,
13/12, 13/11,
14/12, 14/13,
15/13,
16/14, 16/15,
17/14, 17/16,
18/17, 18/16,
19/17, 19/18, 19/37, 19/38,
20/18, 20/15, 20/21, 20/35, 20/38, 20/39,
21/15, 21/9,
23/22,
24/22, 24/23,
25/23, 25/24,
26/23, 26/25, 26/41, 26/43,
27/24, 27/25,
28/27, 28/44,
29/27, 29/28,
30/27, 30/29,
31/22, 31/30,
32/22, 32/31,
33/31, 33/32,
34/32, 34/33,
35/33,
36/34, 36/35,
37/34, 37/36,
38/36, 38/37,
39/35,
41/40,
42/40, 42/41,
43/41, 43/42,
44/42, 44/43,
45/44, 45/28,
46/28, 46/45, 46/64, 46/74,
47/44, 47/45,
48/40, 48/47,
49/40, 49/48,
50/48, 50/49,
51/49, 51/50,
52/50,
53/51, 53/52,
54/51, 54/53,
55/53, 55/54,
56/54, 56/55, 56/72, 56/73,
57/52, 57/55, 57/58, 57/70, 57/73, 57/74,
58/46, 58/52,
60/59,
61/59, 61/60,
62/60, 62/61,
63/61, 63/62,
64/63,
65/63, 65/64,
66/59, 66/65,
67/59, 67/66,
68/66, 68/67,
69/67, 69/68,
70/68,
71/69, 71/70,
72/69, 72/71,
73/71, 73/72,
74/70}
\draw[line width=0] (p-\i) -- (p-\j);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
6/293.28/397.76/0.4/Blue,
13/322.24/397.76/0.4/Green}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/292,
2/263,
3/83,
4/83,
5/217,
6/308,
7/172,
8/188,
9/292,
10/188,
11/52,
12/292,
13/52,
14/172,
15/248,
16/8,
17/188,
18/8,
19/128,
20/128,
21/8,
22/68,
23/97,
24/157,
25/277,
26/143,
27/112,
28/188,
29/292,
30/172,
31/308,
32/68,
33/308,
34/112,
35/112,
36/352,
37/112,
38/352,
39/352,
40/112,
41/23,
42/323,
43/143,
44/68,
45/8,
46/112,
47/8,
48/172,
49/352,
50/232,
51/68,
52/68,
53/188,
54/8,
55/248,
56/308,
57/308,
58/188,
59/337,
60/337,
61/97,
62/217,
63/97,
64/112,
65/352,
66/188,
67/8,
68/68,
69/8,
70/292,
71/172,
72/352,
73/172,
74/172}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
|
Profil
Quote
Link |
StefanVogel
Senior
Dabei seit: 26.11.2005
Mitteilungen: 3446
Aus: Raun
| Beitrag No.1883, eingetragen 2020-01-12
|
2020-01-12 16:36 - haribo in Beitrag No. 1881 schreibt:
diese konstruktion passe ich in der länge auf einen erweiterten kite an, welcher erstaunlicherweise (wiso eigentlich?) auch in einen 60° winkel passt
Das scheint gar keine so einfache Geometrieaufgabe zu sein. Ich muss passen. Wieso ist ∠(P11-P14,P5-P13)=60°?
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1803</Bildtext>
%<Ausrichten von="1" nach="2"/>
%<Winkel size="18" color="blue" id="blauerWinkel" value="60.00000000000001"/>
%<Feinjustieren Anzahl="1"/>
%<Rechenweg>
%P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(2,1,Bew(1)); L(3,1,2); L(4,3,2); L(5,4,2); L(6,3,4); Q(7,1,6,ab(1,6,[1,6]),ab(1,2,3)); M(13,12,6,blauerWinkel); L(14,12,13); RK([5,13],[11,14],360/6); A(6,13);
%</Rechenweg>
%
%<Knopf id="Stopp_alleWinkel" color="grey"/>
%
%<Knopf id="Start_blauerWinkel" color="blue"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#blauerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_blauerWinkel.click+0s" end="Stopp_alleWinkel.click+0s"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Violet}{rgb}{0.93,0.51,0.93}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.71352549156242095485/0.00000000000000000000,
2/2.71352549156242117689/0.00000000000000000000,
3/2.21352549156242117689/0.86602540378443859659,
4/3.21352549156242117689/0.86602540378443859659,
5/3.71352549156242117689/0.00000000000000000000,
6/2.71352549156242117689/1.73205080756887719318,
7/1.75000000000000000000/1.99966737489869483824,
8/0.87500000000000000000/1.51554445662276737750,
9/1.73176274578121058845/0.99983368744934741912,
10/0.85676274578121025538/0.51571076917342051349,
11/0.00000000000000000000/1.03142153834684013880,
12/2.46352549156242117689/2.70029664412073167057,
13/3.42705098312484190970/2.43268007679091402551,
14/3.17705098312484190970/3.40092591334276805881}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%Punkte als \fill[red] (p-1) circle (1.125pt)
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
%\draw[Violet,very thick] (p-5) -- (p-13);
%Kanten als \draw[line width=0] (p-1) -- (p-2);
\foreach \i/\j in {
1/9, 1/10,
2/1,
3/1, 3/2,
4/3, 4/2,
5/4, 5/2,
6/3, 6/4, 6/7, 6/13,
8/7,
9/7, 9/8,
10/8, 10/9,
11/8, 11/10,
12/7, 12/6,
13/12,
14/12, 14/13}
\draw[line width=0] (p-\i) -- (p-\j);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/299,
2/330,
3/150,
4/330,
5/330,
6/254,
7/194,
8/59,
9/359,
10/179,
11/179,
12/74,
13/314,
14/74}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/22b3628422544de6dd6e89f93f63fef4.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1803</Bildtext>
%<Ausrichten von=\"1\" nach=\"2\"/>
%<Winkel size=\"18\" color=\"blue\" id=\"blauerWinkel\" value=\"60.00000000000001\"/>
%<Feinjustieren Anzahl=\"1\"/>
%<Rechenweg>
%P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(2,1,Bew(1)); L(3,1,2); L(4,3,2); L(5,4,2); L(6,3,4); Q(7,1,6,ab(1,6,[1,6]),ab(1,2,3)); M(13,12,6,blauerWinkel); L(14,12,13); RK([5,13],[11,14],360/6); A(6,13);
%</Rechenweg>
%
%<Knopf id=\"Stopp_alleWinkel\" color=\"grey\"/>
%
%<Knopf id=\"Start_blauerWinkel\" color=\"blue\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#blauerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_blauerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0s\"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Violet}{rgb}{0.93,0.51,0.93}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.71352549156242095485/0.00000000000000000000,
2/2.71352549156242117689/0.00000000000000000000,
3/2.21352549156242117689/0.86602540378443859659,
4/3.21352549156242117689/0.86602540378443859659,
5/3.71352549156242117689/0.00000000000000000000,
6/2.71352549156242117689/1.73205080756887719318,
7/1.75000000000000000000/1.99966737489869483824,
8/0.87500000000000000000/1.51554445662276737750,
9/1.73176274578121058845/0.99983368744934741912,
10/0.85676274578121025538/0.51571076917342051349,
11/0.00000000000000000000/1.03142153834684013880,
12/2.46352549156242117689/2.70029664412073167057,
13/3.42705098312484190970/2.43268007679091402551,
14/3.17705098312484190970/3.40092591334276805881}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%Punkte als \fill[red] (p-1) circle (1.125pt)
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
%\draw[Violet,very thick] (p-5) -- (p-13);
%Kanten als \draw[line width=0] (p-1) -- (p-2);
\foreach \i/\j in {
1/9, 1/10,
2/1,
3/1, 3/2,
4/3, 4/2,
5/4, 5/2,
6/3, 6/4, 6/7, 6/13,
8/7,
9/7, 9/8,
10/8, 10/9,
11/8, 11/10,
12/7, 12/6,
13/12,
14/12, 14/13}
\draw[line width=0] (p-\i) -- (p-\j);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/299,
2/330,
3/150,
4/330,
5/330,
6/254,
7/194,
8/59,
9/359,
10/179,
11/179,
12/74,
13/314,
14/74}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
Im Moment kann ich es nur mit dem GAP-Programm nachrechnen, dass es exakt stimmt:
GAP gap> W60:=[[1/2,-1/2*Sqrt(3)],[1/2*Sqrt(3),1/2]]; #60°-Rotationsmatrix
gap> Wbl:=[[1/4,-1/4*Sqrt(15)],[1/4*Sqrt(15),1/4]]*W60^-1; #spitzer Winkel im Dreieck mit Seitenlängen 1,2,2 ("acos(1/4)_Graph")
gap> P[1]:=[0,0];;
gap> P[2]:=[1,0];;
gap> P[3]:=P[1]+W60*(P[2]-P[1]);;
gap> P[4]:=P[3]+W60*(P[2]-P[3]);;
gap> P[5]:=P[2]-(P[1]-P[2]);;
gap> P[6]:=P[3]-(P[1]-P[3]);;
gap> P[7]:=P[6]+(W60*Wbl)^-1*(P[3]-P[6]);;
gap> P[8]:=P[7]+(W60*W60*Wbl)^-1*(P[6]-P[7]);;
gap> P[9]:=P[7]+W60*(P[8]-P[7]);;
gap> P[10]:=P[1]+W60*(P[9]-P[1]);;
gap> P[11]:=P[8]-(P[7]-P[8]);;
gap> P[12]:=P[7]+W60*(P[6]-P[7]);;
gap> P[13]:=P[12]+W60*(P[6]-P[12]);;
gap> P[14]:=P[12]-(P[7]-P[12]);;
gap> Sqrt(((P[13]-P[5])*(P[14]-P[11]))*((P[13]-P[5])*(P[14]-P[11]))/((P[13]-P[5])*(P[13]-P[5]))/((P[14]-P[11])*(P[14]-P[11])));
1/2 |
Ergebnis 1/2 für den Kosinus des Winkels, also 60°.
|
Profil
Quote
Link |
haribo
Senior
Dabei seit: 25.10.2012
Mitteilungen: 2298
| Beitrag No.1884, eingetragen 2020-01-13
|
@stefan,
ja die blauen vier sollten nach konstruktion wieder entfernt werden, mein fehler gestern, sorry (hab es in dem obigen beitragsbild geändert)
dann ist der erweiterte und geöffnete kite ausreichend beweglich um auch bei anderen inneren winkeln in ein 60° winkel zu passen, (konstruieren kann ich das auch mal wieder nur mit itterationsvorgängen...)
damit kann man also weitere 6-fach rotationssymetrische graphen bauen
z.B. diesen hier
aber was dann nicht mehr geht, also wenn man den 60°stossdämpfer daneben legen würde wie in #1881, ist die weisse umgelegte linie
offenbar stabilisiert also diese weisse umgelegte linie den graphen aus #1881, bzw macht ihn unbeweglich
was mich, neben dem überhaupts 60° winkel für den erweiterten kite zusätzlich irritiert ist folgendes: die 6 60° sektoren in #1881 haben gar keine gemeinsame spitze, sie überschneiden sich innen
klar geht das, aber ich hatte das bisher nicht auf dem radar für die winkeltheorie... immer wieder neues also
haribo
|
Profil
Quote
Link |
Slash
Aktiv
Dabei seit: 23.03.2005
Mitteilungen: 7758
Aus: Cuxhaven-Sahlenburg
| Beitrag No.1885, vom Themenstarter, eingetragen 2020-01-15
|
Hier ist mein Rechenweg für den Winkel Alpha.
Beweis: Der Reihe nach bestimmen wir die folgenden Winkel.
Wir setzen alle bekannten Größen in die letzte Gleichung ein:
Es gilt: 
-----------------
Bound to be disappointing so why wait?
|
Profil
Quote
Link |
haribo
Senior
Dabei seit: 25.10.2012
Mitteilungen: 2298
| Beitrag No.1886, eingetragen 2020-01-16
|
erklärungsversuch...
-aus symetriegründen liegt 6-9 parallel zu 11-14
-rotiert man das gesamte rotebild 3 mal um M dann liegt die blaue konstruktion 120° verdreht zur roten (dito die gelbe),
-folglich würde 11-14 11´-14´ im 60° winkel schneiden
6´-9´ liegt wiederum parallel zu 11´-14´ also auch im 60°winkel zu 11-14
- wenn man zeigen kann das sowohl 6´als auch 9´auf der geraden 5-13 liegen hat man es geschafft...
-6´ist trivial weil es bei der rotation auf 5 zu liegen kommt
-die strecken 7-6 und 6-13 haben ohne frage einen schnittwinkel von 120° zueinander,
-beim drehen, um auch 120°, hin zum blauen konstrukt wird also automatisch die strecke 6´-7´ parallel zu 6-13
-damit gibt es ein parallelogramm (grün)6/13/7´/6´(bzw 5)
-die diagonalen jedes parallelogramms halbieren sich gegenseitig
- 9´liegt (wegen blau) zwangsweise auf der halben strecke 6-7´, damit liegt 9´also auch exakt auf der hälfte der diagonalen 5-13 und somit auch auf der schwarzen winkellinie... ergebnis 60° q.e.d.
|
Profil
Quote
Link |
StefanVogel
Senior
Dabei seit: 26.11.2005
Mitteilungen: 3446
Aus: Raun
| Beitrag No.1887, eingetragen 2020-01-18
|
Toll!! Zwei perfekte Beweise! So soll das sein. Auch bei der Fehlersuche muss ich passen, nichts dergleichen zu sehen  Da bleibt für mich jetzt nur noch übrig, etwas zur Beweglichkeit zu schreiben.
2020-01-13 13:04 - haribo in Beitrag No. 1884 schreibt:
@stefan,
ja die blauen vier sollten nach konstruktion wieder entfernt werden, mein fehler gestern, sorry (hab es in dem obigen beitragsbild geändert)
Das ändere ich auch, mit einem dritten beweglichen Winkel in P12 anstelle der Kante P6-P13.
74 Knoten, 8×Grad 3, 62×Grad 4, 4×Grad 6, 0 Überschneidungen
148 Kanten, minimal 0.99999999999999544809, maximal 1.00000000000000266454
einzustellende Kanten, Abstände und Winkel:
|P21-P14|=1.00000000000000066613
∠(P18-P20,P5-P13)=90.00000000000001421085°
∠(P18-P14,P5-P13)=90.00000000000001421085°
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>Anfang für einen neuen, noch unbenannten Streichholzgraph</Bildtext>
%<Ausrichten von="18" nach="20"/>
%<Winkel size="18" color="blue" id="blauerWinkel" value="28.955024371859853"/>
%<Winkel size="18" color="green" id="gruenerWinkel" value="59.999999999999986"/>
%<Winkel size="18" color="orange" id="orangerWinkel" value="15.522487814070073"/>
%<Feinjustieren Anzahl="3"/>
%<Rechenweg>
%P[1]=[-18.114795237025238,-11.925524469987494]; P[2]=[31.54207889274424,-17.773160886543337]; D=ab(1,2); A(2,1,Bew(1)); L(3,1,2); L(4,3,2); L(5,4,2); L(6,3,4); M(7,1,3,blauerWinkel,2); N(11,7,6); L(12,11,6); M(13,12,6,gruenerWinkel); L(14,12,13); M(15,10,9,orangerWinkel,2); N(19,15,9); N(20,17,19); L(21,20,19); RA(21,14);
%
%RK([5,13],[18,20,14],360/4,true);
%</Rechenweg>
%
%<Knopf id="Stopp_alleWinkel" color="grey"/>
%
%<Knopf id="Start_blauerWinkel" color="blue"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#blauerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_blauerWinkel.click+0s" end="Stopp_alleWinkel.click+0s"/>
%
%<Knopf id="Start_gruenerWinkel" color="green"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#gruenerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_gruenerWinkel.click+0s" end="Stopp_alleWinkel.click+0s"/>
%
%<Knopf id="Start_orangerWinkel" color="orange"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#orangerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_orangerWinkel.click+0s" end="Stopp_alleWinkel.click+0s"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LimeGreen}{rgb}{0.20,0.80,0.20}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
\definecolor{Violet}{rgb}{0.93,0.51,0.93}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.85/0.23,
2/2.84/0.12,
3/2.45/1.04,
4/3.44/0.92,
5/3.84/0.00,
6/3.05/1.84,
7/1.99/1.22,
8/1.06/0.85,
9/1.20/1.84,
10/0.27/1.46,
11/2.12/2.22,
12/2.91/2.83,
13/3.84/2.45,
14/3.70/3.44,
15/1.06/2.07,
16/0.14/2.45,
17/0.93/3.06,
18/0.00/3.44,
19/1.99/2.45,
20/1.85/3.44,
21/2.78/3.06,
22/1.85/6.65,
23/2.84/6.76,
24/2.45/5.85,
25/3.44/5.96,
26/3.84/6.88,
27/3.05/5.04,
28/1.99/5.66,
29/1.06/6.03,
30/1.20/5.04,
31/0.27/5.42,
32/2.12/4.67,
33/2.91/4.05,
34/3.84/4.43,
35/1.06/4.81,
36/0.14/4.43,
37/0.93/3.82,
38/1.99/4.43,
39/2.78/3.82,
40/5.82/6.65,
41/4.83/6.76,
42/5.23/5.85,
43/4.23/5.96,
44/4.63/5.04,
45/5.69/5.66,
46/6.61/6.03,
47/6.48/5.04,
48/7.40/5.42,
49/5.55/4.67,
50/4.76/4.05,
51/3.97/3.44,
52/6.61/4.81,
53/7.54/4.43,
54/6.75/3.82,
55/7.68/3.44,
56/5.69/4.43,
57/5.82/3.44,
58/4.90/3.82,
59/5.82/0.23,
60/4.83/0.12,
61/5.23/1.04,
62/4.23/0.92,
63/4.63/1.84,
64/5.69/1.22,
65/6.61/0.85,
66/6.48/1.84,
67/7.40/1.46,
68/5.55/2.22,
69/4.76/2.83,
70/6.61/2.07,
71/7.54/2.45,
72/6.75/3.06,
73/5.69/2.45,
74/4.90/3.06}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
1/53.28/82.24/0.4/Blue,
12/277.76/337.76/0.4/Green,
10/22.24/37.76/0.4/Orange}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
2/1,
3/1, 3/2,
4/3, 4/2,
5/4, 5/2, 5/62, 5/60,
6/3, 6/4,
7/1,
8/1, 8/7,
9/8, 9/7,
10/8, 10/9,
11/7, 11/6,
12/11, 12/6,
13/12, 13/69, 13/51,
14/12, 14/13, 14/33, 14/34, 14/39,
15/10,
16/10, 16/15,
17/16, 17/15,
18/16, 18/17, 18/36, 18/37,
19/15, 19/9,
20/17, 20/19, 20/37, 20/38,
21/20, 21/19, 21/14,
23/22,
24/22, 24/23,
25/23, 25/24,
26/23, 26/25, 26/41, 26/43,
27/24, 27/25,
28/22,
29/22, 29/28,
30/28, 30/29,
31/29, 31/30,
32/27, 32/28,
33/27, 33/32,
34/33, 34/50,
35/31,
36/31, 36/35,
37/35, 37/36,
38/30, 38/35,
39/38, 39/20,
41/40,
42/40, 42/41,
43/41, 43/42,
44/42, 44/43,
45/40,
46/40, 46/45,
47/45, 47/46,
48/46, 48/47,
49/44, 49/45,
50/44, 50/49,
51/50, 51/34, 51/69, 51/74,
52/48,
53/48, 53/52,
54/52, 54/53,
55/53, 55/54, 55/71, 55/72,
56/47, 56/52,
57/54, 57/56, 57/72, 57/73,
58/51, 58/56, 58/57,
60/59,
61/59, 61/60,
62/60, 62/61,
63/61, 63/62,
64/59,
65/59, 65/64,
66/64, 66/65,
67/65, 67/66,
68/63, 68/64,
69/63, 69/68,
70/67,
71/67, 71/70,
72/70, 72/71,
73/66, 73/70,
74/73, 74/57}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,74}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[LimeGreen,very thick] (p-21) -- (p-14);
%\draw[Violet,very thick] (p-5) -- (p-13);
%\draw[Violet,very thick] (p-5) -- (p-13);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
1/53.28/82.24/0.4/Blue,
12/277.76/337.76/0.4/Green,
10/22.24/37.76/0.4/Orange}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/292,
2/323,
3/143,
4/23,
5/217,
6/308,
7/52,
8/172,
9/52,
10/172,
11/188,
12/68,
13/308,
14/292,
15/308,
16/128,
17/68,
18/232,
19/248,
20/128,
21/8,
22/68,
23/97,
24/157,
25/277,
26/37,
27/277,
28/8,
29/68,
30/248,
31/188,
32/172,
33/292,
34/52,
35/52,
36/232,
37/292,
38/112,
39/352,
40/112,
41/143,
42/323,
43/143,
44/128,
45/172,
46/112,
47/292,
48/352,
49/8,
50/8,
51/112,
52/188,
53/308,
54/188,
55/308,
56/68,
57/308,
58/188,
59/248,
60/337,
61/37,
62/217,
63/97,
64/188,
65/308,
66/68,
67/8,
68/352,
69/112,
70/232,
71/352,
72/172,
73/292,
74/172}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/578d1ff6075575c654cc2460cf6a3b40.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>Anfang für einen neuen, noch unbenannten Streichholzgraph</Bildtext>
%<Ausrichten von=\"18\" nach=\"20\"/>
%<Winkel size=\"18\" color=\"blue\" id=\"blauerWinkel\" value=\"28.955024371859853\"/>
%<Winkel size=\"18\" color=\"green\" id=\"gruenerWinkel\" value=\"59.999999999999986\"/>
%<Winkel size=\"18\" color=\"orange\" id=\"orangerWinkel\" value=\"15.522487814070073\"/>
%<Feinjustieren Anzahl=\"3\"/>
%<Rechenweg>
%P[1]=[-18.114795237025238,-11.925524469987494]; P[2]=[31.54207889274424,-17.773160886543337]; D=ab(1,2); A(2,1,Bew(1)); L(3,1,2); L(4,3,2); L(5,4,2); L(6,3,4); M(7,1,3,blauerWinkel,2); N(11,7,6); L(12,11,6); M(13,12,6,gruenerWinkel); L(14,12,13); M(15,10,9,orangerWinkel,2); N(19,15,9); N(20,17,19); L(21,20,19); RA(21,14);
%
%RK([5,13],[18,20,14],360/4,true);
%</Rechenweg>
%
%<Knopf id=\"Stopp_alleWinkel\" color=\"grey\"/>
%
%<Knopf id=\"Start_blauerWinkel\" color=\"blue\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#blauerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_blauerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0s\"/>
%
%<Knopf id=\"Start_gruenerWinkel\" color=\"green\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#gruenerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_gruenerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0s\"/>
%
%<Knopf id=\"Start_orangerWinkel\" color=\"orange\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#orangerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_orangerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0s\"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LimeGreen}{rgb}{0.20,0.80,0.20}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
\definecolor{Violet}{rgb}{0.93,0.51,0.93}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.85/0.23,
2/2.84/0.12,
3/2.45/1.04,
4/3.44/0.92,
5/3.84/0.00,
6/3.05/1.84,
7/1.99/1.22,
8/1.06/0.85,
9/1.20/1.84,
10/0.27/1.46,
11/2.12/2.22,
12/2.91/2.83,
13/3.84/2.45,
14/3.70/3.44,
15/1.06/2.07,
16/0.14/2.45,
17/0.93/3.06,
18/0.00/3.44,
19/1.99/2.45,
20/1.85/3.44,
21/2.78/3.06,
22/1.85/6.65,
23/2.84/6.76,
24/2.45/5.85,
25/3.44/5.96,
26/3.84/6.88,
27/3.05/5.04,
28/1.99/5.66,
29/1.06/6.03,
30/1.20/5.04,
31/0.27/5.42,
32/2.12/4.67,
33/2.91/4.05,
34/3.84/4.43,
35/1.06/4.81,
36/0.14/4.43,
37/0.93/3.82,
38/1.99/4.43,
39/2.78/3.82,
40/5.82/6.65,
41/4.83/6.76,
42/5.23/5.85,
43/4.23/5.96,
44/4.63/5.04,
45/5.69/5.66,
46/6.61/6.03,
47/6.48/5.04,
48/7.40/5.42,
49/5.55/4.67,
50/4.76/4.05,
51/3.97/3.44,
52/6.61/4.81,
53/7.54/4.43,
54/6.75/3.82,
55/7.68/3.44,
56/5.69/4.43,
57/5.82/3.44,
58/4.90/3.82,
59/5.82/0.23,
60/4.83/0.12,
61/5.23/1.04,
62/4.23/0.92,
63/4.63/1.84,
64/5.69/1.22,
65/6.61/0.85,
66/6.48/1.84,
67/7.40/1.46,
68/5.55/2.22,
69/4.76/2.83,
70/6.61/2.07,
71/7.54/2.45,
72/6.75/3.06,
73/5.69/2.45,
74/4.90/3.06}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
1/53.28/82.24/0.4/Blue,
12/277.76/337.76/0.4/Green,
10/22.24/37.76/0.4/Orange}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
2/1,
3/1, 3/2,
4/3, 4/2,
5/4, 5/2, 5/62, 5/60,
6/3, 6/4,
7/1,
8/1, 8/7,
9/8, 9/7,
10/8, 10/9,
11/7, 11/6,
12/11, 12/6,
13/12, 13/69, 13/51,
14/12, 14/13, 14/33, 14/34, 14/39,
15/10,
16/10, 16/15,
17/16, 17/15,
18/16, 18/17, 18/36, 18/37,
19/15, 19/9,
20/17, 20/19, 20/37, 20/38,
21/20, 21/19, 21/14,
23/22,
24/22, 24/23,
25/23, 25/24,
26/23, 26/25, 26/41, 26/43,
27/24, 27/25,
28/22,
29/22, 29/28,
30/28, 30/29,
31/29, 31/30,
32/27, 32/28,
33/27, 33/32,
34/33, 34/50,
35/31,
36/31, 36/35,
37/35, 37/36,
38/30, 38/35,
39/38, 39/20,
41/40,
42/40, 42/41,
43/41, 43/42,
44/42, 44/43,
45/40,
46/40, 46/45,
47/45, 47/46,
48/46, 48/47,
49/44, 49/45,
50/44, 50/49,
51/50, 51/34, 51/69, 51/74,
52/48,
53/48, 53/52,
54/52, 54/53,
55/53, 55/54, 55/71, 55/72,
56/47, 56/52,
57/54, 57/56, 57/72, 57/73,
58/51, 58/56, 58/57,
60/59,
61/59, 61/60,
62/60, 62/61,
63/61, 63/62,
64/59,
65/59, 65/64,
66/64, 66/65,
67/65, 67/66,
68/63, 68/64,
69/63, 69/68,
70/67,
71/67, 71/70,
72/70, 72/71,
73/66, 73/70,
74/73, 74/57}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,74}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[LimeGreen,very thick] (p-21) -- (p-14);
%\draw[Violet,very thick] (p-5) -- (p-13);
%\draw[Violet,very thick] (p-5) -- (p-13);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
1/53.28/82.24/0.4/Blue,
12/277.76/337.76/0.4/Green,
10/22.24/37.76/0.4/Orange}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/292,
2/323,
3/143,
4/23,
5/217,
6/308,
7/52,
8/172,
9/52,
10/172,
11/188,
12/68,
13/308,
14/292,
15/308,
16/128,
17/68,
18/232,
19/248,
20/128,
21/8,
22/68,
23/97,
24/157,
25/277,
26/37,
27/277,
28/8,
29/68,
30/248,
31/188,
32/172,
33/292,
34/52,
35/52,
36/232,
37/292,
38/112,
39/352,
40/112,
41/143,
42/323,
43/143,
44/128,
45/172,
46/112,
47/292,
48/352,
49/8,
50/8,
51/112,
52/188,
53/308,
54/188,
55/308,
56/68,
57/308,
58/188,
59/248,
60/337,
61/37,
62/217,
63/97,
64/188,
65/308,
66/68,
67/8,
68/352,
69/112,
70/232,
71/352,
72/172,
73/292,
74/172}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
Dieser dritte Winkel muss jetzt mit verwendet werden, um die dritte Bedingung ∠(P18-P14,P5-P13)=90° einzustellen. So gesehen ändert sich an der Beweglichkeit vermutlich nichts und
2020-01-13 13:04 - haribo in Beitrag No. 1884 schreibt:
offenbar stabilisiert also diese weisse umgelegte linie den graphen aus #1881, bzw macht ihn unbeweglich
. Das extra GAP-Programm (Button "acos(1/4)", weil mit exakten Punktkoordinaten rechnen möglich) gibt ebenfalls als Ergebnis Beweglichkeit=0, also unbeweglich aus:
GAP
GAP W60:=[[1/2,-1/2*Sqrt(3)],[1/2*Sqrt(3),1/2]];
Wbl:=[[1/4,-1/4*Sqrt(15)],[1/4*Sqrt(15),1/4]]*W60^-1; #acos(1/4)_Graph
P:=[];
P[1]:=[0,0];
P[2]:=[1,0];
P[3]:=P[1]+W60*(P[2]-P[1]);;
P[4]:=P[3]+W60*(P[2]-P[3]);;
P[5]:=P[2]-(P[1]-P[2]);;
P[6]:=P[3]-(P[1]-P[3]);;
P[7]:=P[1]+W60*Wbl^-2*(P[3]-P[1]);;
P[8]:=P[1]+W60*(P[7]-P[1]);;
P[9]:=P[8]+W60*(P[7]-P[8]);;
P[10]:=P[8]-(P[1]-P[8]);;
P[11]:=P[7]-(P[1]-P[7]);;
P[12]:=P[11]+W60*(P[6]-P[11]);;
P[13]:=P[12]+W60*(P[6]-P[12]);;
P[14]:=P[12]-(P[11]-P[12]);;
P[15]:=P[10]+Wbl*(P[9]-P[10]);;
P[16]:=P[10]+W60*(P[15]-P[10]);;
P[17]:=P[16]+W60*(P[15]-P[16]);;
P[18]:=P[16]-(P[10]-P[16]);;
P[19]:=P[9]+W60*Wbl*(P[7]-P[9]);;
P[20]:=P[19]+W60^-2*(P[9]-P[19]);;
P[21]:=P[19]-(P[9]-P[19]);;
P[33]:=P[14]+W60^-1*(P[21]-P[14]);;
P[34]:=P[33]+W60*(P[14]-P[33]);;
P[36]:=P[18]+W60^3*Wbl^-1*(P[16]-P[18]);;
P[37]:=P[20]-(P[21]-P[20]);;
P[38]:=P[20]+(W60*Wbl)^-1*(P[37]-P[20]);;
P[39]:=P[20]-(P[17]-P[20]);;
P[50]:=P[34]+W60*Wbl*(P[14]-P[34]);;
P[51]:=P[50]+W60*(P[34]-P[50]);;
P[58]:=P[51]+Wbl^-1*(P[50]-P[51]);;
P[62]:=P[5]+Wbl^-3*(P[4]-P[5]);;
P[63]:=P[62]-(P[5]-P[62]);;
P[68]:=P[63]+W60*W60*Wbl*(P[62]-P[63]);;
P[69]:=P[51]+W60*(P[13]-P[51]);;
P[74]:=P[51]+W60^-1*(P[50]-P[51]);;
P[27]:=P[33]+W60*(P[34]-P[33]);;
P[30]:=P[38]-(P[39]-P[38]);;
P[31]:=P[36]-(P[18]-P[36]);;
P[32]:=P[33]-(P[14]-P[33]);;
P[35]:=P[31]+W60*(P[36]-P[31]);;
P[44]:=P[50]+W60^-1*(P[34]-P[50]);;
P[49]:=P[50]-(P[51]-P[50]);;
P[56]:=P[58]+(W60^3*Wbl^-1)^-1*(P[51]-P[58]);;
P[57]:=P[56]+W60*(P[58]-P[56]);;
P[60]:=P[62]+W60*(P[5]-P[62]);;
P[61]:=P[62]+W60*(P[60]-P[62]);;
P[64]:=P[68]+W60*Wbl*(P[63]-P[68]);;
P[65]:=P[64]+W60^-2*(P[68]-P[64]);;
P[66]:=P[64]+W60*(P[65]-P[64]);;
P[67]:=P[66]+W60*(P[65]-P[66]);;
P[70]:=P[67]+Wbl^-1*(P[66]-P[67]);;
P[71]:=P[70]+W60*(P[67]-P[70]);;
P[72]:=P[57]-(P[58]-P[57]);;
P[73]:=P[57]+W60*(P[74]-P[57]);;
P[24]:=P[27]+(W60*Wbl)^-1*(P[32]-P[27]);;
P[25]:=P[24]+W60*(P[27]-P[24]);;
P[26]:=P[25]-(P[27]-P[25]);;
P[28]:=P[30]+W60*Wbl*(P[38]-P[30]);;
P[29]:=P[30]+W60*(P[28]-P[30]);;
P[42]:=P[44]+W60*Wbl*(P[49]-P[44]);;
P[43]:=P[44]+W60*(P[42]-P[44]);;
P[45]:=P[49]+(W60*Wbl)^-1*(P[44]-P[49]);;
P[46]:=P[45]+W60^2*(P[49]-P[45]);;
P[47]:=P[56]-(P[58]-P[56]);;
P[48]:=P[46]+W60*(P[47]-P[46]);;
P[52]:=P[48]+Wbl*(P[47]-P[48]);;
P[53]:=P[48]+W60*(P[52]-P[48]);;
P[54]:=P[57]-(P[74]-P[57]);;
P[55]:=P[53]-(P[48]-P[53]);;
P[59]:=P[61]-(P[63]-P[61]);;
P[22]:=P[24]-(P[27]-P[24]);;
P[23]:=P[22]+W60*(P[24]-P[22]);;
P[40]:=P[42]-(P[44]-P[42]);;
P[41]:=P[26]+W60*(P[43]-P[26]);;
Kante:=[ [1,2], [1,3], [2,3], [3,4], [2,4], [4,5], [2,5], [5,62],[5,60],[3,6], [4,6], [1,7], [1,8], [7,8], [8,9], [7,9], [8,10], [9,10], [7,11], [6,11], [11,12], [6,12], [12,13], [13,69],[13,51],[12,14], [13,14], [14,33],[14,34],[14,39],[10,15], [10,16], [15,16], [16,17], [15,17], [16,18], [17,18], [18,36],[18,37],[15,19], [9,19], [17,20], [19,20], [20,37],[20,38],[20,21], [19,21], [14,21], [22,23], [22,24], [23,24], [23,25], [24,25], [23,26], [25,26], [26,41],[26,43],[24,27], [25,27], [22,28], [22,29], [28,29], [28,30], [29,30], [29,31], [30,31], [27,32], [28,32], [27,33], [32,33], [33,34], [34,50],[31,35], [31,36], [35,36], [35,37], [36,37], [30,38], [35,38], [38,39], [20,39], [40,41], [40,42], [41,42], [41,43], [42,43], [42,44], [43,44], [40,45], [40,46], [45,46], [45,47], [46,47], [46,48], [47,48], [44,49], [45,49], [44,50], [49,50], [50,51], [34,51], [51,69],[51,74],[48,52], [48,53], [52,53], [52,54], [53,54], [53,55], [54,55], [55,71],[55,72],[47,56], [52,56], [54,57], [56,57], [57,72],[57,73],[51,58], [56,58], [57,58], [59,60], [59,61], [60,61], [60,62], [61,62], [61,63], [62,63], [59,64], [59,65], [64,65], [64,66], [65,66], [65,67], [66,67], [63,68], [64,68], [63,69], [68,69], [67,70], [67,71], [70,71], [70,72], [71,72], [66,73], [70,73], [73,74], [57,74], ];;
Size(Kante);
RESTKANTEN:=[[21,14],[5,13],[5,13],];;
for K in Kante do Print(" ",(P[K[1]]-P[K[2]])^2); od;
PUNKTEZAHL:=Size(P); KOORDINATENZAHL:=2*PUNKTEZAHL; KANTENZAHL:=Size(Kante);
n:=Maximum(KOORDINATENZAHL,KANTENZAHL); A:=NullMat(n,n);;
for i in [1..KANTENZAHL] do
A[2*Kante[i][1]-1][i]:=P[Kante[i][2]][1]-P[Kante[i][1]][1];
A[2*Kante[i][1] ][i]:=P[Kante[i][2]][2]-P[Kante[i][1]][2];
A[2*Kante[i][2]-1][i]:=P[Kante[i][1]][1]-P[Kante[i][2]][1];
A[2*Kante[i][2] ][i]:=P[Kante[i][1]][2]-P[Kante[i][2]][2];
od;
Nenner:=Lcm(List(Flat(A),i->DenominatorCyc(i)));
A:=Nenner*A;;P:=Nenner*P;;
AlterNenner:=1;
RankA:=Rank(A);
Print("gerechnet_mit_Button=\"",gerechnet_mit_Button,"\";");
Print("Beweglichkeit=",KOORDINATENZAHL-RankA-3);
Print("Einsetzkanten=",KANTENZAHL-RankA); |
Um beim Zurechtziehen des Graphen Beweglichkeit festzustellen, sollte die Eingabe des Graphen besser so erfolgen, dass keine Beschränkung der Beweglichkeit durch nachträgliches Umlegen von Kanten oder durch einschränkende Symmetriebedingungen erfolgt. Mühsam, eine solche Eingabe des gesamten Graphen von Hand zu machen. Mit zum Beispiel Button neue Eingabe "wenig Winkel" geht das auch automatisch:
74 Knoten, 8×Grad 3, 62×Grad 4, 4×Grad 6, 0 Überschneidungen
148 Kanten, minimal 0.99999949693408940465, maximal 1.00000024068354642637
einzustellende Kanten, Abstände und Winkel:
|P20-P38|=1.00000000000000044409
|P14-P21|=1.00000000000000022204
|P35-P38|=1.00000000000000088818
|P28-P32|=0.99999999999999156231
|P57-P72|=1.00000024068354642637
|P51-P58|=1.00000000000055733196
|P66-P73|=0.99999981613629274069
|P70-P73|=0.99999949693408940465
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>Anfang für einen neuen, noch unbenannten Streichholzgraph</Bildtext>
%<Ausrichten von="1" nach="2"/>
%<Winkel size="18" color="blue" id="blauerWinkel" value="-166.5674634422104"/>
%<Winkel size="18" color="green" id="gruenerWinkel" value="88.95502437185986"/>
%<Winkel size="18" color="orange" id="orangerWinkel" value="59.999999999999964"/>
%<Winkel size="18" color="violet" id="vierterWinkel" value="-60"/>
%<Winkel size="18" color="teal" id="fuenfterWinkel" value="75.52248781407006"/>
%<Feinjustieren Anzahl="5"/>
%<Rechenweg>
%P[1]=[-18.114795237025238,-11.925524469987494]; P[2]=[31.54207889274424,-17.773160886543337]; D=ab(1,2); A(1,2); L(3,1,2); L(4,3,2); L(5,4,2); L(6,3,4); M(60,5,2,blauerWinkel); L(62,5,60); M(59,60,5,-174.9999999999999); L(95,60,59); Q(61,62,60,D,ab(95,60,59,"gedreht")); L(63,62,61); M(7,1,2,gruenerWinkel); L(8,1,7); L(9,8,7); L(10,8,9); M(96,6,3,-70.52248781407008); L(12,96,6); Q(11,7,6,D,ab(96,6,12,"gedreht")); M(13,12,6,orangerWinkel); L(14,12,13); M(51,13,12,-70.52248781406995); L(97,51,13); M(68,63,61,80.52248781407002); L(98,63,68); Q(69,13,63,ab(97,13,51,"gedreht"),ab(98,63,68,"gedreht")); M(33,14,12,-70.52248781407002); L(99,33,14); M(100,51,13,-159.47751218593012); L(50,100,51); Q(34,14,51,ab(99,14,33,"gedreht"),ab(100,51,50,"gedreht")); M(101,59,60,-83.95502437185985); L(65,101,59); L(66,101,65); L(67,66,65); Q(64,68,59,D,ab(101,59,65,66,67,"gedreht")); M(39,14,12,vierterWinkel); M(15,10,8,fuenfterWinkel); L(16,10,15); L(17,16,15); L(18,16,17); N(19,15,9); M(102,19,9,-115); L(21,102,19); Q(20,17,19,D,ab(102,19,21,"gedreht")); M(38,20,17,-114.99999999999997); L(103,38,20); A(39,20,ab(103,20,38,"gedreht")); A(14,21); M(36,18,16,169.47751218592992); L(104,36,18); M(31,36,18,185); L(105,31,36); Q(35,36,104,ab(105,36,31,"gedreht"),D); Q(37,18,20,ab(104,18,31,35,36,"gedreht"),D); A(35,38); M(29,31,35,80.52248781407005); M(22,29,31,-174.99999999999983); L(28,22,29); L(107,28,29); Q(106,29,31,ab(107,29,22,28,"gedreht"),D); Q(30,31,38,ab(106,31,22,28,29,"gedreht"),D); M(23,22,28,93.95502437185986); L(24,23,22); L(25,23,24); L(26,23,25); L(108,25,24); M(109,33,14,125.00000000000007); L(32,33,109); Q(27,22,33,ab(108,22,23,24,25,26,"gedreht"),ab(109,33,32,"gedreht")); A(28,32); M(41,26,23,171.56746344221023); L(43,41,26); M(40,41,26,-175); L(111,40,41); Q(42,41,43,ab(111,41,40,"gedreht"),D); L(110,42,43); M(112,50,34,-55.000000000000014); L(49,112,50); Q(44,26,50,ab(110,26,40,41,42,43,"gedreht"),ab(112,50,49,"gedreht")); M(113,40,41,93.95502437185985); L(46,40,113); L(47,46,113); L(48,46,47); Q(45,40,49,ab(113,40,46,47,48,"gedreht"),D); M(52,48,46,80.52248781407002); L(53,48,52); L(54,53,52); L(114,53,54); M(70,67,65,-70.52248781406996); L(71,70,67); M(115,71,67,185); L(116,71,115); Q(72,70,71,D,ab(116,71,115,"gedreht")); Q(55,48,67,ab(114,48,52,53,54,"gedreht"),ab(115,67,70,71,72,"gedreht")); N(56,52,47); M(117,56,47,-115.00000000000007); L(58,117,56); Q(57,54,56,D,ab(117,56,58,"gedreht")); A(57,72); A(51,58); M(73,57,54,-115.00000000000017); L(118,73,57); Q(74,57,51,ab(118,57,73,"gedreht"),D); A(66,73); A(70,73);
%R(20,38); // oder R(20,39);
%R(14,21);
%R(35,38);
%R(28,32);
%R(57,72);
%R(51,58);
%R(66,73);
%R(70,73);
%</Rechenweg>
%
%<Knopf id="Stopp_alleWinkel" color="LightGrey"/>
%
%<Knopf id="Start_blauerWinkel" color="blue"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#blauerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_blauerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_gruenerWinkel" color="green"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#gruenerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_gruenerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_orangerWinkel" color="orange"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#orangerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_orangerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_vierterWinkel" color="violet"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#vierterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_vierterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_fuenfterWinkel" color="teal"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#fuenfterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_fuenfterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LimeGreen}{rgb}{0.20,0.80,0.20}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
\definecolor{Teal}{rgb}{0.00,0.50,0.50}
\definecolor{Violet}{rgb}{0.93,0.51,0.93}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.85122958682191685043/0.23390545666223369614,
2/2.84436706941730665932/0.11695272833111682032,
3/2.44908236189625894141/1.03551138187480851194,
4/3.44221984449164830622/0.91855865354369159448,
5/3.83750455201269646821/0.00000000000000000000,
6/3.04693513697060103240/1.83711730708738341100,
7/1.98627496519077961779/1.22474487139158849658,
8/1.06066017177982185871/0.84627789235802808321,
9/1.19570555014868484811/1.83711730708738274487,
10/0.27009075673772686699/1.45865032805382210945,
11/2.12132034355964282923/2.21558428612094360233,
12/2.91188975860173737686/2.82795672181673829471,
13/3.83750455201269513594/2.44948974278317788134,
14/3.70245917364383192449/3.44032915751253298708,
15/1.06066017177982141462/2.07102276374961702388,
16/0.13504537836886357227/2.44948974278317699316,
17/0.92561479341095820317/3.06186217847897168554,
18/0.00000000000000000000/3.44032915751253209891,
19/1.98627496519077939574/2.44948974278317788134,
20/1.85122958682191596225/3.44032915751253254300,
21/2.77684438023287416542/3.06186217847897212962,
22/1.85122958682191640634/6.64675285836282991880,
23/2.84436706941730621523/6.76370558669395105511,
24/2.44908236189626160595/5.84514693315025724019,
25/3.44221984449165052666/5.96209966148137837649,
26/3.83750455201269513594/6.88065831502506952688,
27/3.04693513697060724965/5.04354100793768544975,
28/1.98627496519077872961/5.65591344363347392488,
29/1.06066017177982030439/6.03438042266703611460,
30/1.19570555014868329380/5.04354100793768100885,
31/0.27009075673772575676/5.42200798697124053405,
32/2.12132034355964771422/4.66507402890412858909,
33/2.91188975860174004140/4.05270159320833123218,
34/3.83750455201269957684/4.43116857224188720465,
35/1.06066017177981986030/4.80963555127544761802,
36/0.13504537836886273960/4.43116857224188631648,
37/0.92561479341095764806/3.81879613654609340045,
38/1.98627496519077872961/4.43116857224188809283,
39/2.77684438023287416542/3.81879613654609340045,
40/5.82377951720347208919/6.64675285836280504981,
41/4.83064203460808272439/6.76370558669393684426,
42/5.22592674212911756371/5.84514693315024125297,
43/4.23278925953372908708/5.96209966148137215924,
44/4.62807396705476392640/5.04354100793767479161,
45/5.68873434919859555237/5.65591341496214194962,
46/6.61434906225764063237/6.03438059051191277860,
47/6.47930389425276498372/5.04354114711125145476,
48/7.40491860731180828736/5.42200832266102228374,
49/5.55368876046573411998/4.66507402890414279995,
50/4.76311934542365733591/4.05270159320832323857,
51/3.97254993038155967966/3.44032915751253209891,
52/6.61434877154106359853/4.80963643012396246945,
53/7.53996330492708466409/4.43116881514933691477,
54/6.74939346915633997526/3.81879692261227710048,
55/7.67500800254235926445/3.44032930763765065763,
56/5.68873405848201496582/4.43116925457419963408,
57/5.82377875609729134254/3.44032974706251515329,
58/4.89816422271127116517/3.81879736203714070797,
59/5.82377951720347564191/0.23390545666222936627,
60/4.83064203460808627710/0.11695272833111461375,
61/5.22592674212913532727/1.03551138187480540331,
62/4.23278925953374507429/0.91855865354369103937,
63/4.62807396705479590082/1.83711730708738141260,
64/5.68873413883461331864/1.22474487139159138316,
65/6.61434893224557018954/0.84627789235802985957,
66/6.47930355387670786627/1.83711730708738452122,
67/7.40491834728766651352/1.45865032805382321968,
68/5.55368876046575188354/2.21558428612094626686,
69/4.76311934542365378320/2.82795672181673696244,
70/6.61434859186873058690/2.07102232432475252821,
71/7.53996317491501244490/2.44948981784573716070,
72/6.74939341949607651827/3.06186181411666646923,
73/5.68873468957494310416/2.44949015353735344291,
74/4.89816446376787961725/3.06186154253864328822}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
5/173.28/366.72/0.4/Blue,
1/353.28/442.24/0.4/Green,
12/277.76/337.76/0.4/Orange,
14/217.76/517.76/0.4/Violet,
10/322.24/397.76/0.4/Teal}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
1/2,
3/1, 3/2,
4/3, 4/2,
5/4, 5/2,
6/3, 6/4,
7/1,
8/1, 8/7,
9/8, 9/7,
10/8, 10/9,
11/7, 11/6,
12/11, 12/6,
13/12,
14/12, 14/13, 14/21,
15/10,
16/10, 16/15,
17/16, 17/15,
18/16, 18/17,
19/15, 19/9,
20/17, 20/19,
21/20, 21/19,
22/29,
23/22,
24/23, 24/22,
25/23, 25/24,
26/23, 26/25,
27/24, 27/25, 27/33,
28/22, 28/29, 28/32,
29/31,
30/28, 30/29, 30/31, 30/38,
31/36,
32/33, 32/27,
33/14,
34/14, 34/33, 34/51,
35/31, 35/36, 35/37, 35/38,
36/18,
37/18, 37/36, 37/20,
38/20,
39/14, 39/20, 39/38,
40/41,
41/26,
42/40, 42/41, 42/43,
43/41, 43/26,
44/42, 44/43, 44/50,
45/40, 45/49,
46/40, 46/45,
47/46, 47/45,
48/46, 48/47,
49/44, 49/50,
50/34, 50/51,
51/13, 51/58,
52/48,
53/48, 53/52,
54/53, 54/52,
55/53, 55/54, 55/71,
56/52, 56/47,
57/54, 57/56, 57/72,
58/57, 58/56,
59/60,
60/5,
61/62, 61/59, 61/60,
62/5, 62/60,
63/62, 63/61,
64/68, 64/59,
65/64, 65/59,
66/64, 66/65, 66/73,
67/66, 67/65,
68/63,
69/13, 69/51, 69/63, 69/68,
70/67, 70/73,
71/70, 71/67,
72/70, 72/71, 72/55,
73/57,
74/57, 74/73, 74/51}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,74}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[LimeGreen,very thick] (p-20) -- (p-38);
\draw[LimeGreen,very thick] (p-14) -- (p-21);
\draw[LimeGreen,very thick] (p-35) -- (p-38);
\draw[LimeGreen,very thick] (p-28) -- (p-32);
\draw[LimeGreen,very thick] (p-57) -- (p-72);
\draw[LimeGreen,very thick] (p-51) -- (p-58);
\draw[LimeGreen,very thick] (p-66) -- (p-73);
\draw[LimeGreen,very thick] (p-70) -- (p-73);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
5/173.28/366.72/0.4/Blue,
1/353.28/442.24/0.4/Green,
12/277.76/337.76/0.4/Orange,
14/217.76/517.76/0.4/Violet,
10/322.24/397.76/0.4/Teal}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/292,
2/323,
3/143,
4/23,
5/217,
6/308,
7/52,
8/172,
9/52,
10/172,
11/188,
12/68,
13/308,
14/68,
15/308,
16/128,
17/68,
18/232,
19/248,
20/128,
21/8,
22/68,
23/157,
24/277,
25/37,
26/143,
27/52,
28/308,
29/128,
30/308,
31/112,
32/172,
33/292,
34/52,
35/52,
36/232,
37/352,
38/112,
39/352,
40/23,
41/143,
42/323,
43/203,
44/263,
45/172,
46/112,
47/232,
48/68,
49/8,
50/248,
51/248,
52/188,
53/8,
54/188,
55/52,
56/68,
57/52,
58/188,
59/248,
60/277,
61/337,
62/157,
63/232,
64/128,
65/308,
66/128,
67/8,
68/352,
69/352,
70/232,
71/52,
72/112,
73/292,
74/172}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/43012dc2dd73bb4519e2b0ea678d74ea.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>Anfang für einen neuen, noch unbenannten Streichholzgraph</Bildtext>
%<Ausrichten von=\"1\" nach=\"2\"/>
%<Winkel size=\"18\" color=\"blue\" id=\"blauerWinkel\" value=\"-166.5674634422104\"/>
%<Winkel size=\"18\" color=\"green\" id=\"gruenerWinkel\" value=\"88.95502437185986\"/>
%<Winkel size=\"18\" color=\"orange\" id=\"orangerWinkel\" value=\"59.999999999999964\"/>
%<Winkel size=\"18\" color=\"violet\" id=\"vierterWinkel\" value=\"-60\"/>
%<Winkel size=\"18\" color=\"teal\" id=\"fuenfterWinkel\" value=\"75.52248781407006\"/>
%<Feinjustieren Anzahl=\"5\"/>
%<Rechenweg>
%P[1]=[-18.114795237025238,-11.925524469987494]; P[2]=[31.54207889274424,-17.773160886543337]; D=ab(1,2); A(1,2); L(3,1,2); L(4,3,2); L(5,4,2); L(6,3,4); M(60,5,2,blauerWinkel); L(62,5,60); M(59,60,5,-174.9999999999999); L(95,60,59); Q(61,62,60,D,ab(95,60,59,\"gedreht\")); L(63,62,61); M(7,1,2,gruenerWinkel); L(8,1,7); L(9,8,7); L(10,8,9); M(96,6,3,-70.52248781407008); L(12,96,6); Q(11,7,6,D,ab(96,6,12,\"gedreht\")); M(13,12,6,orangerWinkel); L(14,12,13); M(51,13,12,-70.52248781406995); L(97,51,13); M(68,63,61,80.52248781407002); L(98,63,68); Q(69,13,63,ab(97,13,51,\"gedreht\"),ab(98,63,68,\"gedreht\")); M(33,14,12,-70.52248781407002); L(99,33,14); M(100,51,13,-159.47751218593012); L(50,100,51); Q(34,14,51,ab(99,14,33,\"gedreht\"),ab(100,51,50,\"gedreht\")); M(101,59,60,-83.95502437185985); L(65,101,59); L(66,101,65); L(67,66,65); Q(64,68,59,D,ab(101,59,65,66,67,\"gedreht\")); M(39,14,12,vierterWinkel); M(15,10,8,fuenfterWinkel); L(16,10,15); L(17,16,15); L(18,16,17); N(19,15,9); M(102,19,9,-115); L(21,102,19); Q(20,17,19,D,ab(102,19,21,\"gedreht\")); M(38,20,17,-114.99999999999997); L(103,38,20); A(39,20,ab(103,20,38,\"gedreht\")); A(14,21); M(36,18,16,169.47751218592992); L(104,36,18); M(31,36,18,185); L(105,31,36); Q(35,36,104,ab(105,36,31,\"gedreht\"),D); Q(37,18,20,ab(104,18,31,35,36,\"gedreht\"),D); A(35,38); M(29,31,35,80.52248781407005); M(22,29,31,-174.99999999999983); L(28,22,29); L(107,28,29); Q(106,29,31,ab(107,29,22,28,\"gedreht\"),D); Q(30,31,38,ab(106,31,22,28,29,\"gedreht\"),D); M(23,22,28,93.95502437185986); L(24,23,22); L(25,23,24); L(26,23,25); L(108,25,24); M(109,33,14,125.00000000000007); L(32,33,109); Q(27,22,33,ab(108,22,23,24,25,26,\"gedreht\"),ab(109,33,32,\"gedreht\")); A(28,32); M(41,26,23,171.56746344221023); L(43,41,26); M(40,41,26,-175); L(111,40,41); Q(42,41,43,ab(111,41,40,\"gedreht\"),D); L(110,42,43); M(112,50,34,-55.000000000000014); L(49,112,50); Q(44,26,50,ab(110,26,40,41,42,43,\"gedreht\"),ab(112,50,49,\"gedreht\")); M(113,40,41,93.95502437185985); L(46,40,113); L(47,46,113); L(48,46,47); Q(45,40,49,ab(113,40,46,47,48,\"gedreht\"),D); M(52,48,46,80.52248781407002); L(53,48,52); L(54,53,52); L(114,53,54); M(70,67,65,-70.52248781406996); L(71,70,67); M(115,71,67,185); L(116,71,115); Q(72,70,71,D,ab(116,71,115,\"gedreht\")); Q(55,48,67,ab(114,48,52,53,54,\"gedreht\"),ab(115,67,70,71,72,\"gedreht\")); N(56,52,47); M(117,56,47,-115.00000000000007); L(58,117,56); Q(57,54,56,D,ab(117,56,58,\"gedreht\")); A(57,72); A(51,58); M(73,57,54,-115.00000000000017); L(118,73,57); Q(74,57,51,ab(118,57,73,\"gedreht\"),D); A(66,73); A(70,73);
%R(20,38); // oder R(20,39);
%R(14,21);
%R(35,38);
%R(28,32);
%R(57,72);
%R(51,58);
%R(66,73);
%R(70,73);
%</Rechenweg>
%
%<Knopf id=\"Stopp_alleWinkel\" color=\"LightGrey\"/>
%
%<Knopf id=\"Start_blauerWinkel\" color=\"blue\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#blauerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_blauerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_gruenerWinkel\" color=\"green\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#gruenerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_gruenerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_orangerWinkel\" color=\"orange\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#orangerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_orangerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_vierterWinkel\" color=\"violet\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#vierterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_vierterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_fuenfterWinkel\" color=\"teal\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#fuenfterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_fuenfterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LimeGreen}{rgb}{0.20,0.80,0.20}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
\definecolor{Teal}{rgb}{0.00,0.50,0.50}
\definecolor{Violet}{rgb}{0.93,0.51,0.93}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.85122958682191685043/0.23390545666223369614,
2/2.84436706941730665932/0.11695272833111682032,
3/2.44908236189625894141/1.03551138187480851194,
4/3.44221984449164830622/0.91855865354369159448,
5/3.83750455201269646821/0.00000000000000000000,
6/3.04693513697060103240/1.83711730708738341100,
7/1.98627496519077961779/1.22474487139158849658,
8/1.06066017177982185871/0.84627789235802808321,
9/1.19570555014868484811/1.83711730708738274487,
10/0.27009075673772686699/1.45865032805382210945,
11/2.12132034355964282923/2.21558428612094360233,
12/2.91188975860173737686/2.82795672181673829471,
13/3.83750455201269513594/2.44948974278317788134,
14/3.70245917364383192449/3.44032915751253298708,
15/1.06066017177982141462/2.07102276374961702388,
16/0.13504537836886357227/2.44948974278317699316,
17/0.92561479341095820317/3.06186217847897168554,
18/0.00000000000000000000/3.44032915751253209891,
19/1.98627496519077939574/2.44948974278317788134,
20/1.85122958682191596225/3.44032915751253254300,
21/2.77684438023287416542/3.06186217847897212962,
22/1.85122958682191640634/6.64675285836282991880,
23/2.84436706941730621523/6.76370558669395105511,
24/2.44908236189626160595/5.84514693315025724019,
25/3.44221984449165052666/5.96209966148137837649,
26/3.83750455201269513594/6.88065831502506952688,
27/3.04693513697060724965/5.04354100793768544975,
28/1.98627496519077872961/5.65591344363347392488,
29/1.06066017177982030439/6.03438042266703611460,
30/1.19570555014868329380/5.04354100793768100885,
31/0.27009075673772575676/5.42200798697124053405,
32/2.12132034355964771422/4.66507402890412858909,
33/2.91188975860174004140/4.05270159320833123218,
34/3.83750455201269957684/4.43116857224188720465,
35/1.06066017177981986030/4.80963555127544761802,
36/0.13504537836886273960/4.43116857224188631648,
37/0.92561479341095764806/3.81879613654609340045,
38/1.98627496519077872961/4.43116857224188809283,
39/2.77684438023287416542/3.81879613654609340045,
40/5.82377951720347208919/6.64675285836280504981,
41/4.83064203460808272439/6.76370558669393684426,
42/5.22592674212911756371/5.84514693315024125297,
43/4.23278925953372908708/5.96209966148137215924,
44/4.62807396705476392640/5.04354100793767479161,
45/5.68873434919859555237/5.65591341496214194962,
46/6.61434906225764063237/6.03438059051191277860,
47/6.47930389425276498372/5.04354114711125145476,
48/7.40491860731180828736/5.42200832266102228374,
49/5.55368876046573411998/4.66507402890414279995,
50/4.76311934542365733591/4.05270159320832323857,
51/3.97254993038155967966/3.44032915751253209891,
52/6.61434877154106359853/4.80963643012396246945,
53/7.53996330492708466409/4.43116881514933691477,
54/6.74939346915633997526/3.81879692261227710048,
55/7.67500800254235926445/3.44032930763765065763,
56/5.68873405848201496582/4.43116925457419963408,
57/5.82377875609729134254/3.44032974706251515329,
58/4.89816422271127116517/3.81879736203714070797,
59/5.82377951720347564191/0.23390545666222936627,
60/4.83064203460808627710/0.11695272833111461375,
61/5.22592674212913532727/1.03551138187480540331,
62/4.23278925953374507429/0.91855865354369103937,
63/4.62807396705479590082/1.83711730708738141260,
64/5.68873413883461331864/1.22474487139159138316,
65/6.61434893224557018954/0.84627789235802985957,
66/6.47930355387670786627/1.83711730708738452122,
67/7.40491834728766651352/1.45865032805382321968,
68/5.55368876046575188354/2.21558428612094626686,
69/4.76311934542365378320/2.82795672181673696244,
70/6.61434859186873058690/2.07102232432475252821,
71/7.53996317491501244490/2.44948981784573716070,
72/6.74939341949607651827/3.06186181411666646923,
73/5.68873468957494310416/2.44949015353735344291,
74/4.89816446376787961725/3.06186154253864328822}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
5/173.28/366.72/0.4/Blue,
1/353.28/442.24/0.4/Green,
12/277.76/337.76/0.4/Orange,
14/217.76/517.76/0.4/Violet,
10/322.24/397.76/0.4/Teal}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
1/2,
3/1, 3/2,
4/3, 4/2,
5/4, 5/2,
6/3, 6/4,
7/1,
8/1, 8/7,
9/8, 9/7,
10/8, 10/9,
11/7, 11/6,
12/11, 12/6,
13/12,
14/12, 14/13, 14/21,
15/10,
16/10, 16/15,
17/16, 17/15,
18/16, 18/17,
19/15, 19/9,
20/17, 20/19,
21/20, 21/19,
22/29,
23/22,
24/23, 24/22,
25/23, 25/24,
26/23, 26/25,
27/24, 27/25, 27/33,
28/22, 28/29, 28/32,
29/31,
30/28, 30/29, 30/31, 30/38,
31/36,
32/33, 32/27,
33/14,
34/14, 34/33, 34/51,
35/31, 35/36, 35/37, 35/38,
36/18,
37/18, 37/36, 37/20,
38/20,
39/14, 39/20, 39/38,
40/41,
41/26,
42/40, 42/41, 42/43,
43/41, 43/26,
44/42, 44/43, 44/50,
45/40, 45/49,
46/40, 46/45,
47/46, 47/45,
48/46, 48/47,
49/44, 49/50,
50/34, 50/51,
51/13, 51/58,
52/48,
53/48, 53/52,
54/53, 54/52,
55/53, 55/54, 55/71,
56/52, 56/47,
57/54, 57/56, 57/72,
58/57, 58/56,
59/60,
60/5,
61/62, 61/59, 61/60,
62/5, 62/60,
63/62, 63/61,
64/68, 64/59,
65/64, 65/59,
66/64, 66/65, 66/73,
67/66, 67/65,
68/63,
69/13, 69/51, 69/63, 69/68,
70/67, 70/73,
71/70, 71/67,
72/70, 72/71, 72/55,
73/57,
74/57, 74/73, 74/51}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,74}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[LimeGreen,very thick] (p-20) -- (p-38);
\draw[LimeGreen,very thick] (p-14) -- (p-21);
\draw[LimeGreen,very thick] (p-35) -- (p-38);
\draw[LimeGreen,very thick] (p-28) -- (p-32);
\draw[LimeGreen,very thick] (p-57) -- (p-72);
\draw[LimeGreen,very thick] (p-51) -- (p-58);
\draw[LimeGreen,very thick] (p-66) -- (p-73);
\draw[LimeGreen,very thick] (p-70) -- (p-73);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
5/173.28/366.72/0.4/Blue,
1/353.28/442.24/0.4/Green,
12/277.76/337.76/0.4/Orange,
14/217.76/517.76/0.4/Violet,
10/322.24/397.76/0.4/Teal}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/292,
2/323,
3/143,
4/23,
5/217,
6/308,
7/52,
8/172,
9/52,
10/172,
11/188,
12/68,
13/308,
14/68,
15/308,
16/128,
17/68,
18/232,
19/248,
20/128,
21/8,
22/68,
23/157,
24/277,
25/37,
26/143,
27/52,
28/308,
29/128,
30/308,
31/112,
32/172,
33/292,
34/52,
35/52,
36/232,
37/352,
38/112,
39/352,
40/23,
41/143,
42/323,
43/203,
44/263,
45/172,
46/112,
47/232,
48/68,
49/8,
50/248,
51/248,
52/188,
53/8,
54/188,
55/52,
56/68,
57/52,
58/188,
59/248,
60/277,
61/337,
62/157,
63/232,
64/128,
65/308,
66/128,
67/8,
68/352,
69/352,
70/232,
71/52,
72/112,
73/292,
74/172}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
Es entsteht ein Graph mit 5 beweglichen Winkeln und 8 Einsetzkanten. Das sind Kanten, die am Ende passend in den Graph eingesetzt werden. 5 von diesen Kanten kann man mit den beweglichen Winkeln einstellen, die übrigen 3 müssen passen. Üblicherweise ist dann der Graph schon starr. Nur in Ausnahmefällen liegt eine Beweglichkeit vor und die macht sich eventuell bemerkbar, wenn man den Graph mit geringfügig geänderten beweglichen Winkeln erneut zurechtzieht. Dann kann es passieren, dass der Graph nicht wieder in die gleiche Position zurückgezogen wird sondern in eine andere mögliche Position entlang der Bewegungsbahn. Das Variieren der Winkel geht allerdings nur in einem kleinen Bereich, beispielsweise um 0,001°, ansonsten entstehen an anderer Stelle Überschneidungen öder ähnliches. Das ist eine ziemliche Fummelei. Obiger Graph wird immer wieder in die gleiche Position zurechtgezogen, also kein Anzeichen für eine Beweglichkeit. Ich suche nochmal ein anderes Beispiel für einen beweglichen Graph heraus, in einem neuen Beitrag, dann ist das noch deutlicher zu sehen. Wirklich exakte Ergebnisse sind nur das GAP-Programm mit Button "acos(1/4)" oder entsprechende geometrische Überlegungen.
|
Profil
Quote
Link |
Slash
Aktiv
Dabei seit: 23.03.2005
Mitteilungen: 7758
Aus: Cuxhaven-Sahlenburg
| Beitrag No.1888, vom Themenstarter, eingetragen 2020-01-18
|
Dieser Graph ist ein extremes Beispiel für einen starren Graphen mit falschen Kanten was die Genauigkeit (6 richtige Nachkommastellen) angeht, oder?
-----------------
Bound to be disappointing so why wait?
|
Profil
Quote
Link |
StefanVogel
Senior
Dabei seit: 26.11.2005
Mitteilungen: 3446
Aus: Raun
| Beitrag No.1889, eingetragen 2020-01-18
|
Der Graph wäre exakt gezeichnet richtig. Er ist ein Beispiel dafür, dass sich die ursprüngliche Rechengenauigkeit von etwa 14 Nachkommastellen durch langatmige Eingabe ohne Ausnutzung von Symmetrieen auf 6 Nachkommastellen verschlechtern kann, wobei ich jetzt nicht nachgeschaut habe, aus welchem konkreten Grund die Ungenauigkeit entsteht. Für die Feststellung der Beweglichkeit mittels Zurechtziehen muss man aber diese ungenaue Eingabe in Kauf nehmen und irgendwie damit zurechtkommen. Ist nicht einfach alles. Das GAP-Programm sagt jedenfalls auch für den ungenauen Graph, dass alle Kantenlängen exakt Eins sind, weil es aus der ungenauen Eingabe versucht, die exakte Eingabe zu rekonstruieren, also ein 30.000001° Winkel wird als exakt 30° angenommen. Hier der Ausschnitt aus der GAP-Berechnung für den ungenaueren Graph:
GAP
GAP gap> P:=[];
gap> P[1]:=[0,0];
gap> P[2]:=[1,0];
gap> P[3]:=P[1]+W60*(P[2]-P[1]);;
gap> P[4]:=P[3]+W60*(P[2]-P[3]);;
gap> P[5]:=P[2]-(P[1]-P[2]);;
gap> P[6]:=P[3]-(P[1]-P[3]);;
gap> P[7]:=P[1]+W60*Wbl^-2*(P[3]-P[1]);;
gap> P[8]:=P[1]+W60*(P[7]-P[1]);;
gap> P[9]:=P[8]+W60*(P[7]-P[8]);;
gap> P[10]:=P[8]-(P[1]-P[8]);;
gap> P[11]:=P[7]-(P[1]-P[7]);;
gap> P[12]:=P[11]+W60*(P[6]-P[11]);;
gap> P[13]:=P[12]+W60*(P[6]-P[12]);;
gap> P[14]:=P[12]-(P[11]-P[12]);;
gap> P[15]:=P[10]+Wbl*(P[9]-P[10]);;
gap> P[16]:=P[10]+W60*(P[15]-P[10]);;
gap> P[17]:=P[16]+W60*(P[15]-P[16]);;
gap> P[18]:=P[16]-(P[10]-P[16]);;
gap> P[19]:=P[9]+W60*Wbl*(P[7]-P[9]);;
gap> P[20]:=P[19]+W60^-2*(P[9]-P[19]);;
gap> P[21]:=P[19]-(P[9]-P[19]);;
gap> P[33]:=P[14]+W60^-1*(P[21]-P[14]);;
gap> P[34]:=P[33]+W60*(P[14]-P[33]);;
gap> P[36]:=P[18]+W60^3*Wbl^-1*(P[16]-P[18]);;
gap> P[37]:=P[20]-(P[21]-P[20]);;
gap> P[38]:=P[20]+(W60*Wbl)^-1*(P[37]-P[20]);;
gap> P[39]:=P[20]-(P[17]-P[20]);;
gap> P[50]:=P[34]+W60*Wbl*(P[14]-P[34]);;
gap> P[51]:=P[50]+W60*(P[34]-P[50]);;
gap> P[58]:=P[51]+Wbl^-1*(P[50]-P[51]);;
gap> P[62]:=P[5]+Wbl^-3*(P[4]-P[5]);;
gap> P[63]:=P[62]-(P[5]-P[62]);;
gap> P[68]:=P[63]+W60*W60*Wbl*(P[62]-P[63]);;
gap> P[69]:=P[51]+W60*(P[13]-P[51]);;
gap> P[74]:=P[51]+W60^-1*(P[50]-P[51]);;
gap> P[27]:=P[33]+W60*(P[34]-P[33]);;
gap> P[30]:=P[38]-(P[39]-P[38]);;
gap> P[31]:=P[36]-(P[18]-P[36]);;
gap> P[32]:=P[33]-(P[14]-P[33]);;
gap> P[35]:=P[31]+W60*(P[36]-P[31]);;
gap> P[44]:=P[50]+W60^-1*(P[34]-P[50]);;
gap> P[49]:=P[50]-(P[51]-P[50]);;
gap> P[56]:=P[58]+(W60^3*Wbl^-1)^-1*(P[51]-P[58]);;
gap> P[57]:=P[56]+W60*(P[58]-P[56]);;
gap> P[60]:=P[62]+W60*(P[5]-P[62]);;
gap> P[61]:=P[62]+W60*(P[60]-P[62]);;
gap> P[64]:=P[68]+W60*Wbl*(P[63]-P[68]);;
gap> P[65]:=P[64]+W60^-2*(P[68]-P[64]);;
gap> P[66]:=P[64]+W60*(P[65]-P[64]);;
gap> P[67]:=P[66]+W60*(P[65]-P[66]);;
gap> P[70]:=P[67]+Wbl^-1*(P[66]-P[67]);;
gap> P[71]:=P[70]+W60*(P[67]-P[70]);;
gap> P[72]:=P[57]-(P[58]-P[57]);;
gap> P[73]:=P[57]+W60*(P[74]-P[57]);;
gap> P[24]:=P[27]+(W60*Wbl)^-1*(P[32]-P[27]);;
gap> P[25]:=P[24]+W60*(P[27]-P[24]);;
gap> P[26]:=P[25]-(P[27]-P[25]);;
gap> P[28]:=P[32]+W60*Wbl*(P[27]-P[32]);;
gap> P[29]:=P[31]+W60*(P[30]-P[31]);;
gap> P[42]:=P[44]+W60*Wbl*(P[49]-P[44]);;
gap> P[43]:=P[44]+W60*(P[42]-P[44]);;
gap> P[45]:=P[49]+(W60*Wbl)^-1*(P[44]-P[49]);;
gap> P[46]:=P[45]+W60^2*(P[49]-P[45]);;
gap> P[47]:=P[56]-(P[58]-P[56]);;
gap> P[48]:=P[46]+W60*(P[47]-P[46]);;
gap> P[52]:=P[48]+Wbl*(P[47]-P[48]);;
gap> P[53]:=P[48]+W60*(P[52]-P[48]);;
gap> P[54]:=P[57]-(P[74]-P[57]);;
gap> P[55]:=P[53]-(P[48]-P[53]);;
gap> P[59]:=P[60]-(P[5]-P[60]);;
gap> P[22]:=P[29]-(P[31]-P[29]);;
gap> P[23]:=P[22]+W60*(P[24]-P[22]);;
gap> P[40]:=P[42]-(P[44]-P[42]);;
gap> P[41]:=P[26]+W60*(P[43]-P[26]);;
gap> Kante:=[ [1,2],[1,3], [2,3], [3,4], [2,4], [4,5], [2,5], [3,6], [4,6], [1,7], [1,8], [7,8], [8,9], [7,9], [8,10], [9,10], [7,11], [6,11], [11,12], [6,12], [12,13], [12,14], [13,14], [14,21],[10,15], [10,16], [15,16], [16,17], [15,17], [16,18], [17,18], [15,19], [9,19], [17,20], [19,20], [20,21], [19,21], [22,29],[22,23], [23,24], [22,24], [23,25], [24,25], [23,26], [25,26], [24,27], [25,27], [27,33],[22,28], [28,29],[28,32],[29,31],[28,30], [29,30], [30,31],[30,38],[31,36],[32,33],[27,32], [14,33], [14,34], [33,34], [34,51],[31,35], [35,36],[35,37],[35,38],[18,36], [18,37], [36,37], [20,37], [20,38], [14,39], [20,39], [38,39], [40,41],[26,41], [40,42], [41,42], [42,43],[41,43], [26,43], [42,44], [43,44], [44,50],[40,45], [45,49],[40,46], [45,46], [46,47], [45,47], [46,48], [47,48], [44,49], [49,50],[34,50], [50,51],[13,51], [51,58],[48,52], [48,53], [52,53], [53,54], [52,54], [53,55], [54,55], [55,71],[52,56], [47,56], [54,57], [56,57], [57,72],[57,58], [56,58], [59,60],[5,60], [61,62],[59,61], [60,61], [5,62], [60,62], [62,63], [61,63], [64,68],[59,64], [64,65], [59,65], [64,66], [65,66], [66,73],[66,67], [65,67], [63,68], [13,69], [51,69], [63,69], [68,69], [67,70], [70,73],[70,71], [67,71], [70,72], [71,72], [55,72], [57,73], [57,74], [73,74], [51,74], ];;
gap> Size(Kante);
gap> RESTKANTEN:=[[20,38],[14,21],[35,38],[28,32],[57,72],[51,58],[66,73],[70,73],];;
148
gap>
gap> for K in Kante do Print(" ",(P[K[1]]-P[K[2]])^2); od;
gap>
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
|
Die vielen Einsen am Ende sind alle Kantenlängen exakt 1.
|
Profil
Quote
Link |
Slash
Aktiv
Dabei seit: 23.03.2005
Mitteilungen: 7758
Aus: Cuxhaven-Sahlenburg
| Beitrag No.1890, vom Themenstarter, eingetragen 2020-01-18
|
Nach Feinjustieren des letzten Graphen werden auch 11 richtige Nachkommastellen angezeigt, also 0 oder 9.
P11,P21 ist jetzt auch wie bei haribo 1.07046626931915200842.
-----------------
Bound to be disappointing so why wait?
|
Profil
Quote
Link |
StefanVogel
Senior
Dabei seit: 26.11.2005
Mitteilungen: 3446
Aus: Raun
| Beitrag No.1891, eingetragen 2020-01-18
|
Dafür ändert sich beim Feinjustieren der vierte Winkel von vorher exakt -60°=300° auf 300.0000000000152°, also dadurch wird die Ungenauigkeit mehr auf die Winkel verlagert. Diese werden beim Feinjustieren so variiert, dass möglichst das gewünschte Ergebnis herauskommt. Wird mit möglichst exakten Winkeln losgerechnet, stimmen die Kantenlängen nicht so gut und wird so gerechnet, dass die genauesten Kantenlängen herauskommen, stimmen die Winkel nicht so gut. Irgendwo dazwischen geht Genauigkeit verloren.
|
Profil
Quote
Link |
StefanVogel
Senior
Dabei seit: 26.11.2005
Mitteilungen: 3446
Aus: Raun
| Beitrag No.1892, eingetragen 2020-01-19
|
Den #467-2 habe ich ohne die beiden Kanten P22-P78 und P12-P77 eingegeben und erhalte nach Button neue Eingabe "wenig Winkel" folgenden Graph
88 Knoten, 4×Grad 3, 80×Grad 4, 2×Grad 5, 2×Grad 7, 0 Überschneidungen
178 Kanten, minimal 0.99999999999998800959, maximal 1.00000000000000910383
einzustellende Kanten, Abstände und Winkel:
|P42-P80|=1.00000000000000555112
|P75-P83|=0.99999999999999711342
|P86-P87|=1.00000000000000421885
|P85-P87|=0.99999999999999833467
|P55-P87|=1.00000000000000421885
|P60-P61|=1.00000000000000177636
|P65-P66|=1.00000000000000643929
|P65-P85|=0.99999999999998800959
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78);</Bildtext>
%<Ausrichten von="1" nach="2"/>
%<Winkel size="18" color="blue" id="blauerWinkel" value="90"/>
%<Winkel size="18" color="green" id="gruenerWinkel" value="90"/>
%<Winkel size="18" color="orange" id="orangerWinkel" value="89.99999999999994"/>
%<Feinjustieren Anzahl="3"/>
%<Rechenweg>
%P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(1,2); L(3,1,2); L(4,3,2); L(5,4,2); M(6,1,2,blauerWinkel); L(9,1,6); L(10,9,6); L(11,9,10); N(7,6,3); M(109,7,3,95.00000000000001); L(73,7,109); Q(8,7,4,ab(109,7,73,"gedreht"),D); M(110,8,4,35.000000000000014); L(37,8,110); M(111,5,2,-85.00000000000001); L(38,111,5); Q(36,8,5,ab(110,8,37,"gedreht"),ab(111,5,38,"gedreht")); M(112,37,8,154.99999999999997); L(43,37,112); M(113,38,5,-144.99999999999994); L(44,113,38); Q(40,37,38,ab(112,37,43,"gedreht"),ab(113,38,44,"gedreht")); M(114,44,38,-85.00000000000017); M(71,114,44,125.00000000000043); M(69,71,114,125.00000000000016); L(116,69,71); Q(115,71,114,ab(116,71,69,"gedreht"),D); Q(72,114,44,ab(115,114,69,71,"gedreht"),D); Q(46,43,44,D,ab(114,44,69,71,72,"gedreht")); M(117,8,4,125.00000000000001); L(75,8,117); Q(74,8,43,ab(117,8,75,"gedreht"),D); M(118,73,7,-144.99999999999994); L(77,73,118); Q(76,73,75,ab(118,73,77,"gedreht"),D); M(12,10,6,gruenerWinkel); M(119,11,9,95.00000000000006); L(14,11,119); L(15,14,119); L(16,14,15); Q(13,11,12,ab(119,11,14,15,16,"gedreht"),D); N(17,15,12); M(120,16,14,94.99999999999991); L(19,16,120); L(20,19,120); L(21,19,20); Q(18,16,17,ab(120,16,19,20,21,"gedreht"),D); N(22,20,17); M(121,21,19,95.00000000000006); L(24,21,121); L(25,24,121); L(26,24,25); Q(23,21,22,ab(121,21,24,25,26,"gedreht"),D); M(27,25,23,orangerWinkel); M(122,26,24,95.00000000000001); L(29,26,122); L(30,29,122); L(31,29,30); Q(28,26,27,ab(122,26,29,30,31,"gedreht"),D); N(32,30,27); M(123,31,29,95.00000000000009); L(34,31,123); M(124,32,27,-114.99999999999997); L(35,124,32); Q(33,31,32,ab(123,31,34,"gedreht"),ab(124,32,35,"gedreht")); M(125,34,31,154.99999999999991); L(41,34,125); M(126,35,32,-144.99999999999986); L(42,126,35); Q(39,34,35,ab(125,34,41,"gedreht"),ab(126,35,42,"gedreht")); M(127,41,34,95.00000000000006); L(47,41,127); L(48,47,127); L(49,47,48); Q(45,41,42,ab(127,41,47,48,49,"gedreht"),D); M(128,42,35,-174.99999999999991); L(88,128,42); Q(50,48,42,D,ab(128,42,88,"gedreht")); M(129,49,47,95.00000000000014); L(52,49,129); L(53,52,129); L(54,52,53); Q(51,49,50,ab(129,49,52,53,54,"gedreht"),D); N(78,27,77); N(79,78,76); N(80,32,79); M(130,42,35,34.999999999999915); L(81,42,130); A(80,42,ab(130,42,81,"gedreht")); M(131,81,42,155.0000000000003); M(83,131,81,-115.0000000000004); L(132,131,83); Q(86,81,131,D,ab(132,131,83,"gedreht")); Q(82,81,79,ab(131,81,83,86,"gedreht"),D); A(75,83); M(87,86,81,-84.99999999999967); L(133,86,87); A(88,86,ab(133,86,87,"gedreht")); N(84,83,74); M(134,84,74,155.00000000000026); L(85,84,134); Q(70,84,71,ab(134,84,85,"gedreht"),D); A(85,87); M(67,69,71,-85.00000000000058); M(64,67,69,185); L(66,67,64); L(136,67,66); Q(135,69,67,D,ab(136,67,64,66,"gedreht")); Q(68,70,69,D,ab(135,69,64,66,67,"gedreht")); M(56,54,52,94.99999999999955); L(57,54,56); L(58,57,56); L(137,57,58); M(62,64,66,-84.99999999999945); M(138,62,64,185); L(61,62,138); L(139,62,61); Q(63,64,62,D,ab(139,62,138,61,"gedreht")); Q(59,54,64,ab(137,54,56,57,58,"gedreht"),ab(138,64,61,62,63,"gedreht")); N(55,56,53); A(55,87); N(60,58,55); A(60,61); N(65,63,60); A(65,66); A(65,85);
%R(42,80); // oder R(42,81);
%R(75,83);
%R(86,87); // oder R(86,88);
%R(85,87);
%R(55,87);
%R(60,61);
%R(65,66);
%R(65,85);
%</Rechenweg>
%
%<Knopf id="Stopp_alleWinkel" color="LightGrey"/>
%
%<Knopf id="Start_blauerWinkel" color="blue"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#blauerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_blauerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_gruenerWinkel" color="green"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#gruenerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_gruenerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_orangerWinkel" color="orange"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#orangerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_orangerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LimeGreen}{rgb}{0.20,0.80,0.20}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/2.73/0.00,
2/3.73/0.00,
3/3.23/0.87,
4/4.23/0.87,
5/4.73/0.00,
6/2.73/1.00,
7/3.23/1.87,
8/4.23/1.87,
9/1.87/0.50,
10/1.87/1.50,
11/1.00/1.00,
12/2.37/2.37,
13/1.50/1.87,
14/0.50/1.87,
15/1.00/2.73,
16/0.00/2.73,
17/1.87/3.23,
18/0.87/3.23,
19/0.00/3.73,
20/0.87/4.23,
21/0.00/4.73,
22/1.87/4.23,
23/1.00/4.73,
24/0.50/5.60,
25/1.50/5.60,
26/1.00/6.46,
27/2.37/5.10,
28/1.87/5.96,
29/1.87/6.96,
30/2.73/6.46,
31/2.73/7.46,
32/3.23/5.60,
33/3.23/6.60,
34/3.73/7.46,
35/4.10/6.10,
36/4.73/1.00,
37/5.23/1.87,
38/5.60/0.50,
39/4.60/6.96,
40/6.10/1.37,
41/4.60/7.96,
42/5.10/6.10,
43/6.10/2.37,
44/6.60/0.50,
45/5.10/7.10,
46/6.60/1.50,
47/5.60/7.96,
48/6.10/7.10,
49/6.60/7.96,
50/6.10/6.10,
51/6.60/6.96,
52/7.46/7.46,
53/7.46/6.46,
54/8.33/6.96,
55/6.96/5.60,
56/7.83/6.10,
57/8.83/6.10,
58/8.33/5.23,
59/9.33/5.23,
60/7.46/4.73,
61/8.46/4.73,
62/9.33/4.23,
63/8.46/3.73,
64/9.33/3.23,
65/7.46/3.73,
66/8.33/3.23,
67/8.83/2.37,
68/7.83/2.37,
69/8.33/1.50,
70/6.96/2.87,
71/7.46/2.00,
72/7.46/1.00,
73/3.73/2.73,
74/5.10/2.37,
75/4.23/2.87,
76/3.73/3.73,
77/2.87/3.23,
78/2.87/4.23,
79/3.73/4.73,
80/4.23/5.60,
81/5.10/5.10,
82/4.60/4.23,
83/5.10/3.37,
84/5.96/2.87,
85/6.46/3.73,
86/5.60/4.23,
87/6.46/4.73,
88/5.60/5.23}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
1/0.00/90.00/0.4/Blue,
10/330.00/420.00/0.4/Green,
25/240.00/330.00/0.4/Orange}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
1/2,
3/1, 3/2,
4/3, 4/2,
5/4, 5/2,
6/1,
7/6, 7/3,
8/7, 8/4,
9/1, 9/6,
10/9, 10/6,
11/9, 11/10,
12/10,
13/11, 13/12,
14/11, 14/13,
15/14, 15/13,
16/14, 16/15,
17/15, 17/12,
18/16, 18/17,
19/16, 19/18,
20/19, 20/18,
21/19, 21/20,
22/20, 22/17,
23/21, 23/22,
24/21, 24/23,
25/24, 25/23,
26/24, 26/25,
27/25,
28/26, 28/27,
29/26, 29/28,
30/29, 30/28,
31/29, 31/30,
32/30, 32/27,
33/31, 33/32,
34/31, 34/33,
35/33, 35/32,
36/8, 36/5,
37/8, 37/36,
38/36, 38/5,
39/34, 39/35,
40/37, 40/38,
41/34, 41/39,
42/39, 42/35,
43/37, 43/40,
44/40, 44/38,
45/41, 45/42,
46/43, 46/44,
47/41, 47/45,
48/47, 48/45,
49/47, 49/48,
50/48, 50/42,
51/49, 51/50,
52/49, 52/51,
53/52, 53/51,
54/52, 54/53,
55/56, 55/53, 55/87,
56/54,
57/54, 57/56,
58/57, 58/56,
59/57, 59/58, 59/62,
60/58, 60/55, 60/61,
61/62, 61/59,
62/64,
63/64, 63/61, 63/62,
64/67,
65/63, 65/60, 65/66, 65/85,
66/67, 66/64,
67/69,
68/70, 68/66, 68/67, 68/69,
69/71,
70/84, 70/71,
71/46,
72/69, 72/71, 72/46, 72/44,
73/7, 73/8,
74/8, 74/43,
75/8, 75/74, 75/83,
76/73, 76/75,
77/73, 77/76,
78/27, 78/77,
79/78, 79/76,
80/32, 80/79, 80/42,
81/42, 81/80,
82/81, 82/79,
83/82,
84/83, 84/74,
85/84, 85/70, 85/87,
86/81, 86/83, 86/82,
87/86,
88/50, 88/42, 88/86, 88/87}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,88}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[LimeGreen,very thick] (p-42) -- (p-80);
\draw[LimeGreen,very thick] (p-75) -- (p-83);
\draw[LimeGreen,very thick] (p-86) -- (p-87);
\draw[LimeGreen,very thick] (p-85) -- (p-87);
\draw[LimeGreen,very thick] (p-55) -- (p-87);
\draw[LimeGreen,very thick] (p-60) -- (p-61);
\draw[LimeGreen,very thick] (p-65) -- (p-66);
\draw[LimeGreen,very thick] (p-65) -- (p-85);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
1/0.00/90.00/0.4/Blue,
10/330.00/420.00/0.4/Green,
25/240.00/330.00/0.4/Orange}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/210,
2/330,
3/150,
4/30,
5/330,
6/60,
7/210,
8/330,
9/180,
10/60,
11/180,
12/348,
13/330,
14/270,
15/30,
16/150,
17/318,
18/360,
19/240,
20/360,
21/120,
22/48,
23/330,
24/150,
25/330,
26/90,
27/167,
28/300,
29/60,
30/360,
31/60,
32/240,
33/270,
34/30,
35/360,
36/270,
37/180,
38/360,
39/90,
40/90,
41/150,
42/60,
43/60,
44/330,
45/210,
46/120,
47/30,
48/330,
49/30,
50/30,
51/180,
52/360,
53/300,
54/90,
55/93,
56/150,
57/90,
58/270,
59/330,
60/137,
61/180,
62/360,
63/240,
64/300,
65/318,
66/90,
67/270,
68/150,
69/360,
70/330,
71/120,
72/360,
73/300,
74/360,
75/120,
76/60,
77/180,
78/257,
79/123,
80/180,
81/90,
82/210,
83/270,
84/210,
85/90,
86/240,
87/360,
88/120}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/cc12b05e49e781f159b9383d05aecd95.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78);</Bildtext>
%<Ausrichten von=\"1\" nach=\"2\"/>
%<Winkel size=\"18\" color=\"blue\" id=\"blauerWinkel\" value=\"90\"/>
%<Winkel size=\"18\" color=\"green\" id=\"gruenerWinkel\" value=\"90\"/>
%<Winkel size=\"18\" color=\"orange\" id=\"orangerWinkel\" value=\"89.99999999999994\"/>
%<Feinjustieren Anzahl=\"3\"/>
%<Rechenweg>
%P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(1,2); L(3,1,2); L(4,3,2); L(5,4,2); M(6,1,2,blauerWinkel); L(9,1,6); L(10,9,6); L(11,9,10); N(7,6,3); M(109,7,3,95.00000000000001); L(73,7,109); Q(8,7,4,ab(109,7,73,\"gedreht\"),D); M(110,8,4,35.000000000000014); L(37,8,110); M(111,5,2,-85.00000000000001); L(38,111,5); Q(36,8,5,ab(110,8,37,\"gedreht\"),ab(111,5,38,\"gedreht\")); M(112,37,8,154.99999999999997); L(43,37,112); M(113,38,5,-144.99999999999994); L(44,113,38); Q(40,37,38,ab(112,37,43,\"gedreht\"),ab(113,38,44,\"gedreht\")); M(114,44,38,-85.00000000000017); M(71,114,44,125.00000000000043); M(69,71,114,125.00000000000016); L(116,69,71); Q(115,71,114,ab(116,71,69,\"gedreht\"),D); Q(72,114,44,ab(115,114,69,71,\"gedreht\"),D); Q(46,43,44,D,ab(114,44,69,71,72,\"gedreht\")); M(117,8,4,125.00000000000001); L(75,8,117); Q(74,8,43,ab(117,8,75,\"gedreht\"),D); M(118,73,7,-144.99999999999994); L(77,73,118); Q(76,73,75,ab(118,73,77,\"gedreht\"),D); M(12,10,6,gruenerWinkel); M(119,11,9,95.00000000000006); L(14,11,119); L(15,14,119); L(16,14,15); Q(13,11,12,ab(119,11,14,15,16,\"gedreht\"),D); N(17,15,12); M(120,16,14,94.99999999999991); L(19,16,120); L(20,19,120); L(21,19,20); Q(18,16,17,ab(120,16,19,20,21,\"gedreht\"),D); N(22,20,17); M(121,21,19,95.00000000000006); L(24,21,121); L(25,24,121); L(26,24,25); Q(23,21,22,ab(121,21,24,25,26,\"gedreht\"),D); M(27,25,23,orangerWinkel); M(122,26,24,95.00000000000001); L(29,26,122); L(30,29,122); L(31,29,30); Q(28,26,27,ab(122,26,29,30,31,\"gedreht\"),D); N(32,30,27); M(123,31,29,95.00000000000009); L(34,31,123); M(124,32,27,-114.99999999999997); L(35,124,32); Q(33,31,32,ab(123,31,34,\"gedreht\"),ab(124,32,35,\"gedreht\")); M(125,34,31,154.99999999999991); L(41,34,125); M(126,35,32,-144.99999999999986); L(42,126,35); Q(39,34,35,ab(125,34,41,\"gedreht\"),ab(126,35,42,\"gedreht\")); M(127,41,34,95.00000000000006); L(47,41,127); L(48,47,127); L(49,47,48); Q(45,41,42,ab(127,41,47,48,49,\"gedreht\"),D); M(128,42,35,-174.99999999999991); L(88,128,42); Q(50,48,42,D,ab(128,42,88,\"gedreht\")); M(129,49,47,95.00000000000014); L(52,49,129); L(53,52,129); L(54,52,53); Q(51,49,50,ab(129,49,52,53,54,\"gedreht\"),D); N(78,27,77); N(79,78,76); N(80,32,79); M(130,42,35,34.999999999999915); L(81,42,130); A(80,42,ab(130,42,81,\"gedreht\")); M(131,81,42,155.0000000000003); M(83,131,81,-115.0000000000004); L(132,131,83); Q(86,81,131,D,ab(132,131,83,\"gedreht\")); Q(82,81,79,ab(131,81,83,86,\"gedreht\"),D); A(75,83); M(87,86,81,-84.99999999999967); L(133,86,87); A(88,86,ab(133,86,87,\"gedreht\")); N(84,83,74); M(134,84,74,155.00000000000026); L(85,84,134); Q(70,84,71,ab(134,84,85,\"gedreht\"),D); A(85,87); M(67,69,71,-85.00000000000058); M(64,67,69,185); L(66,67,64); L(136,67,66); Q(135,69,67,D,ab(136,67,64,66,\"gedreht\")); Q(68,70,69,D,ab(135,69,64,66,67,\"gedreht\")); M(56,54,52,94.99999999999955); L(57,54,56); L(58,57,56); L(137,57,58); M(62,64,66,-84.99999999999945); M(138,62,64,185); L(61,62,138); L(139,62,61); Q(63,64,62,D,ab(139,62,138,61,\"gedreht\")); Q(59,54,64,ab(137,54,56,57,58,\"gedreht\"),ab(138,64,61,62,63,\"gedreht\")); N(55,56,53); A(55,87); N(60,58,55); A(60,61); N(65,63,60); A(65,66); A(65,85);
%R(42,80); // oder R(42,81);
%R(75,83);
%R(86,87); // oder R(86,88);
%R(85,87);
%R(55,87);
%R(60,61);
%R(65,66);
%R(65,85);
%</Rechenweg>
%
%<Knopf id=\"Stopp_alleWinkel\" color=\"LightGrey\"/>
%
%<Knopf id=\"Start_blauerWinkel\" color=\"blue\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#blauerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_blauerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_gruenerWinkel\" color=\"green\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#gruenerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_gruenerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_orangerWinkel\" color=\"orange\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#orangerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_orangerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LimeGreen}{rgb}{0.20,0.80,0.20}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/2.73/0.00,
2/3.73/0.00,
3/3.23/0.87,
4/4.23/0.87,
5/4.73/0.00,
6/2.73/1.00,
7/3.23/1.87,
8/4.23/1.87,
9/1.87/0.50,
10/1.87/1.50,
11/1.00/1.00,
12/2.37/2.37,
13/1.50/1.87,
14/0.50/1.87,
15/1.00/2.73,
16/0.00/2.73,
17/1.87/3.23,
18/0.87/3.23,
19/0.00/3.73,
20/0.87/4.23,
21/0.00/4.73,
22/1.87/4.23,
23/1.00/4.73,
24/0.50/5.60,
25/1.50/5.60,
26/1.00/6.46,
27/2.37/5.10,
28/1.87/5.96,
29/1.87/6.96,
30/2.73/6.46,
31/2.73/7.46,
32/3.23/5.60,
33/3.23/6.60,
34/3.73/7.46,
35/4.10/6.10,
36/4.73/1.00,
37/5.23/1.87,
38/5.60/0.50,
39/4.60/6.96,
40/6.10/1.37,
41/4.60/7.96,
42/5.10/6.10,
43/6.10/2.37,
44/6.60/0.50,
45/5.10/7.10,
46/6.60/1.50,
47/5.60/7.96,
48/6.10/7.10,
49/6.60/7.96,
50/6.10/6.10,
51/6.60/6.96,
52/7.46/7.46,
53/7.46/6.46,
54/8.33/6.96,
55/6.96/5.60,
56/7.83/6.10,
57/8.83/6.10,
58/8.33/5.23,
59/9.33/5.23,
60/7.46/4.73,
61/8.46/4.73,
62/9.33/4.23,
63/8.46/3.73,
64/9.33/3.23,
65/7.46/3.73,
66/8.33/3.23,
67/8.83/2.37,
68/7.83/2.37,
69/8.33/1.50,
70/6.96/2.87,
71/7.46/2.00,
72/7.46/1.00,
73/3.73/2.73,
74/5.10/2.37,
75/4.23/2.87,
76/3.73/3.73,
77/2.87/3.23,
78/2.87/4.23,
79/3.73/4.73,
80/4.23/5.60,
81/5.10/5.10,
82/4.60/4.23,
83/5.10/3.37,
84/5.96/2.87,
85/6.46/3.73,
86/5.60/4.23,
87/6.46/4.73,
88/5.60/5.23}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
1/0.00/90.00/0.4/Blue,
10/330.00/420.00/0.4/Green,
25/240.00/330.00/0.4/Orange}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
1/2,
3/1, 3/2,
4/3, 4/2,
5/4, 5/2,
6/1,
7/6, 7/3,
8/7, 8/4,
9/1, 9/6,
10/9, 10/6,
11/9, 11/10,
12/10,
13/11, 13/12,
14/11, 14/13,
15/14, 15/13,
16/14, 16/15,
17/15, 17/12,
18/16, 18/17,
19/16, 19/18,
20/19, 20/18,
21/19, 21/20,
22/20, 22/17,
23/21, 23/22,
24/21, 24/23,
25/24, 25/23,
26/24, 26/25,
27/25,
28/26, 28/27,
29/26, 29/28,
30/29, 30/28,
31/29, 31/30,
32/30, 32/27,
33/31, 33/32,
34/31, 34/33,
35/33, 35/32,
36/8, 36/5,
37/8, 37/36,
38/36, 38/5,
39/34, 39/35,
40/37, 40/38,
41/34, 41/39,
42/39, 42/35,
43/37, 43/40,
44/40, 44/38,
45/41, 45/42,
46/43, 46/44,
47/41, 47/45,
48/47, 48/45,
49/47, 49/48,
50/48, 50/42,
51/49, 51/50,
52/49, 52/51,
53/52, 53/51,
54/52, 54/53,
55/56, 55/53, 55/87,
56/54,
57/54, 57/56,
58/57, 58/56,
59/57, 59/58, 59/62,
60/58, 60/55, 60/61,
61/62, 61/59,
62/64,
63/64, 63/61, 63/62,
64/67,
65/63, 65/60, 65/66, 65/85,
66/67, 66/64,
67/69,
68/70, 68/66, 68/67, 68/69,
69/71,
70/84, 70/71,
71/46,
72/69, 72/71, 72/46, 72/44,
73/7, 73/8,
74/8, 74/43,
75/8, 75/74, 75/83,
76/73, 76/75,
77/73, 77/76,
78/27, 78/77,
79/78, 79/76,
80/32, 80/79, 80/42,
81/42, 81/80,
82/81, 82/79,
83/82,
84/83, 84/74,
85/84, 85/70, 85/87,
86/81, 86/83, 86/82,
87/86,
88/50, 88/42, 88/86, 88/87}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,88}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[LimeGreen,very thick] (p-42) -- (p-80);
\draw[LimeGreen,very thick] (p-75) -- (p-83);
\draw[LimeGreen,very thick] (p-86) -- (p-87);
\draw[LimeGreen,very thick] (p-85) -- (p-87);
\draw[LimeGreen,very thick] (p-55) -- (p-87);
\draw[LimeGreen,very thick] (p-60) -- (p-61);
\draw[LimeGreen,very thick] (p-65) -- (p-66);
\draw[LimeGreen,very thick] (p-65) -- (p-85);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
1/0.00/90.00/0.4/Blue,
10/330.00/420.00/0.4/Green,
25/240.00/330.00/0.4/Orange}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/210,
2/330,
3/150,
4/30,
5/330,
6/60,
7/210,
8/330,
9/180,
10/60,
11/180,
12/348,
13/330,
14/270,
15/30,
16/150,
17/318,
18/360,
19/240,
20/360,
21/120,
22/48,
23/330,
24/150,
25/330,
26/90,
27/167,
28/300,
29/60,
30/360,
31/60,
32/240,
33/270,
34/30,
35/360,
36/270,
37/180,
38/360,
39/90,
40/90,
41/150,
42/60,
43/60,
44/330,
45/210,
46/120,
47/30,
48/330,
49/30,
50/30,
51/180,
52/360,
53/300,
54/90,
55/93,
56/150,
57/90,
58/270,
59/330,
60/137,
61/180,
62/360,
63/240,
64/300,
65/318,
66/90,
67/270,
68/150,
69/360,
70/330,
71/120,
72/360,
73/300,
74/360,
75/120,
76/60,
77/180,
78/257,
79/123,
80/180,
81/90,
82/210,
83/270,
84/210,
85/90,
86/240,
87/360,
88/120}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
Er enthält 3 bewegliche Winkel und 8 einzustellende Kanten, noch kein Zeichen für Beweglichkeit (es müssten weniger einzustellende Kanten als Winkel sein). Auch der Versuch, die Winkel zu verändern, ist erfolglos (Graph mit Kursor wie Text markieren, ins Streichholzprogramm großes Eingabefenster kopieren, Button "neu zeichnen", dann mit Button "-0.01" den blauen Winkel ändern oder auch andere Winkel anklicken und ändern, dann entstehen nicht passende Kanten). Wenn ich aber den blauen Winkel um -0.01° verändere und dann den Graph mit Button Feinjustieren(3) wieder zurechtziehe, so wird nicht mehr der Ausgangswert 90° erreicht:
blauerWinkel = 89.99483124096407
gruenerWinkel = 90.00516875903601
orangerWinkel = 89.99483124096504
ein Zeichen für Beweglichkeit des Graphen. Das Ergebnis lässt auch vermuten, das gruenerWinkel=180°-blauerWinkel und orangerWinkel=blauerWinkel ist. Das übernehme ich in die Eingabe und wenn man jetzt den blauen Winkel verändert (Animationsknopf "Start_blauerWinkel" links vom Graph im Streichholzprogramm), so bleiben diesmal alle Kantenlängen erhalten, der Graph ist beweglich.
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78);</Bildtext>
%<Ausrichten von="1" nach="2"/>
%<Winkel size="18" color="blue" id="blauerWinkel" value="90"/>
%<Winkel size="18" color="green" id="gruenerWinkel" value="90"/>
%<Winkel size="18" color="orange" id="orangerWinkel" value="89.99999999999994"/>
%<Feinjustieren Anzahl="3"/>
%<Rechenweg>
%P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(1,2); L(3,1,2); L(4,3,2); L(5,4,2); M(6,1,2,blauerWinkel); L(9,1,6); L(10,9,6); L(11,9,10); N(7,6,3); M(109,7,3,95.00000000000001); L(73,7,109); Q(8,7,4,ab(109,7,73,"gedreht"),D); M(110,8,4,35.000000000000014); L(37,8,110); M(111,5,2,-85.00000000000001); L(38,111,5); Q(36,8,5,ab(110,8,37,"gedreht"),ab(111,5,38,"gedreht")); M(112,37,8,154.99999999999997); L(43,37,112); M(113,38,5,-144.99999999999994); L(44,113,38); Q(40,37,38,ab(112,37,43,"gedreht"),ab(113,38,44,"gedreht")); M(114,44,38,-85.00000000000017); M(71,114,44,125.00000000000043); M(69,71,114,125.00000000000016); L(116,69,71); Q(115,71,114,ab(116,71,69,"gedreht"),D); Q(72,114,44,ab(115,114,69,71,"gedreht"),D); Q(46,43,44,D,ab(114,44,69,71,72,"gedreht")); M(117,8,4,125.00000000000001); L(75,8,117); Q(74,8,43,ab(117,8,75,"gedreht"),D); M(118,73,7,-144.99999999999994); L(77,73,118); Q(76,73,75,ab(118,73,77,"gedreht"),D); M(12,10,6,180-blauerWinkel); M(119,11,9,95.00000000000006); L(14,11,119); L(15,14,119); L(16,14,15); Q(13,11,12,ab(119,11,14,15,16,"gedreht"),D); N(17,15,12); M(120,16,14,94.99999999999991); L(19,16,120); L(20,19,120); L(21,19,20); Q(18,16,17,ab(120,16,19,20,21,"gedreht"),D); N(22,20,17); M(121,21,19,95.00000000000006); L(24,21,121); L(25,24,121); L(26,24,25); Q(23,21,22,ab(121,21,24,25,26,"gedreht"),D); M(27,25,23,blauerWinkel); M(122,26,24,95.00000000000001); L(29,26,122); L(30,29,122); L(31,29,30); Q(28,26,27,ab(122,26,29,30,31,"gedreht"),D); N(32,30,27); M(123,31,29,95.00000000000009); L(34,31,123); M(124,32,27,-114.99999999999997); L(35,124,32); Q(33,31,32,ab(123,31,34,"gedreht"),ab(124,32,35,"gedreht")); M(125,34,31,154.99999999999991); L(41,34,125); M(126,35,32,-144.99999999999986); L(42,126,35); Q(39,34,35,ab(125,34,41,"gedreht"),ab(126,35,42,"gedreht")); M(127,41,34,95.00000000000006); L(47,41,127); L(48,47,127); L(49,47,48); Q(45,41,42,ab(127,41,47,48,49,"gedreht"),D); M(128,42,35,-174.99999999999991); L(88,128,42); Q(50,48,42,D,ab(128,42,88,"gedreht")); M(129,49,47,95.00000000000014); L(52,49,129); L(53,52,129); L(54,52,53); Q(51,49,50,ab(129,49,52,53,54,"gedreht"),D); N(78,27,77); N(79,78,76); N(80,32,79); M(130,42,35,34.999999999999915); L(81,42,130); A(80,42,ab(130,42,81,"gedreht")); M(131,81,42,155.0000000000003); M(83,131,81,-115.0000000000004); L(132,131,83); Q(86,81,131,D,ab(132,131,83,"gedreht")); Q(82,81,79,ab(131,81,83,86,"gedreht"),D); A(75,83); M(87,86,81,-84.99999999999967); L(133,86,87); A(88,86,ab(133,86,87,"gedreht")); N(84,83,74); M(134,84,74,155.00000000000026); L(85,84,134); Q(70,84,71,ab(134,84,85,"gedreht"),D); A(85,87); M(67,69,71,-85.00000000000058); M(64,67,69,185); L(66,67,64); L(136,67,66); Q(135,69,67,D,ab(136,67,64,66,"gedreht")); Q(68,70,69,D,ab(135,69,64,66,67,"gedreht")); M(56,54,52,94.99999999999955); L(57,54,56); L(58,57,56); L(137,57,58); M(62,64,66,-84.99999999999945); M(138,62,64,185); L(61,62,138); L(139,62,61); Q(63,64,62,D,ab(139,62,138,61,"gedreht")); Q(59,54,64,ab(137,54,56,57,58,"gedreht"),ab(138,64,61,62,63,"gedreht")); N(55,56,53); A(55,87); N(60,58,55); A(60,61); N(65,63,60); A(65,66); A(65,85);
%R(42,80); // oder R(42,81);
%R(75,83);
%R(86,87); // oder R(86,88);
%R(85,87);
%R(55,87);
%R(60,61);
%R(65,66);
%R(65,85);
%</Rechenweg>
%
%<Knopf id="Stopp_alleWinkel" color="LightGrey"/>
%
%<Knopf id="Start_blauerWinkel" color="blue"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#blauerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_blauerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_gruenerWinkel" color="green"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#gruenerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_gruenerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_orangerWinkel" color="orange"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#orangerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_orangerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{LimeGreen}{rgb}{0.20,0.80,0.20}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/2.73/0.00,
2/3.73/0.00,
3/3.23/0.87,
4/4.23/0.87,
5/4.73/0.00,
6/2.73/1.00,
7/3.23/1.87,
8/4.23/1.87,
9/1.87/0.50,
10/1.87/1.50,
11/1.00/1.00,
12/2.37/2.37,
13/1.50/1.87,
14/0.50/1.87,
15/1.00/2.73,
16/0.00/2.73,
17/1.87/3.23,
18/0.87/3.23,
19/0.00/3.73,
20/0.87/4.23,
21/0.00/4.73,
22/1.87/4.23,
23/1.00/4.73,
24/0.50/5.60,
25/1.50/5.60,
26/1.00/6.46,
27/2.37/5.10,
28/1.87/5.96,
29/1.87/6.96,
30/2.73/6.46,
31/2.73/7.46,
32/3.23/5.60,
33/3.23/6.60,
34/3.73/7.46,
35/4.10/6.10,
36/4.73/1.00,
37/5.23/1.87,
38/5.60/0.50,
39/4.60/6.96,
40/6.10/1.37,
41/4.60/7.96,
42/5.10/6.10,
43/6.10/2.37,
44/6.60/0.50,
45/5.10/7.10,
46/6.60/1.50,
47/5.60/7.96,
48/6.10/7.10,
49/6.60/7.96,
50/6.10/6.10,
51/6.60/6.96,
52/7.46/7.46,
53/7.46/6.46,
54/8.33/6.96,
55/6.96/5.60,
56/7.83/6.10,
57/8.83/6.10,
58/8.33/5.23,
59/9.33/5.23,
60/7.46/4.73,
61/8.46/4.73,
62/9.33/4.23,
63/8.46/3.73,
64/9.33/3.23,
65/7.46/3.73,
66/8.33/3.23,
67/8.83/2.37,
68/7.83/2.37,
69/8.33/1.50,
70/6.96/2.87,
71/7.46/2.00,
72/7.46/1.00,
73/3.73/2.73,
74/5.10/2.37,
75/4.23/2.87,
76/3.73/3.73,
77/2.87/3.23,
78/2.87/4.23,
79/3.73/4.73,
80/4.23/5.60,
81/5.10/5.10,
82/4.60/4.23,
83/5.10/3.37,
84/5.96/2.87,
85/6.46/3.73,
86/5.60/4.23,
87/6.46/4.73,
88/5.60/5.23}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
1/0.00/90.00/0.4/Blue,
25/240.00/330.00/0.4/Blue}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
1/2,
3/1, 3/2,
4/3, 4/2,
5/4, 5/2,
6/1,
7/6, 7/3,
8/7, 8/4,
9/1, 9/6,
10/9, 10/6,
11/9, 11/10,
12/10,
13/11, 13/12,
14/11, 14/13,
15/14, 15/13,
16/14, 16/15,
17/15, 17/12,
18/16, 18/17,
19/16, 19/18,
20/19, 20/18,
21/19, 21/20,
22/20, 22/17,
23/21, 23/22,
24/21, 24/23,
25/24, 25/23,
26/24, 26/25,
27/25,
28/26, 28/27,
29/26, 29/28,
30/29, 30/28,
31/29, 31/30,
32/30, 32/27,
33/31, 33/32,
34/31, 34/33,
35/33, 35/32,
36/8, 36/5,
37/8, 37/36,
38/36, 38/5,
39/34, 39/35,
40/37, 40/38,
41/34, 41/39,
42/39, 42/35,
43/37, 43/40,
44/40, 44/38,
45/41, 45/42,
46/43, 46/44,
47/41, 47/45,
48/47, 48/45,
49/47, 49/48,
50/48, 50/42,
51/49, 51/50,
52/49, 52/51,
53/52, 53/51,
54/52, 54/53,
55/56, 55/53, 55/87,
56/54,
57/54, 57/56,
58/57, 58/56,
59/57, 59/58, 59/62,
60/58, 60/55, 60/61,
61/62, 61/59,
62/64,
63/64, 63/61, 63/62,
64/67,
65/63, 65/60, 65/66, 65/85,
66/67, 66/64,
67/69,
68/70, 68/66, 68/67, 68/69,
69/71,
70/84, 70/71,
71/46,
72/69, 72/71, 72/46, 72/44,
73/7, 73/8,
74/8, 74/43,
75/8, 75/74, 75/83,
76/73, 76/75,
77/73, 77/76,
78/27, 78/77,
79/78, 79/76,
80/32, 80/79, 80/42,
81/42, 81/80,
82/81, 82/79,
83/82,
84/83, 84/74,
85/84, 85/70, 85/87,
86/81, 86/83, 86/82,
87/86,
88/50, 88/42, 88/86, 88/87}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,88}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[LimeGreen,very thick] (p-42) -- (p-80);
\draw[LimeGreen,very thick] (p-75) -- (p-83);
\draw[LimeGreen,very thick] (p-86) -- (p-87);
\draw[LimeGreen,very thick] (p-85) -- (p-87);
\draw[LimeGreen,very thick] (p-55) -- (p-87);
\draw[LimeGreen,very thick] (p-60) -- (p-61);
\draw[LimeGreen,very thick] (p-65) -- (p-66);
\draw[LimeGreen,very thick] (p-65) -- (p-85);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
1/0.00/90.00/0.4/Blue,
25/240.00/330.00/0.4/Blue}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/210,
2/330,
3/150,
4/30,
5/330,
6/60,
7/210,
8/330,
9/180,
10/60,
11/180,
12/348,
13/330,
14/270,
15/30,
16/150,
17/318,
18/360,
19/240,
20/360,
21/120,
22/48,
23/330,
24/150,
25/330,
26/180,
27/167,
28/300,
29/60,
30/300,
31/60,
32/240,
33/120,
34/30,
35/210,
36/270,
37/180,
38/360,
39/300,
40/90,
41/150,
42/60,
43/60,
44/330,
45/270,
46/120,
47/150,
48/330,
49/30,
50/30,
51/180,
52/360,
53/240,
54/90,
55/93,
56/210,
57/30,
58/210,
59/60,
60/137,
61/180,
62/60,
63/240,
64/30,
65/318,
66/150,
67/330,
68/150,
69/360,
70/330,
71/120,
72/360,
73/300,
74/360,
75/120,
76/60,
77/180,
78/257,
79/123,
80/180,
81/90,
82/150,
83/270,
84/210,
85/90,
86/240,
87/360,
88/120}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/0f242ffc47404006d9821d1de3b2da85.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78);</Bildtext>
%<Ausrichten von=\"1\" nach=\"2\"/>
%<Winkel size=\"18\" color=\"blue\" id=\"blauerWinkel\" value=\"90\"/>
%<Winkel size=\"18\" color=\"green\" id=\"gruenerWinkel\" value=\"90\"/>
%<Winkel size=\"18\" color=\"orange\" id=\"orangerWinkel\" value=\"89.99999999999994\"/>
%<Feinjustieren Anzahl=\"3\"/>
%<Rechenweg>
%P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(1,2); L(3,1,2); L(4,3,2); L(5,4,2); M(6,1,2,blauerWinkel); L(9,1,6); L(10,9,6); L(11,9,10); N(7,6,3); M(109,7,3,95.00000000000001); L(73,7,109); Q(8,7,4,ab(109,7,73,\"gedreht\"),D); M(110,8,4,35.000000000000014); L(37,8,110); M(111,5,2,-85.00000000000001); L(38,111,5); Q(36,8,5,ab(110,8,37,\"gedreht\"),ab(111,5,38,\"gedreht\")); M(112,37,8,154.99999999999997); L(43,37,112); M(113,38,5,-144.99999999999994); L(44,113,38); Q(40,37,38,ab(112,37,43,\"gedreht\"),ab(113,38,44,\"gedreht\")); M(114,44,38,-85.00000000000017); M(71,114,44,125.00000000000043); M(69,71,114,125.00000000000016); L(116,69,71); Q(115,71,114,ab(116,71,69,\"gedreht\"),D); Q(72,114,44,ab(115,114,69,71,\"gedreht\"),D); Q(46,43,44,D,ab(114,44,69,71,72,\"gedreht\")); M(117,8,4,125.00000000000001); L(75,8,117); Q(74,8,43,ab(117,8,75,\"gedreht\"),D); M(118,73,7,-144.99999999999994); L(77,73,118); Q(76,73,75,ab(118,73,77,\"gedreht\"),D); M(12,10,6,180-blauerWinkel); M(119,11,9,95.00000000000006); L(14,11,119); L(15,14,119); L(16,14,15); Q(13,11,12,ab(119,11,14,15,16,\"gedreht\"),D); N(17,15,12); M(120,16,14,94.99999999999991); L(19,16,120); L(20,19,120); L(21,19,20); Q(18,16,17,ab(120,16,19,20,21,\"gedreht\"),D); N(22,20,17); M(121,21,19,95.00000000000006); L(24,21,121); L(25,24,121); L(26,24,25); Q(23,21,22,ab(121,21,24,25,26,\"gedreht\"),D); M(27,25,23,blauerWinkel); M(122,26,24,95.00000000000001); L(29,26,122); L(30,29,122); L(31,29,30); Q(28,26,27,ab(122,26,29,30,31,\"gedreht\"),D); N(32,30,27); M(123,31,29,95.00000000000009); L(34,31,123); M(124,32,27,-114.99999999999997); L(35,124,32); Q(33,31,32,ab(123,31,34,\"gedreht\"),ab(124,32,35,\"gedreht\")); M(125,34,31,154.99999999999991); L(41,34,125); M(126,35,32,-144.99999999999986); L(42,126,35); Q(39,34,35,ab(125,34,41,\"gedreht\"),ab(126,35,42,\"gedreht\")); M(127,41,34,95.00000000000006); L(47,41,127); L(48,47,127); L(49,47,48); Q(45,41,42,ab(127,41,47,48,49,\"gedreht\"),D); M(128,42,35,-174.99999999999991); L(88,128,42); Q(50,48,42,D,ab(128,42,88,\"gedreht\")); M(129,49,47,95.00000000000014); L(52,49,129); L(53,52,129); L(54,52,53); Q(51,49,50,ab(129,49,52,53,54,\"gedreht\"),D); N(78,27,77); N(79,78,76); N(80,32,79); M(130,42,35,34.999999999999915); L(81,42,130); A(80,42,ab(130,42,81,\"gedreht\")); M(131,81,42,155.0000000000003); M(83,131,81,-115.0000000000004); L(132,131,83); Q(86,81,131,D,ab(132,131,83,\"gedreht\")); Q(82,81,79,ab(131,81,83,86,\"gedreht\"),D); A(75,83); M(87,86,81,-84.99999999999967); L(133,86,87); A(88,86,ab(133,86,87,\"gedreht\")); N(84,83,74); M(134,84,74,155.00000000000026); L(85,84,134); Q(70,84,71,ab(134,84,85,\"gedreht\"),D); A(85,87); M(67,69,71,-85.00000000000058); M(64,67,69,185); L(66,67,64); L(136,67,66); Q(135,69,67,D,ab(136,67,64,66,\"gedreht\")); Q(68,70,69,D,ab(135,69,64,66,67,\"gedreht\")); M(56,54,52,94.99999999999955); L(57,54,56); L(58,57,56); L(137,57,58); M(62,64,66,-84.99999999999945); M(138,62,64,185); L(61,62,138); L(139,62,61); Q(63,64,62,D,ab(139,62,138,61,\"gedreht\")); Q(59,54,64,ab(137,54,56,57,58,\"gedreht\"),ab(138,64,61,62,63,\"gedreht\")); N(55,56,53); A(55,87); N(60,58,55); A(60,61); N(65,63,60); A(65,66); A(65,85);
%R(42,80); // oder R(42,81);
%R(75,83);
%R(86,87); // oder R(86,88);
%R(85,87);
%R(55,87);
%R(60,61);
%R(65,66);
%R(65,85);
%</Rechenweg>
%
%<Knopf id=\"Stopp_alleWinkel\" color=\"LightGrey\"/>
%
%<Knopf id=\"Start_blauerWinkel\" color=\"blue\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#blauerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_blauerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_gruenerWinkel\" color=\"green\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#gruenerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_gruenerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_orangerWinkel\" color=\"orange\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#orangerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_orangerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{LimeGreen}{rgb}{0.20,0.80,0.20}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/2.73/0.00,
2/3.73/0.00,
3/3.23/0.87,
4/4.23/0.87,
5/4.73/0.00,
6/2.73/1.00,
7/3.23/1.87,
8/4.23/1.87,
9/1.87/0.50,
10/1.87/1.50,
11/1.00/1.00,
12/2.37/2.37,
13/1.50/1.87,
14/0.50/1.87,
15/1.00/2.73,
16/0.00/2.73,
17/1.87/3.23,
18/0.87/3.23,
19/0.00/3.73,
20/0.87/4.23,
21/0.00/4.73,
22/1.87/4.23,
23/1.00/4.73,
24/0.50/5.60,
25/1.50/5.60,
26/1.00/6.46,
27/2.37/5.10,
28/1.87/5.96,
29/1.87/6.96,
30/2.73/6.46,
31/2.73/7.46,
32/3.23/5.60,
33/3.23/6.60,
34/3.73/7.46,
35/4.10/6.10,
36/4.73/1.00,
37/5.23/1.87,
38/5.60/0.50,
39/4.60/6.96,
40/6.10/1.37,
41/4.60/7.96,
42/5.10/6.10,
43/6.10/2.37,
44/6.60/0.50,
45/5.10/7.10,
46/6.60/1.50,
47/5.60/7.96,
48/6.10/7.10,
49/6.60/7.96,
50/6.10/6.10,
51/6.60/6.96,
52/7.46/7.46,
53/7.46/6.46,
54/8.33/6.96,
55/6.96/5.60,
56/7.83/6.10,
57/8.83/6.10,
58/8.33/5.23,
59/9.33/5.23,
60/7.46/4.73,
61/8.46/4.73,
62/9.33/4.23,
63/8.46/3.73,
64/9.33/3.23,
65/7.46/3.73,
66/8.33/3.23,
67/8.83/2.37,
68/7.83/2.37,
69/8.33/1.50,
70/6.96/2.87,
71/7.46/2.00,
72/7.46/1.00,
73/3.73/2.73,
74/5.10/2.37,
75/4.23/2.87,
76/3.73/3.73,
77/2.87/3.23,
78/2.87/4.23,
79/3.73/4.73,
80/4.23/5.60,
81/5.10/5.10,
82/4.60/4.23,
83/5.10/3.37,
84/5.96/2.87,
85/6.46/3.73,
86/5.60/4.23,
87/6.46/4.73,
88/5.60/5.23}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
1/0.00/90.00/0.4/Blue,
25/240.00/330.00/0.4/Blue}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
1/2,
3/1, 3/2,
4/3, 4/2,
5/4, 5/2,
6/1,
7/6, 7/3,
8/7, 8/4,
9/1, 9/6,
10/9, 10/6,
11/9, 11/10,
12/10,
13/11, 13/12,
14/11, 14/13,
15/14, 15/13,
16/14, 16/15,
17/15, 17/12,
18/16, 18/17,
19/16, 19/18,
20/19, 20/18,
21/19, 21/20,
22/20, 22/17,
23/21, 23/22,
24/21, 24/23,
25/24, 25/23,
26/24, 26/25,
27/25,
28/26, 28/27,
29/26, 29/28,
30/29, 30/28,
31/29, 31/30,
32/30, 32/27,
33/31, 33/32,
34/31, 34/33,
35/33, 35/32,
36/8, 36/5,
37/8, 37/36,
38/36, 38/5,
39/34, 39/35,
40/37, 40/38,
41/34, 41/39,
42/39, 42/35,
43/37, 43/40,
44/40, 44/38,
45/41, 45/42,
46/43, 46/44,
47/41, 47/45,
48/47, 48/45,
49/47, 49/48,
50/48, 50/42,
51/49, 51/50,
52/49, 52/51,
53/52, 53/51,
54/52, 54/53,
55/56, 55/53, 55/87,
56/54,
57/54, 57/56,
58/57, 58/56,
59/57, 59/58, 59/62,
60/58, 60/55, 60/61,
61/62, 61/59,
62/64,
63/64, 63/61, 63/62,
64/67,
65/63, 65/60, 65/66, 65/85,
66/67, 66/64,
67/69,
68/70, 68/66, 68/67, 68/69,
69/71,
70/84, 70/71,
71/46,
72/69, 72/71, 72/46, 72/44,
73/7, 73/8,
74/8, 74/43,
75/8, 75/74, 75/83,
76/73, 76/75,
77/73, 77/76,
78/27, 78/77,
79/78, 79/76,
80/32, 80/79, 80/42,
81/42, 81/80,
82/81, 82/79,
83/82,
84/83, 84/74,
85/84, 85/70, 85/87,
86/81, 86/83, 86/82,
87/86,
88/50, 88/42, 88/86, 88/87}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,88}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[LimeGreen,very thick] (p-42) -- (p-80);
\draw[LimeGreen,very thick] (p-75) -- (p-83);
\draw[LimeGreen,very thick] (p-86) -- (p-87);
\draw[LimeGreen,very thick] (p-85) -- (p-87);
\draw[LimeGreen,very thick] (p-55) -- (p-87);
\draw[LimeGreen,very thick] (p-60) -- (p-61);
\draw[LimeGreen,very thick] (p-65) -- (p-66);
\draw[LimeGreen,very thick] (p-65) -- (p-85);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
1/0.00/90.00/0.4/Blue,
25/240.00/330.00/0.4/Blue}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/210,
2/330,
3/150,
4/30,
5/330,
6/60,
7/210,
8/330,
9/180,
10/60,
11/180,
12/348,
13/330,
14/270,
15/30,
16/150,
17/318,
18/360,
19/240,
20/360,
21/120,
22/48,
23/330,
24/150,
25/330,
26/180,
27/167,
28/300,
29/60,
30/300,
31/60,
32/240,
33/120,
34/30,
35/210,
36/270,
37/180,
38/360,
39/300,
40/90,
41/150,
42/60,
43/60,
44/330,
45/270,
46/120,
47/150,
48/330,
49/30,
50/30,
51/180,
52/360,
53/240,
54/90,
55/93,
56/210,
57/30,
58/210,
59/60,
60/137,
61/180,
62/60,
63/240,
64/30,
65/318,
66/150,
67/330,
68/150,
69/360,
70/330,
71/120,
72/360,
73/300,
74/360,
75/120,
76/60,
77/180,
78/257,
79/123,
80/180,
81/90,
82/150,
83/270,
84/210,
85/90,
86/240,
87/360,
88/120}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
|
Profil
Quote
Link |
haribo
Senior
Dabei seit: 25.10.2012
Mitteilungen: 2298
| Beitrag No.1893, eingetragen 2020-01-20
|
2020-01-18 15:41 - Slash in Beitrag No. 1890 schreibt:
P11,P21 ist jetzt auch wie bei haribo 1.07046626931915200842.
ok, also soweit herzlichen dank für die aufwendigste untersucheng in der geschichte der 4/6er
der graph aus #1881 ist also starr, dann kann man ja mal anfangen wieder kreativ zu werden... wenn man 9-19 herausnimmt wie beweglich verhält sich dann die strecke 15-11?, just playing around without target
und ich würde immer gerne einen verstellwinkel bei 1-7-11 haben anstelle von 3-1-7... weil es ein winkel ist der in beide richtungen gedrückt werden kann
auch die frage ob man eigentlich alle vier symetrisch zu 9-19 liegenden herausnehmen muss oder nur ein oder zwei für beweglichkeit schon reichen würden... sicherlich unter verlust der symetrien aber die sich ja immer nur der gedankeneinfachheit geschuldet weil niemand bisher den "360°" winkel denken kann, also den komplett unsymetrischen graphen
[Die Antwort wurde nach Beitrag No.1891 begonnen.]
|
Profil
Quote
Link |
StefanVogel
Senior
Dabei seit: 26.11.2005
Mitteilungen: 3446
Aus: Raun
| Beitrag No.1894, eingetragen 2020-01-25 07:52
|
Die Punktnummern beziehe ich auf zuletzt #1887. Der richtige Ansatz ist vier Kanten entfernen, dann ist der Graph nach der Knotenabweichungsgleichung garantiert beweglich.
74 Knoten, 16×Grad 3, 54×Grad 4, 4×Grad 6, 0 Überschneidungen
144 Kanten, minimal 0.99999999999999544809, maximal 1.00000000000000266454
einzustellende Kanten, Abstände und Winkel:
|P21-P14|=1.00000000000000066613
∠(P18-P20,P5-P13)=90.00000000000001421085°
∠(P18-P14,P5-P13)=90.00000000000001421085°
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1894-1</Bildtext>
%<Ausrichten von="18" nach="20"/>
%<Winkel size="18" color="blue" id="blauerWinkel" value="28.955024371859853"/>
%<Winkel size="18" color="green" id="gruenerWinkel" value="59.999999999999986"/>
%<Winkel size="18" color="orange" id="orangerWinkel" value="15.522487814070073"/>
%<Winkel size="18" color="violet" id="vierterWinkel" value="164.47751218592992472622"/>
%<Feinjustieren Anzahl="3"/>
%<Rechenweg>
%P[1]=[-18.114795237025238,-11.925524469987494]; P[2]=[31.54207889274424,-17.773160886543337]; D=ab(1,2); A(2,1,Bew(1)); L(3,1,2); L(4,3,2); L(5,4,2); L(6,3,4); M(7,1,3,blauerWinkel,2); N(11,7,6); L(12,11,6); M(13,12,6,gruenerWinkel); L(14,12,13); M(15,10,9,orangerWinkel,2); M(19,15,10,vierterWinkel); N(20,17,19); L(21,20,19); RA(21,14);
%
%RK([5,13],[18,20,14],360/4,true);
%</Rechenweg>
%
%<Knopf id="Stopp_alleWinkel" color="grey"/>
%
%<Knopf id="Start_blauerWinkel" color="blue"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#blauerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_blauerWinkel.click+0s" end="Stopp_alleWinkel.click+0s"/>
%
%<Knopf id="Start_gruenerWinkel" color="green"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#gruenerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_gruenerWinkel.click+0s" end="Stopp_alleWinkel.click+0s"/>
%
%<Knopf id="Start_orangerWinkel" color="orange"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#orangerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_orangerWinkel.click+0s" end="Stopp_alleWinkel.click+0s"/>
%
%<Knopf id="Start_vierterWinkel" color="violet"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#vierterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_vierterWinkel.click+0s" end="Stopp_alleWinkel.click+0s"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LimeGreen}{rgb}{0.20,0.80,0.20}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
\definecolor{Violet}{rgb}{0.93,0.51,0.93}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.85/0.23,
2/2.84/0.12,
3/2.45/1.04,
4/3.44/0.92,
5/3.84/0.00,
6/3.05/1.84,
7/1.99/1.22,
8/1.06/0.85,
9/1.20/1.84,
10/0.27/1.46,
11/2.12/2.22,
12/2.91/2.83,
13/3.84/2.45,
14/3.70/3.44,
15/1.06/2.07,
16/0.14/2.45,
17/0.93/3.06,
18/0.00/3.44,
19/1.99/2.45,
20/1.85/3.44,
21/2.78/3.06,
22/1.85/6.65,
23/2.84/6.76,
24/2.45/5.85,
25/3.44/5.96,
26/3.84/6.88,
27/3.05/5.04,
28/1.99/5.66,
29/1.06/6.03,
30/1.20/5.04,
31/0.27/5.42,
32/2.12/4.67,
33/2.91/4.05,
34/3.84/4.43,
35/1.06/4.81,
36/0.14/4.43,
37/0.93/3.82,
38/1.99/4.43,
39/2.78/3.82,
40/5.82/6.65,
41/4.83/6.76,
42/5.23/5.85,
43/4.23/5.96,
44/4.63/5.04,
45/5.69/5.66,
46/6.61/6.03,
47/6.48/5.04,
48/7.40/5.42,
49/5.55/4.67,
50/4.76/4.05,
51/3.97/3.44,
52/6.61/4.81,
53/7.54/4.43,
54/6.75/3.82,
55/7.68/3.44,
56/5.69/4.43,
57/5.82/3.44,
58/4.90/3.82,
59/5.82/0.23,
60/4.83/0.12,
61/5.23/1.04,
62/4.23/0.92,
63/4.63/1.84,
64/5.69/1.22,
65/6.61/0.85,
66/6.48/1.84,
67/7.40/1.46,
68/5.55/2.22,
69/4.76/2.83,
70/6.61/2.07,
71/7.54/2.45,
72/6.75/3.06,
73/5.69/2.45,
74/4.90/3.06}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
1/53.28/82.24/0.4/Blue,
12/277.76/337.76/0.4/Green,
10/22.24/37.76/0.4/Orange,
15/217.76/382.24/0.4/Violet}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
2/1,
3/1, 3/2,
4/3, 4/2,
5/4, 5/2, 5/62, 5/60,
6/3, 6/4,
7/1,
8/1, 8/7,
9/8, 9/7,
10/8, 10/9,
11/7, 11/6,
12/11, 12/6,
13/12, 13/69, 13/51,
14/12, 14/13, 14/33, 14/34, 14/39,
15/10,
16/10, 16/15,
17/16, 17/15,
18/16, 18/17, 18/36, 18/37,
19/15,
20/17, 20/19, 20/37, 20/38,
21/20, 21/19, 21/14,
23/22,
24/22, 24/23,
25/23, 25/24,
26/23, 26/25, 26/41, 26/43,
27/24, 27/25,
28/22,
29/22, 29/28,
30/28, 30/29,
31/29, 31/30,
32/27, 32/28,
33/27, 33/32,
34/33, 34/50,
35/31,
36/31, 36/35,
37/35, 37/36,
38/35,
39/38, 39/20,
41/40,
42/40, 42/41,
43/41, 43/42,
44/42, 44/43,
45/40,
46/40, 46/45,
47/45, 47/46,
48/46, 48/47,
49/44, 49/45,
50/44, 50/49,
51/50, 51/34, 51/69, 51/74,
52/48,
53/48, 53/52,
54/52, 54/53,
55/53, 55/54, 55/71, 55/72,
56/52,
57/54, 57/56, 57/72, 57/73,
58/51, 58/56, 58/57,
60/59,
61/59, 61/60,
62/60, 62/61,
63/61, 63/62,
64/59,
65/59, 65/64,
66/64, 66/65,
67/65, 67/66,
68/63, 68/64,
69/63, 69/68,
70/67,
71/67, 71/70,
72/70, 72/71,
73/70,
74/73, 74/57}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,74}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[LimeGreen,very thick] (p-21) -- (p-14);
%\draw[Violet,very thick] (p-5) -- (p-13);
%\draw[Violet,very thick] (p-5) -- (p-13);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
1/53.28/82.24/0.4/Blue,
12/277.76/337.76/0.4/Green,
10/22.24/37.76/0.4/Orange,
15/217.76/382.24/0.4/Violet}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/292,
2/323,
3/143,
4/23,
5/217,
6/308,
7/52,
8/172,
9/52,
10/172,
11/188,
12/68,
13/308,
14/292,
15/308,
16/128,
17/68,
18/232,
19/248,
20/128,
21/8,
22/68,
23/97,
24/157,
25/277,
26/37,
27/277,
28/8,
29/68,
30/248,
31/188,
32/172,
33/292,
34/52,
35/52,
36/232,
37/292,
38/112,
39/352,
40/112,
41/143,
42/323,
43/143,
44/128,
45/172,
46/112,
47/292,
48/352,
49/8,
50/8,
51/112,
52/188,
53/308,
54/188,
55/308,
56/68,
57/308,
58/188,
59/248,
60/337,
61/37,
62/217,
63/97,
64/188,
65/308,
66/68,
67/8,
68/352,
69/112,
70/232,
71/352,
72/172,
73/292,
74/172}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/5c3d8189ed7be79f27ab0338bab3788d.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1894-1</Bildtext>
%<Ausrichten von=\"18\" nach=\"20\"/>
%<Winkel size=\"18\" color=\"blue\" id=\"blauerWinkel\" value=\"28.955024371859853\"/>
%<Winkel size=\"18\" color=\"green\" id=\"gruenerWinkel\" value=\"59.999999999999986\"/>
%<Winkel size=\"18\" color=\"orange\" id=\"orangerWinkel\" value=\"15.522487814070073\"/>
%<Winkel size=\"18\" color=\"violet\" id=\"vierterWinkel\" value=\"164.47751218592992472622\"/>
%<Feinjustieren Anzahl=\"3\"/>
%<Rechenweg>
%P[1]=[-18.114795237025238,-11.925524469987494]; P[2]=[31.54207889274424,-17.773160886543337]; D=ab(1,2); A(2,1,Bew(1)); L(3,1,2); L(4,3,2); L(5,4,2); L(6,3,4); M(7,1,3,blauerWinkel,2); N(11,7,6); L(12,11,6); M(13,12,6,gruenerWinkel); L(14,12,13); M(15,10,9,orangerWinkel,2); M(19,15,10,vierterWinkel); N(20,17,19); L(21,20,19); RA(21,14);
%
%RK([5,13],[18,20,14],360/4,true);
%</Rechenweg>
%
%<Knopf id=\"Stopp_alleWinkel\" color=\"grey\"/>
%
%<Knopf id=\"Start_blauerWinkel\" color=\"blue\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#blauerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_blauerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0s\"/>
%
%<Knopf id=\"Start_gruenerWinkel\" color=\"green\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#gruenerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_gruenerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0s\"/>
%
%<Knopf id=\"Start_orangerWinkel\" color=\"orange\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#orangerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_orangerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0s\"/>
%
%<Knopf id=\"Start_vierterWinkel\" color=\"violet\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#vierterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_vierterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0s\"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LimeGreen}{rgb}{0.20,0.80,0.20}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
\definecolor{Violet}{rgb}{0.93,0.51,0.93}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.85/0.23,
2/2.84/0.12,
3/2.45/1.04,
4/3.44/0.92,
5/3.84/0.00,
6/3.05/1.84,
7/1.99/1.22,
8/1.06/0.85,
9/1.20/1.84,
10/0.27/1.46,
11/2.12/2.22,
12/2.91/2.83,
13/3.84/2.45,
14/3.70/3.44,
15/1.06/2.07,
16/0.14/2.45,
17/0.93/3.06,
18/0.00/3.44,
19/1.99/2.45,
20/1.85/3.44,
21/2.78/3.06,
22/1.85/6.65,
23/2.84/6.76,
24/2.45/5.85,
25/3.44/5.96,
26/3.84/6.88,
27/3.05/5.04,
28/1.99/5.66,
29/1.06/6.03,
30/1.20/5.04,
31/0.27/5.42,
32/2.12/4.67,
33/2.91/4.05,
34/3.84/4.43,
35/1.06/4.81,
36/0.14/4.43,
37/0.93/3.82,
38/1.99/4.43,
39/2.78/3.82,
40/5.82/6.65,
41/4.83/6.76,
42/5.23/5.85,
43/4.23/5.96,
44/4.63/5.04,
45/5.69/5.66,
46/6.61/6.03,
47/6.48/5.04,
48/7.40/5.42,
49/5.55/4.67,
50/4.76/4.05,
51/3.97/3.44,
52/6.61/4.81,
53/7.54/4.43,
54/6.75/3.82,
55/7.68/3.44,
56/5.69/4.43,
57/5.82/3.44,
58/4.90/3.82,
59/5.82/0.23,
60/4.83/0.12,
61/5.23/1.04,
62/4.23/0.92,
63/4.63/1.84,
64/5.69/1.22,
65/6.61/0.85,
66/6.48/1.84,
67/7.40/1.46,
68/5.55/2.22,
69/4.76/2.83,
70/6.61/2.07,
71/7.54/2.45,
72/6.75/3.06,
73/5.69/2.45,
74/4.90/3.06}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
1/53.28/82.24/0.4/Blue,
12/277.76/337.76/0.4/Green,
10/22.24/37.76/0.4/Orange,
15/217.76/382.24/0.4/Violet}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
2/1,
3/1, 3/2,
4/3, 4/2,
5/4, 5/2, 5/62, 5/60,
6/3, 6/4,
7/1,
8/1, 8/7,
9/8, 9/7,
10/8, 10/9,
11/7, 11/6,
12/11, 12/6,
13/12, 13/69, 13/51,
14/12, 14/13, 14/33, 14/34, 14/39,
15/10,
16/10, 16/15,
17/16, 17/15,
18/16, 18/17, 18/36, 18/37,
19/15,
20/17, 20/19, 20/37, 20/38,
21/20, 21/19, 21/14,
23/22,
24/22, 24/23,
25/23, 25/24,
26/23, 26/25, 26/41, 26/43,
27/24, 27/25,
28/22,
29/22, 29/28,
30/28, 30/29,
31/29, 31/30,
32/27, 32/28,
33/27, 33/32,
34/33, 34/50,
35/31,
36/31, 36/35,
37/35, 37/36,
38/35,
39/38, 39/20,
41/40,
42/40, 42/41,
43/41, 43/42,
44/42, 44/43,
45/40,
46/40, 46/45,
47/45, 47/46,
48/46, 48/47,
49/44, 49/45,
50/44, 50/49,
51/50, 51/34, 51/69, 51/74,
52/48,
53/48, 53/52,
54/52, 54/53,
55/53, 55/54, 55/71, 55/72,
56/52,
57/54, 57/56, 57/72, 57/73,
58/51, 58/56, 58/57,
60/59,
61/59, 61/60,
62/60, 62/61,
63/61, 63/62,
64/59,
65/59, 65/64,
66/64, 66/65,
67/65, 67/66,
68/63, 68/64,
69/63, 69/68,
70/67,
71/67, 71/70,
72/70, 72/71,
73/70,
74/73, 74/57}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,74}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[LimeGreen,very thick] (p-21) -- (p-14);
%\draw[Violet,very thick] (p-5) -- (p-13);
%\draw[Violet,very thick] (p-5) -- (p-13);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
1/53.28/82.24/0.4/Blue,
12/277.76/337.76/0.4/Green,
10/22.24/37.76/0.4/Orange,
15/217.76/382.24/0.4/Violet}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/292,
2/323,
3/143,
4/23,
5/217,
6/308,
7/52,
8/172,
9/52,
10/172,
11/188,
12/68,
13/308,
14/292,
15/308,
16/128,
17/68,
18/232,
19/248,
20/128,
21/8,
22/68,
23/97,
24/157,
25/277,
26/37,
27/277,
28/8,
29/68,
30/248,
31/188,
32/172,
33/292,
34/52,
35/52,
36/232,
37/292,
38/112,
39/352,
40/112,
41/143,
42/323,
43/143,
44/128,
45/172,
46/112,
47/292,
48/352,
49/8,
50/8,
51/112,
52/188,
53/308,
54/188,
55/308,
56/68,
57/308,
58/188,
59/248,
60/337,
61/37,
62/217,
63/97,
64/188,
65/308,
66/68,
67/8,
68/352,
69/112,
70/232,
71/352,
72/172,
73/292,
74/172}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
Da kann ich den vierten Winkel (violett, in P15) beliebig in 1° Schritten verändern und anschließend die übrigen drei Winkel mit Button "Feinjustieren(3,3)" neu einstellen. In Richtung kleinerer vierter Winkel erhalte ich
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1894-1</Bildtext>
%<Ausrichten von="18" nach="20"/>
%<Winkel size="18" color="blue" id="blauerWinkel" value="18.947361232912655"/>
%<Winkel size="18" color="green" id="gruenerWinkel" value="63.525969991157574"/>
%<Winkel size="18" color="orange" id="orangerWinkel" value="44.19774595541346"/>
%<Winkel size="18" color="violet" id="vierterWinkel" value="127.18"/>
%<Feinjustieren Anzahl="3,3"/>
%<Rechenweg>
%P[1]=[-18.170417966471057,-12.057944075335968]; P[2]=[31.48453077044413,-17.921907405228126]; D=ab(1,2); A(2,1,Bew(1)); L(3,1,2); L(4,3,2); L(5,4,2); L(6,3,4); M(7,1,3,blauerWinkel,2); N(11,7,6); L(12,11,6); M(13,12,6,gruenerWinkel); L(14,12,13); M(15,10,9,orangerWinkel,2); M(19,15,10,vierterWinkel); N(20,17,19); L(21,20,19); RA(21,14);
%
%RK([5,13],[18,20,14],360/4,true);
%</Rechenweg>
%
%<Knopf id="Stopp_alleWinkel" color="grey"/>
%
%<Knopf id="Start_blauerWinkel" color="blue"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#blauerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_blauerWinkel.click+0s" end="Stopp_alleWinkel.click+0s"/>
%
%<Knopf id="Start_gruenerWinkel" color="green"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#gruenerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_gruenerWinkel.click+0s" end="Stopp_alleWinkel.click+0s"/>
%
%<Knopf id="Start_orangerWinkel" color="orange"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#orangerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_orangerWinkel.click+0s" end="Stopp_alleWinkel.click+0s"/>
%
%<Knopf id="Start_vierterWinkel" color="violet"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#vierterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_vierterWinkel.click+0s" end="Stopp_alleWinkel.click+0s"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LimeGreen}{rgb}{0.20,0.80,0.20}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
\definecolor{Violet}{rgb}{0.93,0.51,0.93}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/2.23/0.23,
2/3.23/0.12,
3/2.83/1.04,
4/3.82/0.92,
5/4.22/0.00,
6/3.43/1.84,
7/2.54/1.19,
8/1.56/0.98,
9/1.87/1.93,
10/0.89/1.72,
11/2.49/2.19,
12/3.26/2.82,
13/4.22/2.53,
14/3.99/3.51,
15/1.44/2.55,
16/0.44/2.61,
17/1.00/3.44,
18/0.00/3.51,
19/2.44/2.61,
20/2.00/3.51,
21/2.99/3.44,
22/2.23/6.78,
23/3.23/6.90,
24/2.83/5.98,
25/3.82/6.10,
26/4.22/7.01,
27/3.43/5.18,
28/2.54/5.83,
29/1.56/6.04,
30/1.87/5.09,
31/0.89/5.30,
32/2.49/4.83,
33/3.26/4.19,
34/4.22/4.48,
35/1.44/4.47,
36/0.44/4.40,
37/1.00/3.57,
38/2.44/4.40,
39/2.99/3.57,
40/6.21/6.78,
41/5.21/6.90,
42/5.61/5.98,
43/4.61/6.10,
44/5.01/5.18,
45/5.90/5.83,
46/6.88/6.04,
47/6.57/5.09,
48/7.55/5.30,
49/5.95/4.83,
50/5.18/4.19,
51/4.45/3.51,
52/7.00/4.47,
53/7.99/4.40,
54/7.44/3.57,
55/8.44/3.51,
56/6.00/4.40,
57/6.44/3.51,
58/5.44/3.57,
59/6.21/0.23,
60/5.21/0.12,
61/5.61/1.04,
62/4.61/0.92,
63/5.01/1.84,
64/5.90/1.19,
65/6.88/0.98,
66/6.57/1.93,
67/7.55/1.72,
68/5.95/2.19,
69/5.18/2.82,
70/7.00/2.55,
71/7.99/2.61,
72/7.44/3.44,
73/6.00/2.61,
74/5.44/3.44}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
1/53.26/72.21/0.4/Blue,
12/279.62/343.14/0.4/Green,
10/12.21/56.41/0.4/Orange,
15/236.41/363.59/0.4/Violet}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
2/1,
3/1, 3/2,
4/3, 4/2,
5/4, 5/2, 5/62, 5/60,
6/3, 6/4,
7/1,
8/1, 8/7,
9/8, 9/7,
10/8, 10/9,
11/7, 11/6,
12/11, 12/6,
13/12, 13/69, 13/51,
14/12, 14/13, 14/33, 14/34, 14/39,
15/10,
16/10, 16/15,
17/16, 17/15,
18/16, 18/17, 18/36, 18/37,
19/15,
20/17, 20/19, 20/37, 20/38,
21/20, 21/19, 21/14,
23/22,
24/22, 24/23,
25/23, 25/24,
26/23, 26/25, 26/41, 26/43,
27/24, 27/25,
28/22,
29/22, 29/28,
30/28, 30/29,
31/29, 31/30,
32/27, 32/28,
33/27, 33/32,
34/33, 34/50,
35/31,
36/31, 36/35,
37/35, 37/36,
38/35,
39/38, 39/20,
41/40,
42/40, 42/41,
43/41, 43/42,
44/42, 44/43,
45/40,
46/40, 46/45,
47/45, 47/46,
48/46, 48/47,
49/44, 49/45,
50/44, 50/49,
51/50, 51/34, 51/69, 51/74,
52/48,
53/48, 53/52,
54/52, 54/53,
55/53, 55/54, 55/71, 55/72,
56/52,
57/54, 57/56, 57/72, 57/73,
58/51, 58/56, 58/57,
60/59,
61/59, 61/60,
62/60, 62/61,
63/61, 63/62,
64/59,
65/59, 65/64,
66/64, 66/65,
67/65, 67/66,
68/63, 68/64,
69/63, 69/68,
70/67,
71/67, 71/70,
72/70, 72/71,
73/70,
74/73, 74/57}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,74}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[LimeGreen,very thick] (p-21) -- (p-14);
%\draw[Violet,very thick] (p-5) -- (p-13);
%\draw[Violet,very thick] (p-5) -- (p-13);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
1/53.26/72.21/0.4/Blue,
12/279.62/343.14/0.4/Green,
10/12.21/56.41/0.4/Orange,
15/236.41/363.59/0.4/Violet}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/203,
2/263,
3/143,
4/23,
5/323,
6/83,
7/342,
8/162,
9/42,
10/162,
11/190,
12/70,
13/313,
14/287,
15/26,
16/206,
17/26,
18/146,
19/266,
20/214,
21/26,
22/78,
23/97,
24/157,
25/277,
26/37,
27/277,
28/18,
29/138,
30/318,
31/94,
32/170,
33/290,
34/133,
35/334,
36/154,
37/274,
38/94,
39/334,
40/102,
41/83,
42/263,
43/263,
44/130,
45/222,
46/102,
47/282,
48/342,
49/10,
50/13,
51/107,
52/146,
53/326,
54/206,
55/326,
56/86,
57/326,
58/206,
59/337,
60/277,
61/37,
62/97,
63/97,
64/138,
65/318,
66/138,
67/274,
68/350,
69/110,
70/154,
71/334,
72/154,
73/274,
74/154}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/a0202c21c6f7fd86a0f1feb68549f9fe.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1894-1</Bildtext>
%<Ausrichten von=\"18\" nach=\"20\"/>
%<Winkel size=\"18\" color=\"blue\" id=\"blauerWinkel\" value=\"18.947361232912655\"/>
%<Winkel size=\"18\" color=\"green\" id=\"gruenerWinkel\" value=\"63.525969991157574\"/>
%<Winkel size=\"18\" color=\"orange\" id=\"orangerWinkel\" value=\"44.19774595541346\"/>
%<Winkel size=\"18\" color=\"violet\" id=\"vierterWinkel\" value=\"127.18\"/>
%<Feinjustieren Anzahl=\"3,3\"/>
%<Rechenweg>
%P[1]=[-18.170417966471057,-12.057944075335968]; P[2]=[31.48453077044413,-17.921907405228126]; D=ab(1,2); A(2,1,Bew(1)); L(3,1,2); L(4,3,2); L(5,4,2); L(6,3,4); M(7,1,3,blauerWinkel,2); N(11,7,6); L(12,11,6); M(13,12,6,gruenerWinkel); L(14,12,13); M(15,10,9,orangerWinkel,2); M(19,15,10,vierterWinkel); N(20,17,19); L(21,20,19); RA(21,14);
%
%RK([5,13],[18,20,14],360/4,true);
%</Rechenweg>
%
%<Knopf id=\"Stopp_alleWinkel\" color=\"grey\"/>
%
%<Knopf id=\"Start_blauerWinkel\" color=\"blue\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#blauerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_blauerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0s\"/>
%
%<Knopf id=\"Start_gruenerWinkel\" color=\"green\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#gruenerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_gruenerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0s\"/>
%
%<Knopf id=\"Start_orangerWinkel\" color=\"orange\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#orangerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_orangerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0s\"/>
%
%<Knopf id=\"Start_vierterWinkel\" color=\"violet\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#vierterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_vierterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0s\"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LimeGreen}{rgb}{0.20,0.80,0.20}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
\definecolor{Violet}{rgb}{0.93,0.51,0.93}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/2.23/0.23,
2/3.23/0.12,
3/2.83/1.04,
4/3.82/0.92,
5/4.22/0.00,
6/3.43/1.84,
7/2.54/1.19,
8/1.56/0.98,
9/1.87/1.93,
10/0.89/1.72,
11/2.49/2.19,
12/3.26/2.82,
13/4.22/2.53,
14/3.99/3.51,
15/1.44/2.55,
16/0.44/2.61,
17/1.00/3.44,
18/0.00/3.51,
19/2.44/2.61,
20/2.00/3.51,
21/2.99/3.44,
22/2.23/6.78,
23/3.23/6.90,
24/2.83/5.98,
25/3.82/6.10,
26/4.22/7.01,
27/3.43/5.18,
28/2.54/5.83,
29/1.56/6.04,
30/1.87/5.09,
31/0.89/5.30,
32/2.49/4.83,
33/3.26/4.19,
34/4.22/4.48,
35/1.44/4.47,
36/0.44/4.40,
37/1.00/3.57,
38/2.44/4.40,
39/2.99/3.57,
40/6.21/6.78,
41/5.21/6.90,
42/5.61/5.98,
43/4.61/6.10,
44/5.01/5.18,
45/5.90/5.83,
46/6.88/6.04,
47/6.57/5.09,
48/7.55/5.30,
49/5.95/4.83,
50/5.18/4.19,
51/4.45/3.51,
52/7.00/4.47,
53/7.99/4.40,
54/7.44/3.57,
55/8.44/3.51,
56/6.00/4.40,
57/6.44/3.51,
58/5.44/3.57,
59/6.21/0.23,
60/5.21/0.12,
61/5.61/1.04,
62/4.61/0.92,
63/5.01/1.84,
64/5.90/1.19,
65/6.88/0.98,
66/6.57/1.93,
67/7.55/1.72,
68/5.95/2.19,
69/5.18/2.82,
70/7.00/2.55,
71/7.99/2.61,
72/7.44/3.44,
73/6.00/2.61,
74/5.44/3.44}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
1/53.26/72.21/0.4/Blue,
12/279.62/343.14/0.4/Green,
10/12.21/56.41/0.4/Orange,
15/236.41/363.59/0.4/Violet}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
2/1,
3/1, 3/2,
4/3, 4/2,
5/4, 5/2, 5/62, 5/60,
6/3, 6/4,
7/1,
8/1, 8/7,
9/8, 9/7,
10/8, 10/9,
11/7, 11/6,
12/11, 12/6,
13/12, 13/69, 13/51,
14/12, 14/13, 14/33, 14/34, 14/39,
15/10,
16/10, 16/15,
17/16, 17/15,
18/16, 18/17, 18/36, 18/37,
19/15,
20/17, 20/19, 20/37, 20/38,
21/20, 21/19, 21/14,
23/22,
24/22, 24/23,
25/23, 25/24,
26/23, 26/25, 26/41, 26/43,
27/24, 27/25,
28/22,
29/22, 29/28,
30/28, 30/29,
31/29, 31/30,
32/27, 32/28,
33/27, 33/32,
34/33, 34/50,
35/31,
36/31, 36/35,
37/35, 37/36,
38/35,
39/38, 39/20,
41/40,
42/40, 42/41,
43/41, 43/42,
44/42, 44/43,
45/40,
46/40, 46/45,
47/45, 47/46,
48/46, 48/47,
49/44, 49/45,
50/44, 50/49,
51/50, 51/34, 51/69, 51/74,
52/48,
53/48, 53/52,
54/52, 54/53,
55/53, 55/54, 55/71, 55/72,
56/52,
57/54, 57/56, 57/72, 57/73,
58/51, 58/56, 58/57,
60/59,
61/59, 61/60,
62/60, 62/61,
63/61, 63/62,
64/59,
65/59, 65/64,
66/64, 66/65,
67/65, 67/66,
68/63, 68/64,
69/63, 69/68,
70/67,
71/67, 71/70,
72/70, 72/71,
73/70,
74/73, 74/57}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,74}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[LimeGreen,very thick] (p-21) -- (p-14);
%\draw[Violet,very thick] (p-5) -- (p-13);
%\draw[Violet,very thick] (p-5) -- (p-13);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
1/53.26/72.21/0.4/Blue,
12/279.62/343.14/0.4/Green,
10/12.21/56.41/0.4/Orange,
15/236.41/363.59/0.4/Violet}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/203,
2/263,
3/143,
4/23,
5/323,
6/83,
7/342,
8/162,
9/42,
10/162,
11/190,
12/70,
13/313,
14/287,
15/26,
16/206,
17/26,
18/146,
19/266,
20/214,
21/26,
22/78,
23/97,
24/157,
25/277,
26/37,
27/277,
28/18,
29/138,
30/318,
31/94,
32/170,
33/290,
34/133,
35/334,
36/154,
37/274,
38/94,
39/334,
40/102,
41/83,
42/263,
43/263,
44/130,
45/222,
46/102,
47/282,
48/342,
49/10,
50/13,
51/107,
52/146,
53/326,
54/206,
55/326,
56/86,
57/326,
58/206,
59/337,
60/277,
61/37,
62/97,
63/97,
64/138,
65/318,
66/138,
67/274,
68/350,
69/110,
70/154,
71/334,
72/154,
73/274,
74/154}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
und in Richtung größerer vierter Winkel
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1894-1</Bildtext>
%<Ausrichten von="18" nach="20"/>
%<Winkel size="18" color="blue" id="blauerWinkel" value="29.865358953704845"/>
%<Winkel size="18" color="green" id="gruenerWinkel" value="59.5617974746202"/>
%<Winkel size="18" color="orange" id="orangerWinkel" value="3.6331269937373087"/>
%<Winkel size="18" color="violet" id="vierterWinkel" value="186.58"/>
%<Feinjustieren Anzahl="3,3"/>
%<Rechenweg>
%P[1]=[-18.11479523702524,-11.925524469987494]; P[2]=[31.542078892744236,-17.773160886543337]; D=ab(1,2); A(2,1,Bew(1)); L(3,1,2); L(4,3,2); L(5,4,2); L(6,3,4); M(7,1,3,blauerWinkel,2); N(11,7,6); L(12,11,6); M(13,12,6,gruenerWinkel); L(14,12,13); M(15,10,9,orangerWinkel,2); M(19,15,10,vierterWinkel); N(20,17,19); L(21,20,19); RA(21,14);
%
%RK([5,13],[18,20,14],360/4,true);
%</Rechenweg>
%
%<Knopf id="Stopp_alleWinkel" color="grey"/>
%
%<Knopf id="Start_blauerWinkel" color="blue"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#blauerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_blauerWinkel.click+0s" end="Stopp_alleWinkel.click+0s"/>
%
%<Knopf id="Start_gruenerWinkel" color="green"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#gruenerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_gruenerWinkel.click+0s" end="Stopp_alleWinkel.click+0s"/>
%
%<Knopf id="Start_orangerWinkel" color="orange"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#orangerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_orangerWinkel.click+0s" end="Stopp_alleWinkel.click+0s"/>
%
%<Knopf id="Start_vierterWinkel" color="violet"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#vierterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_vierterWinkel.click+0s" end="Stopp_alleWinkel.click+0s"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LimeGreen}{rgb}{0.20,0.80,0.20}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
\definecolor{Violet}{rgb}{0.93,0.51,0.93}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.61/0.23,
2/2.60/0.12,
3/2.20/1.04,
4/3.20/0.92,
5/3.59/0.00,
6/2.80/1.84,
7/1.72/1.23,
8/0.81/0.83,
9/0.925/1.827,
10/0.01/1.43,
11/1.88/2.22,
12/2.666/2.828,
13/3.59/2.44,
14/3.46/3.43,
15/0.898/1.884,
16/0.06/2.43,
17/0.95/2.88,
18/0.12/3.43,
19/1.73/2.43,
20/1.79/3.43,
21/2.626/2.885,
22/1.60/6.63,
23/2.59/6.75,
24/2.20/5.83,
25/3.19/5.95,
26/3.58/6.87,
27/2.80/5.03,
28/1.72/5.64,
29/0.80/6.03,
30/0.920/5.036,
31/0.00/5.43,
32/1.87/4.65,
33/2.664/4.039,
34/3.59/4.43,
35/0.894/4.978,
36/0.06/4.43,
37/0.95/3.98,
38/1.73/4.43,
39/2.624/3.982,
40/5.57/6.64,
41/4.58/6.75,
42/4.97/5.83,
43/3.98/5.95,
44/4.37/5.03,
45/5.45/5.64,
46/6.37/6.04,
47/6.250/5.043,
48/7.17/5.44,
49/5.30/4.65,
50/4.509/4.041,
51/3.71/3.43,
52/6.277/4.985,
53/7.11/4.44,
54/6.22/3.99,
55/7.06/3.44,
56/5.44/4.44,
57/5.39/3.44,
58/4.549/3.985,
59/5.58/0.24,
60/4.58/0.12,
61/4.98/1.04,
62/3.98/0.92,
63/4.38/1.84,
64/5.46/1.23,
65/6.38/0.84,
66/6.254/1.833,
67/7.17/1.44,
68/5.30/2.22,
69/4.510/2.830,
70/6.281/1.891,
71/7.12/2.44,
72/6.22/2.89,
73/5.44/2.44,
74/4.550/2.887}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
1/53.28/83.15/0.4/Blue,
12/277.78/337.34/0.4/Green,
10/23.15/26.78/0.4/Orange,
15/206.78/393.36/0.4/Violet}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
2/1,
3/1, 3/2,
4/3, 4/2,
5/4, 5/2, 5/62, 5/60,
6/3, 6/4,
7/1,
8/1, 8/7,
9/8, 9/7,
10/8, 10/9,
11/7, 11/6,
12/11, 12/6,
13/12, 13/69, 13/51,
14/12, 14/13, 14/33, 14/34, 14/39,
15/10,
16/10, 16/15,
17/16, 17/15,
18/16, 18/17, 18/36, 18/37,
19/15,
20/17, 20/19, 20/37, 20/38,
21/20, 21/19, 21/14,
23/22,
24/22, 24/23,
25/23, 25/24,
26/23, 26/25, 26/41, 26/43,
27/24, 27/25,
28/22,
29/22, 29/28,
30/28, 30/29,
31/29, 31/30,
32/27, 32/28,
33/27, 33/32,
34/33, 34/50,
35/31,
36/31, 36/35,
37/35, 37/36,
38/35,
39/38, 39/20,
41/40,
42/40, 42/41,
43/41, 43/42,
44/42, 44/43,
45/40,
46/40, 46/45,
47/45, 47/46,
48/46, 48/47,
49/44, 49/45,
50/44, 50/49,
51/50, 51/34, 51/69, 51/74,
52/48,
53/48, 53/52,
54/52, 54/53,
55/53, 55/54, 55/71, 55/72,
56/52,
57/54, 57/56, 57/72, 57/73,
58/51, 58/56, 58/57,
60/59,
61/59, 61/60,
62/60, 62/61,
63/61, 63/62,
64/59,
65/59, 65/64,
66/64, 66/65,
67/65, 67/66,
68/63, 68/64,
69/63, 69/68,
70/67,
71/67, 71/70,
72/70, 72/71,
73/70,
74/73, 74/57}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,74}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[LimeGreen,very thick] (p-21) -- (p-14);
%\draw[Violet,very thick] (p-5) -- (p-13);
%\draw[Violet,very thick] (p-5) -- (p-13);
%\draw[LimeGreen,very thick] (p-11) -- (p-21);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
1/53.28/83.15/0.4/Blue,
12/277.78/337.34/0.4/Green,
10/23.15/26.78/0.4/Orange,
15/206.78/393.36/0.4/Violet}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/293,
2/323,
3/143,
4/23,
5/217,
6/308,
7/53,
8/293,
9/53,
10/237,
11/188,
12/68,
13/233,
14/67,
15/297,
16/237,
17/57,
18/243,
19/237,
20/117,
21/357,
22/67,
23/97,
24/157,
25/277,
26/143,
27/277,
28/307,
29/67,
30/247,
31/123,
32/172,
33/292,
34/127,
35/63,
36/243,
37/303,
38/123,
39/3,
40/23,
41/23,
42/23,
43/203,
44/128,
45/233,
46/113,
47/293,
48/57,
49/8,
50/248,
51/247,
52/177,
53/357,
54/237,
55/297,
56/57,
57/63,
58/177,
59/247,
60/217,
61/337,
62/97,
63/97,
64/187,
65/247,
66/67,
67/7,
68/352,
69/353,
70/183,
71/3,
72/183,
73/303,
74/183}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/22d247cb2af1e80ee1318bf93cbeec6d.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1894-1</Bildtext>
%<Ausrichten von=\"18\" nach=\"20\"/>
%<Winkel size=\"18\" color=\"blue\" id=\"blauerWinkel\" value=\"29.865358953704845\"/>
%<Winkel size=\"18\" color=\"green\" id=\"gruenerWinkel\" value=\"59.5617974746202\"/>
%<Winkel size=\"18\" color=\"orange\" id=\"orangerWinkel\" value=\"3.6331269937373087\"/>
%<Winkel size=\"18\" color=\"violet\" id=\"vierterWinkel\" value=\"186.58\"/>
%<Feinjustieren Anzahl=\"3,3\"/>
%<Rechenweg>
%P[1]=[-18.11479523702524,-11.925524469987494]; P[2]=[31.542078892744236,-17.773160886543337]; D=ab(1,2); A(2,1,Bew(1)); L(3,1,2); L(4,3,2); L(5,4,2); L(6,3,4); M(7,1,3,blauerWinkel,2); N(11,7,6); L(12,11,6); M(13,12,6,gruenerWinkel); L(14,12,13); M(15,10,9,orangerWinkel,2); M(19,15,10,vierterWinkel); N(20,17,19); L(21,20,19); RA(21,14);
%
%RK([5,13],[18,20,14],360/4,true);
%</Rechenweg>
%
%<Knopf id=\"Stopp_alleWinkel\" color=\"grey\"/>
%
%<Knopf id=\"Start_blauerWinkel\" color=\"blue\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#blauerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_blauerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0s\"/>
%
%<Knopf id=\"Start_gruenerWinkel\" color=\"green\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#gruenerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_gruenerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0s\"/>
%
%<Knopf id=\"Start_orangerWinkel\" color=\"orange\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#orangerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_orangerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0s\"/>
%
%<Knopf id=\"Start_vierterWinkel\" color=\"violet\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#vierterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_vierterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0s\"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LimeGreen}{rgb}{0.20,0.80,0.20}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
\definecolor{Violet}{rgb}{0.93,0.51,0.93}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.61/0.23,
2/2.60/0.12,
3/2.20/1.04,
4/3.20/0.92,
5/3.59/0.00,
6/2.80/1.84,
7/1.72/1.23,
8/0.81/0.83,
9/0.925/1.827,
10/0.01/1.43,
11/1.88/2.22,
12/2.666/2.828,
13/3.59/2.44,
14/3.46/3.43,
15/0.898/1.884,
16/0.06/2.43,
17/0.95/2.88,
18/0.12/3.43,
19/1.73/2.43,
20/1.79/3.43,
21/2.626/2.885,
22/1.60/6.63,
23/2.59/6.75,
24/2.20/5.83,
25/3.19/5.95,
26/3.58/6.87,
27/2.80/5.03,
28/1.72/5.64,
29/0.80/6.03,
30/0.920/5.036,
31/0.00/5.43,
32/1.87/4.65,
33/2.664/4.039,
34/3.59/4.43,
35/0.894/4.978,
36/0.06/4.43,
37/0.95/3.98,
38/1.73/4.43,
39/2.624/3.982,
40/5.57/6.64,
41/4.58/6.75,
42/4.97/5.83,
43/3.98/5.95,
44/4.37/5.03,
45/5.45/5.64,
46/6.37/6.04,
47/6.250/5.043,
48/7.17/5.44,
49/5.30/4.65,
50/4.509/4.041,
51/3.71/3.43,
52/6.277/4.985,
53/7.11/4.44,
54/6.22/3.99,
55/7.06/3.44,
56/5.44/4.44,
57/5.39/3.44,
58/4.549/3.985,
59/5.58/0.24,
60/4.58/0.12,
61/4.98/1.04,
62/3.98/0.92,
63/4.38/1.84,
64/5.46/1.23,
65/6.38/0.84,
66/6.254/1.833,
67/7.17/1.44,
68/5.30/2.22,
69/4.510/2.830,
70/6.281/1.891,
71/7.12/2.44,
72/6.22/2.89,
73/5.44/2.44,
74/4.550/2.887}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
1/53.28/83.15/0.4/Blue,
12/277.78/337.34/0.4/Green,
10/23.15/26.78/0.4/Orange,
15/206.78/393.36/0.4/Violet}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
2/1,
3/1, 3/2,
4/3, 4/2,
5/4, 5/2, 5/62, 5/60,
6/3, 6/4,
7/1,
8/1, 8/7,
9/8, 9/7,
10/8, 10/9,
11/7, 11/6,
12/11, 12/6,
13/12, 13/69, 13/51,
14/12, 14/13, 14/33, 14/34, 14/39,
15/10,
16/10, 16/15,
17/16, 17/15,
18/16, 18/17, 18/36, 18/37,
19/15,
20/17, 20/19, 20/37, 20/38,
21/20, 21/19, 21/14,
23/22,
24/22, 24/23,
25/23, 25/24,
26/23, 26/25, 26/41, 26/43,
27/24, 27/25,
28/22,
29/22, 29/28,
30/28, 30/29,
31/29, 31/30,
32/27, 32/28,
33/27, 33/32,
34/33, 34/50,
35/31,
36/31, 36/35,
37/35, 37/36,
38/35,
39/38, 39/20,
41/40,
42/40, 42/41,
43/41, 43/42,
44/42, 44/43,
45/40,
46/40, 46/45,
47/45, 47/46,
48/46, 48/47,
49/44, 49/45,
50/44, 50/49,
51/50, 51/34, 51/69, 51/74,
52/48,
53/48, 53/52,
54/52, 54/53,
55/53, 55/54, 55/71, 55/72,
56/52,
57/54, 57/56, 57/72, 57/73,
58/51, 58/56, 58/57,
60/59,
61/59, 61/60,
62/60, 62/61,
63/61, 63/62,
64/59,
65/59, 65/64,
66/64, 66/65,
67/65, 67/66,
68/63, 68/64,
69/63, 69/68,
70/67,
71/67, 71/70,
72/70, 72/71,
73/70,
74/73, 74/57}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,74}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[LimeGreen,very thick] (p-21) -- (p-14);
%\draw[Violet,very thick] (p-5) -- (p-13);
%\draw[Violet,very thick] (p-5) -- (p-13);
%\draw[LimeGreen,very thick] (p-11) -- (p-21);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
1/53.28/83.15/0.4/Blue,
12/277.78/337.34/0.4/Green,
10/23.15/26.78/0.4/Orange,
15/206.78/393.36/0.4/Violet}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/293,
2/323,
3/143,
4/23,
5/217,
6/308,
7/53,
8/293,
9/53,
10/237,
11/188,
12/68,
13/233,
14/67,
15/297,
16/237,
17/57,
18/243,
19/237,
20/117,
21/357,
22/67,
23/97,
24/157,
25/277,
26/143,
27/277,
28/307,
29/67,
30/247,
31/123,
32/172,
33/292,
34/127,
35/63,
36/243,
37/303,
38/123,
39/3,
40/23,
41/23,
42/23,
43/203,
44/128,
45/233,
46/113,
47/293,
48/57,
49/8,
50/248,
51/247,
52/177,
53/357,
54/237,
55/297,
56/57,
57/63,
58/177,
59/247,
60/217,
61/337,
62/97,
63/97,
64/187,
65/247,
66/67,
67/7,
68/352,
69/353,
70/183,
71/3,
72/183,
73/303,
74/183}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
[Graph ins Streichholzprogramm großes Eingabefenster kopieren, Button "neu zeichnen", dann vierterWinkel anklicken, anschließend Button "-1" und Button "Feinjustieren(3,3)" abwechselnd wiederholen]
Eine weitere einstellbare Kante habe ich keine gesehen. Der Versuch, Abstand P11-P21 auf 1 zu bringen, führt zu einem Graph mit vielen zusammenfallenden Knoten 12×Grad 3, 44×Grad 4, 10×Grad 6.
2020-01-20 10:35 - haribo in Beitrag No. 1893 schreibt:
und ich würde immer gerne einen verstellwinkel bei 1-7-11 haben anstelle von 3-1-7... weil es ein winkel ist der in beide richtungen gedrückt werden kann
Das ging nicht ohne die Punkte neu zu nummerieren, ich zeichne sie deshalb blau.
74 Knoten, 16×Grad 3, 54×Grad 4, 4×Grad 6, 0 Überschneidungen
144 Kanten, minimal 0.99999999999999633626, maximal 1.00000000000000444089
einzustellende Kanten, Abstände und Winkel:
|P21-P14|=0.99999999999999988898
∠(P18-P20,P12-P13)=90.00000000000000000000°
∠(P18-P14,P12-P13)=90.00000000000000000000°
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1894-1</Bildtext>
%<Ausrichten von="18" nach="20"/>
%<Winkel size="18" color="blue" id="blauerWinkel" value="180"/>
%<Winkel size="18" color="green" id="gruenerWinkel" value="59.999999999999986"/>
%<Winkel size="18" color="orange" id="orangerWinkel" value="15.522487814070073"/>
%<Winkel size="18" color="violet" id="vierterWinkel" value="164.47751218592992472622"/>
%<Feinjustieren Anzahl="3,3"/>
%<Rechenweg>
%P[1]=[-18.114795237025238,-11.925524469987494]; P[2]=[-57.64326598912998,18.693097314802216]; D=ab(1,2); A(2,1,Bew(1)); L(3,2,1); L(4,2,3); L(5,2,4); M(6,3,1,blauerWinkel); Q(7,6,1,ab(1,2,3),ab(5,1,[2,4])); L(12,11,10); M(13,8,7,gruenerWinkel); L(14,8,13); M(15,5,4,orangerWinkel,2); M(19,15,5,vierterWinkel); N(20,17,19); L(21,20,19); RA(21,14);
%
%RK([12,13],[18,20,14],360/4,true);
%</Rechenweg>
%
%<Knopf id="Stopp_alleWinkel" color="grey"/>
%
%<Knopf id="Start_blauerWinkel" color="blue"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#blauerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_blauerWinkel.click+0s" end="Stopp_alleWinkel.click+0s"/>
%
%<Knopf id="Start_gruenerWinkel" color="green"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#gruenerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_gruenerWinkel.click+0s" end="Stopp_alleWinkel.click+0s"/>
%
%<Knopf id="Start_orangerWinkel" color="orange"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#orangerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_orangerWinkel.click+0s" end="Stopp_alleWinkel.click+0s"/>
%
%<Knopf id="Start_vierterWinkel" color="violet"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#vierterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_vierterWinkel.click+0s" end="Stopp_alleWinkel.click+0s"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LimeGreen}{rgb}{0.20,0.80,0.20}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
\definecolor{Violet}{rgb}{0.93,0.51,0.93}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.85/0.23,
2/1.06/0.85,
3/1.99/1.22,
4/1.20/1.84,
5/0.27/1.46,
6/2.12/2.22,
7/3.05/1.84,
8/2.91/2.83,
9/2.45/1.04,
10/2.84/0.12,
11/3.44/0.92,
12/3.84/0.00,
13/3.84/2.45,
14/3.70/3.44,
15/1.06/2.07,
16/0.14/2.45,
17/0.93/3.06,
18/0.00/3.44,
19/1.99/2.45,
20/1.85/3.44,
21/2.78/3.06,
22/1.85/6.65,
23/1.06/6.03,
24/1.99/5.66,
25/1.20/5.04,
26/0.27/5.42,
27/2.12/4.67,
28/3.05/5.04,
29/2.91/4.05,
30/2.45/5.85,
31/2.84/6.76,
32/3.44/5.96,
33/3.84/6.88,
34/3.84/4.43,
35/1.06/4.81,
36/0.14/4.43,
37/0.93/3.82,
38/1.99/4.43,
39/2.78/3.82,
40/5.82/6.65,
41/6.61/6.03,
42/5.69/5.66,
43/6.48/5.04,
44/7.40/5.42,
45/5.55/4.67,
46/4.63/5.04,
47/4.76/4.05,
48/5.23/5.85,
49/4.83/6.76,
50/4.23/5.96,
51/3.97/3.44,
52/6.61/4.81,
53/7.54/4.43,
54/6.75/3.82,
55/7.68/3.44,
56/5.69/4.43,
57/5.82/3.44,
58/4.90/3.82,
59/5.82/0.23,
60/6.61/0.85,
61/5.69/1.22,
62/6.48/1.84,
63/7.40/1.46,
64/5.55/2.22,
65/4.63/1.84,
66/4.76/2.83,
67/5.23/1.04,
68/4.83/0.12,
69/4.23/0.92,
70/6.61/2.07,
71/7.54/2.45,
72/6.75/3.06,
73/5.69/2.45,
74/4.90/3.06}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
3/262.24/442.24/0.4/Blue,
8/277.76/337.76/0.4/Green,
5/22.24/37.76/0.4/Orange,
15/217.76/382.24/0.4/Violet}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
2/1,
3/2, 3/1,
4/2, 4/3,
5/2, 5/4,
6/3, 6/7,
7/9, 7/11,
8/7, 8/6,
9/1,
10/1, 10/9,
11/9, 11/10,
12/11, 12/10, 12/69, 12/68,
13/8, 13/66, 13/51,
14/8, 14/13, 14/29, 14/34, 14/39,
15/5,
16/5, 16/15,
17/16, 17/15,
18/16, 18/17, 18/36, 18/37,
19/15,
20/17, 20/19, 20/37, 20/38,
21/20, 21/19, 21/14,
23/22,
24/22, 24/23,
25/23, 25/24,
26/23, 26/25,
27/24, 27/28,
28/30, 28/32,
29/27, 29/28,
30/22,
31/22, 31/30,
32/30, 32/31,
33/31, 33/32, 33/49, 33/50,
34/29, 34/47,
35/26,
36/26, 36/35,
37/35, 37/36,
38/35,
39/38, 39/20,
41/40,
42/40, 42/41,
43/41, 43/42,
44/41, 44/43,
45/42, 45/46,
46/48, 46/50,
47/45, 47/46,
48/40,
49/40, 49/48,
50/48, 50/49,
51/47, 51/34, 51/66, 51/74,
52/44,
53/44, 53/52,
54/52, 54/53,
55/53, 55/54, 55/71, 55/72,
56/52,
57/54, 57/56, 57/72, 57/73,
58/51, 58/56, 58/57,
60/59,
61/59, 61/60,
62/60, 62/61,
63/60, 63/62,
64/61, 64/65,
65/67, 65/69,
66/64, 66/65,
67/59,
68/59, 68/67,
69/67, 69/68,
70/63,
71/63, 71/70,
72/70, 72/71,
73/70,
74/73, 74/57}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,74}
\fill[blue] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[LimeGreen,very thick] (p-21) -- (p-14);
%\draw[Violet,very thick] (p-12) -- (p-13);
%\draw[Violet,very thick] (p-12) -- (p-13);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
3/262.24/442.24/0.4/Blue,
8/277.76/337.76/0.4/Green,
5/22.24/37.76/0.4/Orange,
15/217.76/382.24/0.4/Violet}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/292,
2/232,
3/52,
4/52,
5/248,
6/188,
7/83,
8/68,
9/143,
10/323,
11/323,
12/217,
13/232,
14/292,
15/308,
16/188,
17/68,
18/128,
19/248,
20/128,
21/8,
22/68,
23/188,
24/8,
25/308,
26/112,
27/172,
28/52,
29/172,
30/157,
31/157,
32/337,
33/143,
34/128,
35/52,
36/172,
37/352,
38/112,
39/352,
40/23,
41/52,
42/232,
43/232,
44/68,
45/8,
46/263,
47/248,
48/23,
49/143,
50/203,
51/248,
52/128,
53/8,
54/188,
55/308,
56/68,
57/308,
58/188,
59/337,
60/308,
61/128,
62/68,
63/8,
64/352,
65/232,
66/352,
67/337,
68/217,
69/157,
70/232,
71/352,
72/172,
73/292,
74/172}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/82ea008a298d4a0dce7caf7292ceb585.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1894-1</Bildtext>
%<Ausrichten von=\"18\" nach=\"20\"/>
%<Winkel size=\"18\" color=\"blue\" id=\"blauerWinkel\" value=\"180\"/>
%<Winkel size=\"18\" color=\"green\" id=\"gruenerWinkel\" value=\"59.999999999999986\"/>
%<Winkel size=\"18\" color=\"orange\" id=\"orangerWinkel\" value=\"15.522487814070073\"/>
%<Winkel size=\"18\" color=\"violet\" id=\"vierterWinkel\" value=\"164.47751218592992472622\"/>
%<Feinjustieren Anzahl=\"3,3\"/>
%<Rechenweg>
%P[1]=[-18.114795237025238,-11.925524469987494]; P[2]=[-57.64326598912998,18.693097314802216]; D=ab(1,2); A(2,1,Bew(1)); L(3,2,1); L(4,2,3); L(5,2,4); M(6,3,1,blauerWinkel); Q(7,6,1,ab(1,2,3),ab(5,1,[2,4])); L(12,11,10); M(13,8,7,gruenerWinkel); L(14,8,13); M(15,5,4,orangerWinkel,2); M(19,15,5,vierterWinkel); N(20,17,19); L(21,20,19); RA(21,14);
%
%RK([12,13],[18,20,14],360/4,true);
%</Rechenweg>
%
%<Knopf id=\"Stopp_alleWinkel\" color=\"grey\"/>
%
%<Knopf id=\"Start_blauerWinkel\" color=\"blue\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#blauerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_blauerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0s\"/>
%
%<Knopf id=\"Start_gruenerWinkel\" color=\"green\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#gruenerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_gruenerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0s\"/>
%
%<Knopf id=\"Start_orangerWinkel\" color=\"orange\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#orangerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_orangerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0s\"/>
%
%<Knopf id=\"Start_vierterWinkel\" color=\"violet\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#vierterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_vierterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0s\"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LimeGreen}{rgb}{0.20,0.80,0.20}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
\definecolor{Violet}{rgb}{0.93,0.51,0.93}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.85/0.23,
2/1.06/0.85,
3/1.99/1.22,
4/1.20/1.84,
5/0.27/1.46,
6/2.12/2.22,
7/3.05/1.84,
8/2.91/2.83,
9/2.45/1.04,
10/2.84/0.12,
11/3.44/0.92,
12/3.84/0.00,
13/3.84/2.45,
14/3.70/3.44,
15/1.06/2.07,
16/0.14/2.45,
17/0.93/3.06,
18/0.00/3.44,
19/1.99/2.45,
20/1.85/3.44,
21/2.78/3.06,
22/1.85/6.65,
23/1.06/6.03,
24/1.99/5.66,
25/1.20/5.04,
26/0.27/5.42,
27/2.12/4.67,
28/3.05/5.04,
29/2.91/4.05,
30/2.45/5.85,
31/2.84/6.76,
32/3.44/5.96,
33/3.84/6.88,
34/3.84/4.43,
35/1.06/4.81,
36/0.14/4.43,
37/0.93/3.82,
38/1.99/4.43,
39/2.78/3.82,
40/5.82/6.65,
41/6.61/6.03,
42/5.69/5.66,
43/6.48/5.04,
44/7.40/5.42,
45/5.55/4.67,
46/4.63/5.04,
47/4.76/4.05,
48/5.23/5.85,
49/4.83/6.76,
50/4.23/5.96,
51/3.97/3.44,
52/6.61/4.81,
53/7.54/4.43,
54/6.75/3.82,
55/7.68/3.44,
56/5.69/4.43,
57/5.82/3.44,
58/4.90/3.82,
59/5.82/0.23,
60/6.61/0.85,
61/5.69/1.22,
62/6.48/1.84,
63/7.40/1.46,
64/5.55/2.22,
65/4.63/1.84,
66/4.76/2.83,
67/5.23/1.04,
68/4.83/0.12,
69/4.23/0.92,
70/6.61/2.07,
71/7.54/2.45,
72/6.75/3.06,
73/5.69/2.45,
74/4.90/3.06}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
3/262.24/442.24/0.4/Blue,
8/277.76/337.76/0.4/Green,
5/22.24/37.76/0.4/Orange,
15/217.76/382.24/0.4/Violet}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
2/1,
3/2, 3/1,
4/2, 4/3,
5/2, 5/4,
6/3, 6/7,
7/9, 7/11,
8/7, 8/6,
9/1,
10/1, 10/9,
11/9, 11/10,
12/11, 12/10, 12/69, 12/68,
13/8, 13/66, 13/51,
14/8, 14/13, 14/29, 14/34, 14/39,
15/5,
16/5, 16/15,
17/16, 17/15,
18/16, 18/17, 18/36, 18/37,
19/15,
20/17, 20/19, 20/37, 20/38,
21/20, 21/19, 21/14,
23/22,
24/22, 24/23,
25/23, 25/24,
26/23, 26/25,
27/24, 27/28,
28/30, 28/32,
29/27, 29/28,
30/22,
31/22, 31/30,
32/30, 32/31,
33/31, 33/32, 33/49, 33/50,
34/29, 34/47,
35/26,
36/26, 36/35,
37/35, 37/36,
38/35,
39/38, 39/20,
41/40,
42/40, 42/41,
43/41, 43/42,
44/41, 44/43,
45/42, 45/46,
46/48, 46/50,
47/45, 47/46,
48/40,
49/40, 49/48,
50/48, 50/49,
51/47, 51/34, 51/66, 51/74,
52/44,
53/44, 53/52,
54/52, 54/53,
55/53, 55/54, 55/71, 55/72,
56/52,
57/54, 57/56, 57/72, 57/73,
58/51, 58/56, 58/57,
60/59,
61/59, 61/60,
62/60, 62/61,
63/60, 63/62,
64/61, 64/65,
65/67, 65/69,
66/64, 66/65,
67/59,
68/59, 68/67,
69/67, 69/68,
70/63,
71/63, 71/70,
72/70, 72/71,
73/70,
74/73, 74/57}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,74}
\fill[blue] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[LimeGreen,very thick] (p-21) -- (p-14);
%\draw[Violet,very thick] (p-12) -- (p-13);
%\draw[Violet,very thick] (p-12) -- (p-13);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
3/262.24/442.24/0.4/Blue,
8/277.76/337.76/0.4/Green,
5/22.24/37.76/0.4/Orange,
15/217.76/382.24/0.4/Violet}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/292,
2/232,
3/52,
4/52,
5/248,
6/188,
7/83,
8/68,
9/143,
10/323,
11/323,
12/217,
13/232,
14/292,
15/308,
16/188,
17/68,
18/128,
19/248,
20/128,
21/8,
22/68,
23/188,
24/8,
25/308,
26/112,
27/172,
28/52,
29/172,
30/157,
31/157,
32/337,
33/143,
34/128,
35/52,
36/172,
37/352,
38/112,
39/352,
40/23,
41/52,
42/232,
43/232,
44/68,
45/8,
46/263,
47/248,
48/23,
49/143,
50/203,
51/248,
52/128,
53/8,
54/188,
55/308,
56/68,
57/308,
58/188,
59/337,
60/308,
61/128,
62/68,
63/8,
64/352,
65/232,
66/352,
67/337,
68/217,
69/157,
70/232,
71/352,
72/172,
73/292,
74/172}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
|
Profil
Quote
Link |
StefanVogel
Senior
Dabei seit: 26.11.2005
Mitteilungen: 3446
Aus: Raun
| Beitrag No.1895, eingetragen 2020-01-25 11:53
|
Wie in Beitrag No.1876 festgestellt, sollte vor der Suche nach Beweglichkeit eigentlich noch Button neue Eingabe "wenig Winkel" erfolgen, damit auch unsymmetrische Bewegungen gefunden werden können. Doch der funktioniert bei diesem Graph nicht wegen unbekanntem Fehler. Ich habe deshalb Button neue Eingabe "Rahmen zuerst" verwendet. Mit neun beweglichen Winkeln müssen acht Einsetzkanten eingestellt werden. Da kann ich den neunten Winkel beliebig in kleinen Schritten verändern und anschließend die acht Einsetzkanten mit den ersten acht Winkeln einstellen. Das ergibt aber ebenfalls wieder den symmetrischen Graph.
74 Knoten, 16×Grad 3, 54×Grad 4, 4×Grad 6, 0 Überschneidungen
144 Kanten, minimal 0.99999999999993893773, maximal 1.00000000000003885781
einzustellende Kanten, Abstände und Winkel:
|P14-P12|=0.99999999999999955591
|P14-P13|=0.99999999999995181632
|P14-P33|=0.99999999999999800160
|P34-P14|=1.00000000000000466294
|P51-P13|=0.99999999999993893773
|P51-P50|=1.00000000000000088818
|P51-P34|=1.00000000000000799361
|P51-P69|=1.00000000000003885781
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1894-1</Bildtext>
%<Ausrichten von="18" nach="20"/>
%<Winkel size="18" color="blue" id="blauerWinkel" value="139.60333241491008"/>
%<Winkel size="18" color="green" id="gruenerWinkel" value="162.58274312101193"/>
%<Winkel size="18" color="orange" id="orangerWinkel" value="69.00000000000027"/>
%<Winkel size="18" color="violet" id="vierterWinkel" value="102.58274312101196"/>
%<Winkel size="18" color="teal" id="fuenfterWinkel" value="79.60333241491007"/>
%<Winkel size="18" color="lime" id="sechsterWinkel" value="106.62784892815566"/>
%<Winkel size="18" color="LightBlue" id="siebenterWinkel" value="139.60333241491006"/>
%<Winkel size="18" color="LightCoral" id="achterWinkel" value="162.58274312101204"/>
%<Winkel size="18" color="LightCyan" id="neunterWinkel" value="69"/>
%<Feinjustieren Anzahl="8,8"/>
%<Rechenweg>
%P[5]=[81.1989530225137,-23.620797303099177]; P[2]=[31.54207889274424,-17.773160886543337]; D=ab(5,2); A(2,5); N(4,2,5); N(3,2,4); N(1,2,3); M(8,1,2,blauerWinkel); N(7,8,1); N(9,8,7); N(10,8,9); M(16,10,8,gruenerWinkel); N(15,16,10); N(17,16,15); N(18,16,17); M(37,18,16,orangerWinkel); N(36,18,37); N(35,36,37); N(31,36,35); M(30,31,36,vierterWinkel); N(29,31,30); N(28,29,30); N(22,29,28); M(24,22,29,fuenfterWinkel); N(23,22,24); N(25,23,24); N(26,23,25); M(43,26,23,sechsterWinkel); N(41,26,43); N(42,41,43); N(40,41,42); M(46,40,41,siebenterWinkel); N(45,46,40); N(47,46,45); N(48,46,47); M(53,48,46,achterWinkel); N(52,53,48); N(54,53,52); N(55,53,54); M(72,55,53,neunterWinkel); N(71,55,72); N(70,71,72); N(67,71,70); Q(59,67,5,2*D,2*D); A(59,67); A(59,5); H(60,5,59,2); A(60,5); L(62,5,60); H(65,67,59,2); A(65,67); L(66,65,67); A(65,59); L(64,59,65); A(64,66); A(60,59); L(61,60,59); A(62,61); N(6,3,4); N(11,7,6); N(20,37,17); N(27,25,24); N(32,27,28); N(38,35,20); N(44,42,43); N(49,45,44); N(57,72,54); N(63,62,61); N(68,63,64); N(73,70,57); N(19,20,15); N(56,57,52); N(12,11,6); N(21,20,19); N(33,27,32); N(39,38,20); N(50,49,44); N(58,57,56); N(69,63,68); N(74,73,57); N(13,69,12); N(14,39,21); N(34,33,50); N(51,74,58);
%A(14,12); R(14,12,"green");
%A(14,13); R(14,13,"green");
%A(14,33); R(14,33,"green");
%A(34,14); R(34,14,"green");
%A(51,13); R(51,13,"green");
%A(51,50); R(51,50,"green");
%A(51,34); R(51,34,"green");
%A(51,69); R(51,69,"green");
%</Rechenweg>
%
%<Knopf id="Stopp_alleWinkel" color="LightGrey"/>
%
%<Knopf id="Start_blauerWinkel" color="blue"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#blauerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_blauerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_gruenerWinkel" color="green"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#gruenerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_gruenerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_orangerWinkel" color="orange"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#orangerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_orangerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_vierterWinkel" color="violet"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#vierterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_vierterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_fuenfterWinkel" color="teal"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#fuenfterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_fuenfterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_sechsterWinkel" color="lime"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#sechsterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_sechsterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_siebenterWinkel" color="LightBlue"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#siebenterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_siebenterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_achterWinkel" color="LightCoral"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#achterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_achterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_neunterWinkel" color="LightCyan"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#neunterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_neunterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LightBlue}{rgb}{0.68,0.84,0.90}
\definecolor{LightCoral}{rgb}{0.94,0.50,0.50}
\definecolor{LightCyan}{rgb}{0.88,1.00,1.00}
\definecolor{Lime}{rgb}{0.00,1.00,0.00}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
\definecolor{Teal}{rgb}{0.00,0.50,0.50}
\definecolor{Violet}{rgb}{0.93,0.51,0.93}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/2.22/0.23,
2/3.21/0.12,
3/2.82/1.04,
4/3.81/0.92,
5/4.21/0.00,
6/3.42/1.84,
7/2.52/1.19,
8/1.54/0.97,
9/1.83/1.92,
10/0.86/1.70,
11/2.48/2.19,
12/3.25/2.82,
13/4.21/2.53,
14/3.99/3.50,
15/1.43/2.52,
16/0.43/2.60,
17/1.00/3.43,
18/0.00/3.50,
19/2.42/2.60,
20/1.99/3.50,
21/2.99/3.42,
22/2.22/6.77,
23/3.22/6.89,
24/2.82/5.97,
25/3.81/6.09,
26/4.21/7.01,
27/3.42/5.17,
28/2.52/5.82,
29/1.54/6.04,
30/1.84/5.09,
31/0.86/5.31,
32/2.48/4.82,
33/3.25/4.18,
34/4.21/4.48,
35/1.43/4.49,
36/0.43/4.41,
37/1.00/3.58,
38/2.42/4.41,
39/2.99/3.58,
40/6.20/6.77,
41/5.20/6.89,
42/5.60/5.97,
43/4.61/6.09,
44/5.00/5.17,
45/5.90/5.82,
46/6.88/6.04,
47/6.58/5.08,
48/7.56/5.31,
49/5.94/4.82,
50/5.16/4.18,
51/4.43/3.50,
52/6.99/4.48,
53/7.99/4.40,
54/7.42/3.58,
55/8.42/3.50,
56/5.99/4.40,
57/6.42/3.50,
58/5.43/3.58,
59/6.19/0.23,
60/5.20/0.12,
61/5.60/1.03,
62/4.60/0.92,
63/5.00/1.84,
64/5.90/1.19,
65/6.88/0.96,
66/6.58/1.92,
67/7.56/1.70,
68/5.94/2.19,
69/5.16/2.82,
70/6.99/2.52,
71/7.99/2.60,
72/7.42/3.42,
73/5.99/2.60,
74/5.43/3.42}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
1/353.28/492.89/0.4/Blue,
10/312.89/475.47/0.4/Green,
18/295.47/364.47/0.4/Orange,
31/244.47/347.05/0.4/Violet,
22/227.05/306.66/0.4/Teal,
26/186.66/293.28/0.4/Lime,
40/173.28/312.89/0.4/LightBlue,
48/132.89/295.47/0.4/LightCoral,
55/115.47/184.47/0.4/LightCyan}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
1/2, 1/3,
2/5,
3/2, 3/4,
4/2, 4/5,
6/3, 6/4,
7/8, 7/1,
8/1,
9/8, 9/7,
10/8, 10/9,
11/7, 11/6,
12/11, 12/6,
13/69, 13/12,
14/39, 14/21, 14/12, 14/13, 14/33,
15/16, 15/10,
16/10,
17/16, 17/15,
18/16, 18/17,
19/20, 19/15,
20/37, 20/17,
21/20, 21/19,
22/29, 22/28,
23/22, 23/24,
24/22,
25/23, 25/24,
26/23, 26/25,
27/25, 27/24,
28/29, 28/30,
29/31, 29/30,
30/31,
31/36, 31/35,
32/27, 32/28,
33/27, 33/32,
34/33, 34/50, 34/14,
35/36, 35/37,
36/18, 36/37,
37/18,
38/35, 38/20,
39/38, 39/20,
40/41, 40/42,
41/26, 41/43,
42/41, 42/43,
43/26,
44/42, 44/43,
45/46, 45/40,
46/40,
47/46, 47/45,
48/46, 48/47,
49/45, 49/44,
50/49, 50/44,
51/74, 51/58, 51/13, 51/50, 51/34, 51/69,
52/53, 52/48,
53/48,
54/53, 54/52,
55/53, 55/54,
56/57, 56/52,
57/72, 57/54,
58/57, 58/56,
60/5, 60/59,
61/60, 61/59,
62/5, 62/60, 62/61,
63/62, 63/61,
64/59, 64/65, 64/66,
65/67, 65/59,
66/65, 66/67,
67/71, 67/70,
68/63, 68/64,
69/63, 69/68,
70/71, 70/72,
71/55, 71/72,
72/55,
73/70, 73/57,
74/73, 74/57}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,74}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[Green,very thick] (p-14) -- (p-12);
\draw[Green,very thick] (p-14) -- (p-13);
\draw[Green,very thick] (p-14) -- (p-33);
\draw[Green,very thick] (p-34) -- (p-14);
\draw[Green,very thick] (p-51) -- (p-13);
\draw[Green,very thick] (p-51) -- (p-50);
\draw[Green,very thick] (p-51) -- (p-34);
\draw[Green,very thick] (p-51) -- (p-69);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
1/353.28/492.89/0.4/Blue,
10/312.89/475.47/0.4/Green,
18/295.47/364.47/0.4/Orange,
31/244.47/347.05/0.4/Violet,
22/227.05/306.66/0.4/Teal,
26/186.66/293.28/0.4/Lime,
40/173.28/312.89/0.4/LightBlue,
48/132.89/295.47/0.4/LightCoral,
55/115.47/184.47/0.4/LightCyan}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/203,
2/323,
3/83,
4/23,
5/323,
6/83,
7/343,
8/223,
9/43,
10/265,
11/189,
12/193,
13/313,
14/287,
15/25,
16/265,
17/85,
18/145,
19/265,
20/214,
21/25,
22/77,
23/157,
24/157,
25/337,
26/143,
27/51,
28/17,
29/197,
30/257,
31/197,
32/171,
33/291,
34/47,
35/334,
36/154,
37/334,
38/94,
39/334,
40/103,
41/23,
42/263,
43/143,
44/129,
45/163,
46/43,
47/283,
48/343,
49/9,
50/249,
51/253,
52/145,
53/25,
54/205,
55/325,
56/85,
57/34,
58/205,
59/337,
60/277,
61/337,
62/217,
63/97,
64/137,
65/317,
66/77,
67/274,
68/351,
69/347,
70/154,
71/274,
72/94,
73/274,
74/154}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/030ef5cebc021454b7482ad31e6638bf.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1894-1</Bildtext>
%<Ausrichten von=\"18\" nach=\"20\"/>
%<Winkel size=\"18\" color=\"blue\" id=\"blauerWinkel\" value=\"139.60333241491008\"/>
%<Winkel size=\"18\" color=\"green\" id=\"gruenerWinkel\" value=\"162.58274312101193\"/>
%<Winkel size=\"18\" color=\"orange\" id=\"orangerWinkel\" value=\"69.00000000000027\"/>
%<Winkel size=\"18\" color=\"violet\" id=\"vierterWinkel\" value=\"102.58274312101196\"/>
%<Winkel size=\"18\" color=\"teal\" id=\"fuenfterWinkel\" value=\"79.60333241491007\"/>
%<Winkel size=\"18\" color=\"lime\" id=\"sechsterWinkel\" value=\"106.62784892815566\"/>
%<Winkel size=\"18\" color=\"LightBlue\" id=\"siebenterWinkel\" value=\"139.60333241491006\"/>
%<Winkel size=\"18\" color=\"LightCoral\" id=\"achterWinkel\" value=\"162.58274312101204\"/>
%<Winkel size=\"18\" color=\"LightCyan\" id=\"neunterWinkel\" value=\"69\"/>
%<Feinjustieren Anzahl=\"8,8\"/>
%<Rechenweg>
%P[5]=[81.1989530225137,-23.620797303099177]; P[2]=[31.54207889274424,-17.773160886543337]; D=ab(5,2); A(2,5); N(4,2,5); N(3,2,4); N(1,2,3); M(8,1,2,blauerWinkel); N(7,8,1); N(9,8,7); N(10,8,9); M(16,10,8,gruenerWinkel); N(15,16,10); N(17,16,15); N(18,16,17); M(37,18,16,orangerWinkel); N(36,18,37); N(35,36,37); N(31,36,35); M(30,31,36,vierterWinkel); N(29,31,30); N(28,29,30); N(22,29,28); M(24,22,29,fuenfterWinkel); N(23,22,24); N(25,23,24); N(26,23,25); M(43,26,23,sechsterWinkel); N(41,26,43); N(42,41,43); N(40,41,42); M(46,40,41,siebenterWinkel); N(45,46,40); N(47,46,45); N(48,46,47); M(53,48,46,achterWinkel); N(52,53,48); N(54,53,52); N(55,53,54); M(72,55,53,neunterWinkel); N(71,55,72); N(70,71,72); N(67,71,70); Q(59,67,5,2*D,2*D); A(59,67); A(59,5); H(60,5,59,2); A(60,5); L(62,5,60); H(65,67,59,2); A(65,67); L(66,65,67); A(65,59); L(64,59,65); A(64,66); A(60,59); L(61,60,59); A(62,61); N(6,3,4); N(11,7,6); N(20,37,17); N(27,25,24); N(32,27,28); N(38,35,20); N(44,42,43); N(49,45,44); N(57,72,54); N(63,62,61); N(68,63,64); N(73,70,57); N(19,20,15); N(56,57,52); N(12,11,6); N(21,20,19); N(33,27,32); N(39,38,20); N(50,49,44); N(58,57,56); N(69,63,68); N(74,73,57); N(13,69,12); N(14,39,21); N(34,33,50); N(51,74,58);
%A(14,12); R(14,12,\"green\");
%A(14,13); R(14,13,\"green\");
%A(14,33); R(14,33,\"green\");
%A(34,14); R(34,14,\"green\");
%A(51,13); R(51,13,\"green\");
%A(51,50); R(51,50,\"green\");
%A(51,34); R(51,34,\"green\");
%A(51,69); R(51,69,\"green\");
%</Rechenweg>
%
%<Knopf id=\"Stopp_alleWinkel\" color=\"LightGrey\"/>
%
%<Knopf id=\"Start_blauerWinkel\" color=\"blue\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#blauerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_blauerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_gruenerWinkel\" color=\"green\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#gruenerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_gruenerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_orangerWinkel\" color=\"orange\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#orangerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_orangerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_vierterWinkel\" color=\"violet\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#vierterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_vierterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_fuenfterWinkel\" color=\"teal\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#fuenfterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_fuenfterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_sechsterWinkel\" color=\"lime\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#sechsterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_sechsterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_siebenterWinkel\" color=\"LightBlue\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#siebenterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_siebenterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_achterWinkel\" color=\"LightCoral\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#achterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_achterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_neunterWinkel\" color=\"LightCyan\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#neunterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_neunterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LightBlue}{rgb}{0.68,0.84,0.90}
\definecolor{LightCoral}{rgb}{0.94,0.50,0.50}
\definecolor{LightCyan}{rgb}{0.88,1.00,1.00}
\definecolor{Lime}{rgb}{0.00,1.00,0.00}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
\definecolor{Teal}{rgb}{0.00,0.50,0.50}
\definecolor{Violet}{rgb}{0.93,0.51,0.93}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/2.22/0.23,
2/3.21/0.12,
3/2.82/1.04,
4/3.81/0.92,
5/4.21/0.00,
6/3.42/1.84,
7/2.52/1.19,
8/1.54/0.97,
9/1.83/1.92,
10/0.86/1.70,
11/2.48/2.19,
12/3.25/2.82,
13/4.21/2.53,
14/3.99/3.50,
15/1.43/2.52,
16/0.43/2.60,
17/1.00/3.43,
18/0.00/3.50,
19/2.42/2.60,
20/1.99/3.50,
21/2.99/3.42,
22/2.22/6.77,
23/3.22/6.89,
24/2.82/5.97,
25/3.81/6.09,
26/4.21/7.01,
27/3.42/5.17,
28/2.52/5.82,
29/1.54/6.04,
30/1.84/5.09,
31/0.86/5.31,
32/2.48/4.82,
33/3.25/4.18,
34/4.21/4.48,
35/1.43/4.49,
36/0.43/4.41,
37/1.00/3.58,
38/2.42/4.41,
39/2.99/3.58,
40/6.20/6.77,
41/5.20/6.89,
42/5.60/5.97,
43/4.61/6.09,
44/5.00/5.17,
45/5.90/5.82,
46/6.88/6.04,
47/6.58/5.08,
48/7.56/5.31,
49/5.94/4.82,
50/5.16/4.18,
51/4.43/3.50,
52/6.99/4.48,
53/7.99/4.40,
54/7.42/3.58,
55/8.42/3.50,
56/5.99/4.40,
57/6.42/3.50,
58/5.43/3.58,
59/6.19/0.23,
60/5.20/0.12,
61/5.60/1.03,
62/4.60/0.92,
63/5.00/1.84,
64/5.90/1.19,
65/6.88/0.96,
66/6.58/1.92,
67/7.56/1.70,
68/5.94/2.19,
69/5.16/2.82,
70/6.99/2.52,
71/7.99/2.60,
72/7.42/3.42,
73/5.99/2.60,
74/5.43/3.42}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
1/353.28/492.89/0.4/Blue,
10/312.89/475.47/0.4/Green,
18/295.47/364.47/0.4/Orange,
31/244.47/347.05/0.4/Violet,
22/227.05/306.66/0.4/Teal,
26/186.66/293.28/0.4/Lime,
40/173.28/312.89/0.4/LightBlue,
48/132.89/295.47/0.4/LightCoral,
55/115.47/184.47/0.4/LightCyan}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
1/2, 1/3,
2/5,
3/2, 3/4,
4/2, 4/5,
6/3, 6/4,
7/8, 7/1,
8/1,
9/8, 9/7,
10/8, 10/9,
11/7, 11/6,
12/11, 12/6,
13/69, 13/12,
14/39, 14/21, 14/12, 14/13, 14/33,
15/16, 15/10,
16/10,
17/16, 17/15,
18/16, 18/17,
19/20, 19/15,
20/37, 20/17,
21/20, 21/19,
22/29, 22/28,
23/22, 23/24,
24/22,
25/23, 25/24,
26/23, 26/25,
27/25, 27/24,
28/29, 28/30,
29/31, 29/30,
30/31,
31/36, 31/35,
32/27, 32/28,
33/27, 33/32,
34/33, 34/50, 34/14,
35/36, 35/37,
36/18, 36/37,
37/18,
38/35, 38/20,
39/38, 39/20,
40/41, 40/42,
41/26, 41/43,
42/41, 42/43,
43/26,
44/42, 44/43,
45/46, 45/40,
46/40,
47/46, 47/45,
48/46, 48/47,
49/45, 49/44,
50/49, 50/44,
51/74, 51/58, 51/13, 51/50, 51/34, 51/69,
52/53, 52/48,
53/48,
54/53, 54/52,
55/53, 55/54,
56/57, 56/52,
57/72, 57/54,
58/57, 58/56,
60/5, 60/59,
61/60, 61/59,
62/5, 62/60, 62/61,
63/62, 63/61,
64/59, 64/65, 64/66,
65/67, 65/59,
66/65, 66/67,
67/71, 67/70,
68/63, 68/64,
69/63, 69/68,
70/71, 70/72,
71/55, 71/72,
72/55,
73/70, 73/57,
74/73, 74/57}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,74}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[Green,very thick] (p-14) -- (p-12);
\draw[Green,very thick] (p-14) -- (p-13);
\draw[Green,very thick] (p-14) -- (p-33);
\draw[Green,very thick] (p-34) -- (p-14);
\draw[Green,very thick] (p-51) -- (p-13);
\draw[Green,very thick] (p-51) -- (p-50);
\draw[Green,very thick] (p-51) -- (p-34);
\draw[Green,very thick] (p-51) -- (p-69);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
1/353.28/492.89/0.4/Blue,
10/312.89/475.47/0.4/Green,
18/295.47/364.47/0.4/Orange,
31/244.47/347.05/0.4/Violet,
22/227.05/306.66/0.4/Teal,
26/186.66/293.28/0.4/Lime,
40/173.28/312.89/0.4/LightBlue,
48/132.89/295.47/0.4/LightCoral,
55/115.47/184.47/0.4/LightCyan}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/203,
2/323,
3/83,
4/23,
5/323,
6/83,
7/343,
8/223,
9/43,
10/265,
11/189,
12/193,
13/313,
14/287,
15/25,
16/265,
17/85,
18/145,
19/265,
20/214,
21/25,
22/77,
23/157,
24/157,
25/337,
26/143,
27/51,
28/17,
29/197,
30/257,
31/197,
32/171,
33/291,
34/47,
35/334,
36/154,
37/334,
38/94,
39/334,
40/103,
41/23,
42/263,
43/143,
44/129,
45/163,
46/43,
47/283,
48/343,
49/9,
50/249,
51/253,
52/145,
53/25,
54/205,
55/325,
56/85,
57/34,
58/205,
59/337,
60/277,
61/337,
62/217,
63/97,
64/137,
65/317,
66/77,
67/274,
68/351,
69/347,
70/154,
71/274,
72/94,
73/274,
74/154}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
[Graph ins Streichholzprogramm großes Eingabefenster kopieren, Button "neu zeichnen", dann neunterterWinkel anklicken, anschließend Button "+1" und Button "Feinjustieren(8,8)" abwechselnd wiederholen]
|
Profil
Quote
Link |
haribo
Senior
Dabei seit: 25.10.2012
Mitteilungen: 2298
| Beitrag No.1896, eingetragen 2020-01-25 15:32
|
19/12 (bzw 19/8 beim umnummerierten).
könnte man auf 1 einsetzen ( dito die vier symetrischen dazu)danach wieder eine der dabei entstandenen 5er Knoten eine Linie wieder löschen ... Dadurch ist es wieder beweglich also die nächste Möglichkeit suchen usw... In der Hoffnung irgendwann die dreier zu vierern umzuwandeln...
|
Profil
Quote
Link |
StefanVogel
Senior
Dabei seit: 26.11.2005
Mitteilungen: 3446
Aus: Raun
| Beitrag No.1897, eingetragen 2020-01-25 17:06
|
Das beste Ergebnis ist 4 Knoten mit Grad 3. Also 19-8 (nach neuer Nummerierung) einsetzen und dafür 8-14 entfernen. Weil dann geht Punkt 4 nur mit Punkt 6 zu verbinden und dann ist der Graph starr. 21-39 geht nicht mehr einzustellen. Wenn ich anstelle 8-14 der Reihe nach 8-13 oder 8-7 oder 8-6 entferne, immer muss 4-6 rein und der Graph wird starr, mit noch mehr Knoten von Grad 3 und dann sogar 2.
74 Knoten, 4×Grad 3, 68×Grad 4, 2×Grad 6, 0 Überschneidungen
148 Kanten, minimal 0.99999999999993904876, maximal 1.00000000000005773160
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1897-1</Bildtext>
%<Ausrichten von="1" nach="2"/>
%<Winkel size="18" color="blue" id="blauerWinkel" value="88.95502437185986"/>
%<Winkel size="18" color="green" id="gruenerWinkel" value="135.52248781407008"/>
%<Winkel size="18" color="orange" id="orangerWinkel" value="104.47751218592994"/>
%<Winkel size="18" color="violet" id="vierterWinkel" value="75.52248781407008"/>
%<Winkel size="18" color="teal" id="fuenfterWinkel" value="148.95502437185985"/>
%<Winkel size="18" color="lime" id="sechsterWinkel" value="106.56746344221024"/>
%<Winkel size="18" color="LightBlue" id="siebenterWinkel" value="88.95502437185985"/>
%<Winkel size="18" color="LightCoral" id="achterWinkel" value="135.5224878140699"/>
%<Winkel size="18" color="LightCyan" id="neunterWinkel" value="104.4775121859302"/>
%<Feinjustieren Anzahl="9,9"/>
%<Rechenweg>
%P[12]=[81.19895302251368,-23.620797303099163]; P[10]=[31.54207889274421,-17.773160886543323]; D=ab(12,10); A(10,12); N(11,10,12); N(9,10,11); N(1,10,9); M(3,1,10,blauerWinkel); N(2,1,3); N(4,2,3); N(5,2,4); M(16,5,2,gruenerWinkel); N(15,16,5); N(17,16,15); N(18,16,17); M(37,18,16,orangerWinkel); N(36,18,37); N(35,36,37); N(26,36,35); M(25,26,36,vierterWinkel); N(23,26,25); N(24,23,25); N(22,23,24); M(31,22,23,fuenfterWinkel); N(30,31,22); N(32,31,30); N(33,31,32); M(50,33,31,sechsterWinkel); N(49,33,50); N(48,49,50); N(40,49,48); M(42,40,49,siebenterWinkel); N(41,40,42); N(43,41,42); N(44,41,43); M(53,44,41,achterWinkel); N(52,53,44); N(54,53,52); N(55,53,54); M(72,55,53,neunterWinkel); N(71,55,72); N(70,71,72); N(63,71,70); Q(59,63,12,2*D,2*D); A(59,63); A(59,12); H(68,12,59,2); A(68,12); L(69,12,68); H(60,63,59,2); A(60,63); L(62,60,63); A(60,59); L(61,59,60); A(61,62); A(68,59); L(67,68,59); A(69,67); N(7,9,11); N(20,37,17); N(28,32,30); N(38,35,20); N(46,48,50); N(57,72,54); N(65,69,67); N(73,70,57); N(6,3,7); N(19,20,15); N(27,28,24); N(45,42,46); N(56,57,52); N(64,65,61); N(8,19,6); N(21,20,19); N(29,28,38); N(39,38,20); N(47,56,46); N(58,57,56); N(66,65,73); N(74,73,57); N(13,66,8); N(14,39,21); N(34,29,47); N(51,74,58);
%A(8,7); R(8,7,"green");
%A(29,27); R(29,27,"green");
%A(47,45); R(47,45,"green");
%A(66,64); R(66,64,"green");
%A(14,13); R(14,13,"green");
%A(34,14); R(34,14,"green");
%A(51,13); R(51,13,"green");
%A(51,34); R(51,34,"green"); RA(4,6); A(62,64); A(43,45); A(25,27);
%</Rechenweg>
%
%<Knopf id="Stopp_alleWinkel" color="LightGrey"/>
%
%<Knopf id="Start_blauerWinkel" color="blue"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#blauerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_blauerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_gruenerWinkel" color="green"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#gruenerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_gruenerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_orangerWinkel" color="orange"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#orangerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_orangerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_vierterWinkel" color="violet"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#vierterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_vierterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_fuenfterWinkel" color="teal"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#fuenfterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_fuenfterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_sechsterWinkel" color="lime"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#sechsterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_sechsterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_siebenterWinkel" color="LightBlue"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#siebenterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_siebenterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_achterWinkel" color="LightCoral"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#achterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_achterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_neunterWinkel" color="LightCyan"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#neunterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_neunterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LightBlue}{rgb}{0.68,0.84,0.90}
\definecolor{LightCoral}{rgb}{0.94,0.50,0.50}
\definecolor{LightCyan}{rgb}{0.88,1.00,1.00}
\definecolor{Lime}{rgb}{0.00,1.00,0.00}
\definecolor{LimeGreen}{rgb}{0.20,0.80,0.20}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
\definecolor{Teal}{rgb}{0.00,0.50,0.50}
\definecolor{Violet}{rgb}{0.93,0.51,0.93}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.85/0.23,
2/1.06/0.85,
3/1.99/1.22,
4/1.20/1.84,
5/0.27/1.46,
6/2.12/2.22,
7/3.05/1.84,
8/2.91/2.83,
9/2.45/1.04,
10/2.84/0.12,
11/3.44/0.92,
12/3.84/0.00,
13/3.84/2.45,
14/3.70/3.44,
15/1.06/2.07,
16/0.14/2.45,
17/0.93/3.06,
18/0.00/3.44,
19/1.99/2.45,
20/1.85/3.44,
21/2.78/3.06,
22/1.85/6.65,
23/1.06/6.03,
24/1.99/5.66,
25/1.20/5.04,
26/0.27/5.42,
27/2.12/4.67,
28/3.05/5.04,
29/2.91/4.05,
30/2.45/5.85,
31/2.84/6.76,
32/3.44/5.96,
33/3.84/6.88,
34/3.84/4.43,
35/1.06/4.81,
36/0.14/4.43,
37/0.93/3.82,
38/1.99/4.43,
39/2.78/3.82,
40/5.82/6.65,
41/6.61/6.03,
42/5.69/5.66,
43/6.48/5.04,
44/7.40/5.42,
45/5.55/4.67,
46/4.63/5.04,
47/4.76/4.05,
48/5.23/5.85,
49/4.83/6.76,
50/4.23/5.96,
51/3.97/3.44,
52/6.61/4.81,
53/7.54/4.43,
54/6.75/3.82,
55/7.68/3.44,
56/5.69/4.43,
57/5.82/3.44,
58/4.90/3.82,
59/5.82/0.23,
60/6.61/0.85,
61/5.69/1.22,
62/6.48/1.84,
63/7.40/1.46,
64/5.55/2.22,
65/4.63/1.84,
66/4.76/2.83,
67/5.23/1.04,
68/4.83/0.12,
69/4.23/0.92,
70/6.61/2.07,
71/7.54/2.45,
72/6.75/3.06,
73/5.69/2.45,
74/4.90/3.06}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
1/353.28/442.24/0.4/Blue,
5/322.24/457.76/0.4/Green,
18/277.76/382.24/0.4/Orange,
26/262.24/337.76/0.4/Violet,
22/217.76/366.72/0.4/Teal,
33/186.72/293.28/0.4/Lime,
40/173.28/262.24/0.4/LightBlue,
44/142.24/277.76/0.4/LightCoral,
55/97.76/202.24/0.4/LightCyan}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
1/10, 1/9,
2/1, 2/3,
3/1,
4/2, 4/3, 4/6,
5/2, 5/4,
6/3, 6/7,
7/9, 7/11,
8/19, 8/6, 8/7,
9/10, 9/11,
10/12,
11/10, 11/12,
13/66, 13/8,
14/39, 14/21, 14/13,
15/16, 15/5,
16/5,
17/16, 17/15,
18/16, 18/17,
19/20, 19/15,
20/37, 20/17,
21/20, 21/19,
22/23, 22/24,
23/26, 23/25,
24/23, 24/25,
25/26, 25/27,
26/36, 26/35,
27/28, 27/24,
28/32, 28/30,
29/28, 29/38, 29/27,
30/31, 30/22,
31/22,
32/31, 32/30,
33/31, 33/32,
34/29, 34/47, 34/14,
35/36, 35/37,
36/18, 36/37,
37/18,
38/35, 38/20,
39/38, 39/20,
40/49, 40/48,
41/40, 41/42,
42/40,
43/41, 43/42, 43/45,
44/41, 44/43,
45/42, 45/46,
46/48, 46/50,
47/56, 47/46, 47/45,
48/49, 48/50,
49/33, 49/50,
50/33,
51/74, 51/58, 51/13, 51/34,
52/53, 52/44,
53/44,
54/53, 54/52,
55/53, 55/54,
56/57, 56/52,
57/72, 57/54,
58/57, 58/56,
60/63, 60/59,
61/59, 61/60, 61/62,
62/60, 62/63, 62/64,
63/71, 63/70,
64/65, 64/61,
65/69, 65/67,
66/65, 66/73, 66/64,
67/68, 67/59,
68/12, 68/59,
69/12, 69/68, 69/67,
70/71, 70/72,
71/55, 71/72,
72/55,
73/70, 73/57,
74/73, 74/57}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,74}
\fill[blue] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[Green,very thick] (p-8) -- (p-7);
\draw[Green,very thick] (p-29) -- (p-27);
\draw[Green,very thick] (p-47) -- (p-45);
\draw[Green,very thick] (p-66) -- (p-64);
\draw[Green,very thick] (p-14) -- (p-13);
\draw[Green,very thick] (p-34) -- (p-14);
\draw[Green,very thick] (p-51) -- (p-13);
\draw[Green,very thick] (p-51) -- (p-34);
\draw[LimeGreen,very thick] (p-4) -- (p-6);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
1/353.28/442.24/0.4/Blue,
5/322.24/457.76/0.4/Green,
18/277.76/382.24/0.4/Orange,
26/262.24/337.76/0.4/Violet,
22/217.76/366.72/0.4/Teal,
33/186.72/293.28/0.4/Lime,
40/173.28/262.24/0.4/LightBlue,
44/142.24/277.76/0.4/LightCoral,
55/97.76/202.24/0.4/LightCyan}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/292,
2/172,
3/52,
4/52,
5/248,
6/52,
7/308,
8/68,
9/83,
10/323,
11/23,
12/323,
13/235,
14/62,
15/308,
16/128,
17/68,
18/128,
19/248,
20/128,
21/8,
22/68,
23/128,
24/8,
25/308,
26/188,
27/308,
28/52,
29/292,
30/277,
31/97,
32/277,
33/143,
34/55,
35/52,
36/112,
37/292,
38/112,
39/352,
40/112,
41/352,
42/112,
43/292,
44/68,
45/8,
46/263,
47/248,
48/263,
49/83,
50/143,
51/123,
52/188,
53/8,
54/188,
55/52,
56/68,
57/52,
58/188,
59/337,
60/308,
61/248,
62/68,
63/292,
64/352,
65/97,
66/112,
67/37,
68/277,
69/97,
70/172,
71/292,
72/112,
73/292,
74/172}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/ed96b1fe62895f90d8327e84df17df57.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1897-1</Bildtext>
%<Ausrichten von=\"1\" nach=\"2\"/>
%<Winkel size=\"18\" color=\"blue\" id=\"blauerWinkel\" value=\"88.95502437185986\"/>
%<Winkel size=\"18\" color=\"green\" id=\"gruenerWinkel\" value=\"135.52248781407008\"/>
%<Winkel size=\"18\" color=\"orange\" id=\"orangerWinkel\" value=\"104.47751218592994\"/>
%<Winkel size=\"18\" color=\"violet\" id=\"vierterWinkel\" value=\"75.52248781407008\"/>
%<Winkel size=\"18\" color=\"teal\" id=\"fuenfterWinkel\" value=\"148.95502437185985\"/>
%<Winkel size=\"18\" color=\"lime\" id=\"sechsterWinkel\" value=\"106.56746344221024\"/>
%<Winkel size=\"18\" color=\"LightBlue\" id=\"siebenterWinkel\" value=\"88.95502437185985\"/>
%<Winkel size=\"18\" color=\"LightCoral\" id=\"achterWinkel\" value=\"135.5224878140699\"/>
%<Winkel size=\"18\" color=\"LightCyan\" id=\"neunterWinkel\" value=\"104.4775121859302\"/>
%<Feinjustieren Anzahl=\"9,9\"/>
%<Rechenweg>
%P[12]=[81.19895302251368,-23.620797303099163]; P[10]=[31.54207889274421,-17.773160886543323]; D=ab(12,10); A(10,12); N(11,10,12); N(9,10,11); N(1,10,9); M(3,1,10,blauerWinkel); N(2,1,3); N(4,2,3); N(5,2,4); M(16,5,2,gruenerWinkel); N(15,16,5); N(17,16,15); N(18,16,17); M(37,18,16,orangerWinkel); N(36,18,37); N(35,36,37); N(26,36,35); M(25,26,36,vierterWinkel); N(23,26,25); N(24,23,25); N(22,23,24); M(31,22,23,fuenfterWinkel); N(30,31,22); N(32,31,30); N(33,31,32); M(50,33,31,sechsterWinkel); N(49,33,50); N(48,49,50); N(40,49,48); M(42,40,49,siebenterWinkel); N(41,40,42); N(43,41,42); N(44,41,43); M(53,44,41,achterWinkel); N(52,53,44); N(54,53,52); N(55,53,54); M(72,55,53,neunterWinkel); N(71,55,72); N(70,71,72); N(63,71,70); Q(59,63,12,2*D,2*D); A(59,63); A(59,12); H(68,12,59,2); A(68,12); L(69,12,68); H(60,63,59,2); A(60,63); L(62,60,63); A(60,59); L(61,59,60); A(61,62); A(68,59); L(67,68,59); A(69,67); N(7,9,11); N(20,37,17); N(28,32,30); N(38,35,20); N(46,48,50); N(57,72,54); N(65,69,67); N(73,70,57); N(6,3,7); N(19,20,15); N(27,28,24); N(45,42,46); N(56,57,52); N(64,65,61); N(8,19,6); N(21,20,19); N(29,28,38); N(39,38,20); N(47,56,46); N(58,57,56); N(66,65,73); N(74,73,57); N(13,66,8); N(14,39,21); N(34,29,47); N(51,74,58);
%A(8,7); R(8,7,\"green\");
%A(29,27); R(29,27,\"green\");
%A(47,45); R(47,45,\"green\");
%A(66,64); R(66,64,\"green\");
%A(14,13); R(14,13,\"green\");
%A(34,14); R(34,14,\"green\");
%A(51,13); R(51,13,\"green\");
%A(51,34); R(51,34,\"green\"); RA(4,6); A(62,64); A(43,45); A(25,27);
%</Rechenweg>
%
%<Knopf id=\"Stopp_alleWinkel\" color=\"LightGrey\"/>
%
%<Knopf id=\"Start_blauerWinkel\" color=\"blue\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#blauerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_blauerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_gruenerWinkel\" color=\"green\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#gruenerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_gruenerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_orangerWinkel\" color=\"orange\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#orangerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_orangerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_vierterWinkel\" color=\"violet\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#vierterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_vierterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_fuenfterWinkel\" color=\"teal\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#fuenfterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_fuenfterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_sechsterWinkel\" color=\"lime\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#sechsterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_sechsterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_siebenterWinkel\" color=\"LightBlue\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#siebenterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_siebenterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_achterWinkel\" color=\"LightCoral\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#achterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_achterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_neunterWinkel\" color=\"LightCyan\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#neunterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_neunterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LightBlue}{rgb}{0.68,0.84,0.90}
\definecolor{LightCoral}{rgb}{0.94,0.50,0.50}
\definecolor{LightCyan}{rgb}{0.88,1.00,1.00}
\definecolor{Lime}{rgb}{0.00,1.00,0.00}
\definecolor{LimeGreen}{rgb}{0.20,0.80,0.20}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
\definecolor{Teal}{rgb}{0.00,0.50,0.50}
\definecolor{Violet}{rgb}{0.93,0.51,0.93}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.85/0.23,
2/1.06/0.85,
3/1.99/1.22,
4/1.20/1.84,
5/0.27/1.46,
6/2.12/2.22,
7/3.05/1.84,
8/2.91/2.83,
9/2.45/1.04,
10/2.84/0.12,
11/3.44/0.92,
12/3.84/0.00,
13/3.84/2.45,
14/3.70/3.44,
15/1.06/2.07,
16/0.14/2.45,
17/0.93/3.06,
18/0.00/3.44,
19/1.99/2.45,
20/1.85/3.44,
21/2.78/3.06,
22/1.85/6.65,
23/1.06/6.03,
24/1.99/5.66,
25/1.20/5.04,
26/0.27/5.42,
27/2.12/4.67,
28/3.05/5.04,
29/2.91/4.05,
30/2.45/5.85,
31/2.84/6.76,
32/3.44/5.96,
33/3.84/6.88,
34/3.84/4.43,
35/1.06/4.81,
36/0.14/4.43,
37/0.93/3.82,
38/1.99/4.43,
39/2.78/3.82,
40/5.82/6.65,
41/6.61/6.03,
42/5.69/5.66,
43/6.48/5.04,
44/7.40/5.42,
45/5.55/4.67,
46/4.63/5.04,
47/4.76/4.05,
48/5.23/5.85,
49/4.83/6.76,
50/4.23/5.96,
51/3.97/3.44,
52/6.61/4.81,
53/7.54/4.43,
54/6.75/3.82,
55/7.68/3.44,
56/5.69/4.43,
57/5.82/3.44,
58/4.90/3.82,
59/5.82/0.23,
60/6.61/0.85,
61/5.69/1.22,
62/6.48/1.84,
63/7.40/1.46,
64/5.55/2.22,
65/4.63/1.84,
66/4.76/2.83,
67/5.23/1.04,
68/4.83/0.12,
69/4.23/0.92,
70/6.61/2.07,
71/7.54/2.45,
72/6.75/3.06,
73/5.69/2.45,
74/4.90/3.06}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
1/353.28/442.24/0.4/Blue,
5/322.24/457.76/0.4/Green,
18/277.76/382.24/0.4/Orange,
26/262.24/337.76/0.4/Violet,
22/217.76/366.72/0.4/Teal,
33/186.72/293.28/0.4/Lime,
40/173.28/262.24/0.4/LightBlue,
44/142.24/277.76/0.4/LightCoral,
55/97.76/202.24/0.4/LightCyan}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
1/10, 1/9,
2/1, 2/3,
3/1,
4/2, 4/3, 4/6,
5/2, 5/4,
6/3, 6/7,
7/9, 7/11,
8/19, 8/6, 8/7,
9/10, 9/11,
10/12,
11/10, 11/12,
13/66, 13/8,
14/39, 14/21, 14/13,
15/16, 15/5,
16/5,
17/16, 17/15,
18/16, 18/17,
19/20, 19/15,
20/37, 20/17,
21/20, 21/19,
22/23, 22/24,
23/26, 23/25,
24/23, 24/25,
25/26, 25/27,
26/36, 26/35,
27/28, 27/24,
28/32, 28/30,
29/28, 29/38, 29/27,
30/31, 30/22,
31/22,
32/31, 32/30,
33/31, 33/32,
34/29, 34/47, 34/14,
35/36, 35/37,
36/18, 36/37,
37/18,
38/35, 38/20,
39/38, 39/20,
40/49, 40/48,
41/40, 41/42,
42/40,
43/41, 43/42, 43/45,
44/41, 44/43,
45/42, 45/46,
46/48, 46/50,
47/56, 47/46, 47/45,
48/49, 48/50,
49/33, 49/50,
50/33,
51/74, 51/58, 51/13, 51/34,
52/53, 52/44,
53/44,
54/53, 54/52,
55/53, 55/54,
56/57, 56/52,
57/72, 57/54,
58/57, 58/56,
60/63, 60/59,
61/59, 61/60, 61/62,
62/60, 62/63, 62/64,
63/71, 63/70,
64/65, 64/61,
65/69, 65/67,
66/65, 66/73, 66/64,
67/68, 67/59,
68/12, 68/59,
69/12, 69/68, 69/67,
70/71, 70/72,
71/55, 71/72,
72/55,
73/70, 73/57,
74/73, 74/57}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,74}
\fill[blue] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[Green,very thick] (p-8) -- (p-7);
\draw[Green,very thick] (p-29) -- (p-27);
\draw[Green,very thick] (p-47) -- (p-45);
\draw[Green,very thick] (p-66) -- (p-64);
\draw[Green,very thick] (p-14) -- (p-13);
\draw[Green,very thick] (p-34) -- (p-14);
\draw[Green,very thick] (p-51) -- (p-13);
\draw[Green,very thick] (p-51) -- (p-34);
\draw[LimeGreen,very thick] (p-4) -- (p-6);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
1/353.28/442.24/0.4/Blue,
5/322.24/457.76/0.4/Green,
18/277.76/382.24/0.4/Orange,
26/262.24/337.76/0.4/Violet,
22/217.76/366.72/0.4/Teal,
33/186.72/293.28/0.4/Lime,
40/173.28/262.24/0.4/LightBlue,
44/142.24/277.76/0.4/LightCoral,
55/97.76/202.24/0.4/LightCyan}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/292,
2/172,
3/52,
4/52,
5/248,
6/52,
7/308,
8/68,
9/83,
10/323,
11/23,
12/323,
13/235,
14/62,
15/308,
16/128,
17/68,
18/128,
19/248,
20/128,
21/8,
22/68,
23/128,
24/8,
25/308,
26/188,
27/308,
28/52,
29/292,
30/277,
31/97,
32/277,
33/143,
34/55,
35/52,
36/112,
37/292,
38/112,
39/352,
40/112,
41/352,
42/112,
43/292,
44/68,
45/8,
46/263,
47/248,
48/263,
49/83,
50/143,
51/123,
52/188,
53/8,
54/188,
55/52,
56/68,
57/52,
58/188,
59/337,
60/308,
61/248,
62/68,
63/292,
64/352,
65/97,
66/112,
67/37,
68/277,
69/97,
70/172,
71/292,
72/112,
73/292,
74/172}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
ohne 8-13:
74 Knoten, 2×Grad 2, 4×Grad 3, 64×Grad 4, 4×Grad 6, 0 Überschneidungen
148 Kanten, minimal 0.99999999999998623323, maximal 1.00000000000001487699
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1897-2</Bildtext>
%<Ausrichten von="1" nach="2"/>
%<Winkel size="18" color="blue" id="blauerWinkel" value="88.95502437185986"/>
%<Winkel size="18" color="green" id="gruenerWinkel" value="135.5224878140701"/>
%<Winkel size="18" color="orange" id="orangerWinkel" value="104.4775121859299"/>
%<Winkel size="18" color="violet" id="vierterWinkel" value="75.5224878140701"/>
%<Winkel size="18" color="teal" id="fuenfterWinkel" value="148.95502437185988"/>
%<Winkel size="18" color="lime" id="sechsterWinkel" value="106.56746344221018"/>
%<Winkel size="18" color="LightBlue" id="siebenterWinkel" value="88.95502437185979"/>
%<Winkel size="18" color="LightCoral" id="achterWinkel" value="135.52248781407013"/>
%<Winkel size="18" color="LightCyan" id="neunterWinkel" value="104.47751218592983"/>
%<Feinjustieren Anzahl="9,9"/>
%<Rechenweg>
%P[12]=[81.19895302251368,-23.620797303099163]; P[10]=[31.54207889274421,-17.773160886543323]; D=ab(12,10); A(10,12); N(11,10,12); N(9,10,11); N(1,10,9); M(3,1,10,blauerWinkel); N(2,1,3); N(4,2,3); N(5,2,4); M(16,5,2,gruenerWinkel); N(15,16,5); N(17,16,15); N(18,16,17); M(37,18,16,orangerWinkel); N(36,18,37); N(35,36,37); N(26,36,35); M(25,26,36,vierterWinkel); N(23,26,25); N(24,23,25); N(22,23,24); M(31,22,23,fuenfterWinkel); N(30,31,22); N(32,31,30); N(33,31,32); M(50,33,31,sechsterWinkel); N(49,33,50); N(48,49,50); N(40,49,48); M(42,40,49,siebenterWinkel); N(41,40,42); N(43,41,42); N(44,41,43); M(53,44,41,achterWinkel); N(52,53,44); N(54,53,52); N(55,53,54); M(72,55,53,neunterWinkel); N(71,55,72); N(70,71,72); N(63,71,70); Q(59,63,12,2*D,2*D); A(59,63); A(59,12); H(68,12,59,2); A(68,12); L(69,12,68); H(60,63,59,2); A(60,63); L(62,60,63); A(60,59); L(61,59,60); A(61,62); A(68,59); L(67,68,59); A(69,67); N(7,9,11); N(20,37,17); N(28,32,30); N(38,35,20); N(46,48,50); N(57,72,54); N(65,69,67); N(73,70,57); N(6,3,7); N(19,20,15); N(27,28,24); N(45,42,46); N(56,57,52); N(64,65,61); N(8,19,6); N(21,20,19); N(29,28,38); N(39,38,20); N(47,56,46); N(58,57,56); N(66,65,73); N(74,73,57); N(14,39,21); N(51,74,58); N(13,51,14); N(34,14,51);
%A(8,7); R(8,7,"green");
%A(29,27); R(29,27,"green");
%A(47,45); R(47,45,"green");
%A(66,64); R(66,64,"green");
%A(14,8); R(14,8,"green");
%A(14,29); R(14,29,"green");
%A(51,47); R(51,47,"green");
%A(51,66); R(51,66,"green"); RA(4,6); A(62,64); A(43,45); A(25,27);
%</Rechenweg>
%
%<Knopf id="Stopp_alleWinkel" color="LightGrey"/>
%
%<Knopf id="Start_blauerWinkel" color="blue"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#blauerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_blauerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_gruenerWinkel" color="green"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#gruenerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_gruenerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_orangerWinkel" color="orange"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#orangerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_orangerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_vierterWinkel" color="violet"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#vierterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_vierterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_fuenfterWinkel" color="teal"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#fuenfterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_fuenfterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_sechsterWinkel" color="lime"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#sechsterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_sechsterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_siebenterWinkel" color="LightBlue"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#siebenterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_siebenterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_achterWinkel" color="LightCoral"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#achterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_achterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_neunterWinkel" color="LightCyan"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#neunterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_neunterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LightBlue}{rgb}{0.68,0.84,0.90}
\definecolor{LightCoral}{rgb}{0.94,0.50,0.50}
\definecolor{LightCyan}{rgb}{0.88,1.00,1.00}
\definecolor{Lime}{rgb}{0.00,1.00,0.00}
\definecolor{LimeGreen}{rgb}{0.20,0.80,0.20}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
\definecolor{Teal}{rgb}{0.00,0.50,0.50}
\definecolor{Violet}{rgb}{0.93,0.51,0.93}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.85/0.23,
2/1.06/0.85,
3/1.99/1.22,
4/1.20/1.84,
5/0.27/1.46,
6/2.12/2.22,
7/3.05/1.84,
8/2.91/2.83,
9/2.45/1.04,
10/2.84/0.12,
11/3.44/0.92,
12/3.84/0.00,
13/3.84/2.45,
14/3.70/3.44,
15/1.06/2.07,
16/0.14/2.45,
17/0.93/3.06,
18/0.00/3.44,
19/1.99/2.45,
20/1.85/3.44,
21/2.78/3.06,
22/1.85/6.65,
23/1.06/6.03,
24/1.99/5.66,
25/1.20/5.04,
26/0.27/5.42,
27/2.12/4.67,
28/3.05/5.04,
29/2.91/4.05,
30/2.45/5.85,
31/2.84/6.76,
32/3.44/5.96,
33/3.84/6.88,
34/3.84/4.43,
35/1.06/4.81,
36/0.14/4.43,
37/0.93/3.82,
38/1.99/4.43,
39/2.78/3.82,
40/5.82/6.65,
41/6.61/6.03,
42/5.69/5.66,
43/6.48/5.04,
44/7.40/5.42,
45/5.55/4.67,
46/4.63/5.04,
47/4.76/4.05,
48/5.23/5.85,
49/4.83/6.76,
50/4.23/5.96,
51/3.97/3.44,
52/6.61/4.81,
53/7.54/4.43,
54/6.75/3.82,
55/7.68/3.44,
56/5.69/4.43,
57/5.82/3.44,
58/4.90/3.82,
59/5.82/0.23,
60/6.61/0.85,
61/5.69/1.22,
62/6.48/1.84,
63/7.40/1.46,
64/5.55/2.22,
65/4.63/1.84,
66/4.76/2.83,
67/5.23/1.04,
68/4.83/0.12,
69/4.23/0.92,
70/6.61/2.07,
71/7.54/2.45,
72/6.75/3.06,
73/5.69/2.45,
74/4.90/3.06}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
1/353.28/442.24/0.4/Blue,
5/322.24/457.76/0.4/Green,
18/277.76/382.24/0.4/Orange,
26/262.24/337.76/0.4/Violet,
22/217.76/366.72/0.4/Teal,
33/186.72/293.28/0.4/Lime,
40/173.28/262.24/0.4/LightBlue,
44/142.24/277.76/0.4/LightCoral,
55/97.76/202.24/0.4/LightCyan}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
1/10, 1/9,
2/1, 2/3,
3/1,
4/2, 4/3, 4/6,
5/2, 5/4,
6/3, 6/7,
7/9, 7/11,
8/19, 8/6, 8/7,
9/10, 9/11,
10/12,
11/10, 11/12,
13/51, 13/14,
14/39, 14/21, 14/8, 14/29,
15/16, 15/5,
16/5,
17/16, 17/15,
18/16, 18/17,
19/20, 19/15,
20/37, 20/17,
21/20, 21/19,
22/23, 22/24,
23/26, 23/25,
24/23, 24/25,
25/26, 25/27,
26/36, 26/35,
27/28, 27/24,
28/32, 28/30,
29/28, 29/38, 29/27,
30/31, 30/22,
31/22,
32/31, 32/30,
33/31, 33/32,
34/14, 34/51,
35/36, 35/37,
36/18, 36/37,
37/18,
38/35, 38/20,
39/38, 39/20,
40/49, 40/48,
41/40, 41/42,
42/40,
43/41, 43/42, 43/45,
44/41, 44/43,
45/42, 45/46,
46/48, 46/50,
47/56, 47/46, 47/45,
48/49, 48/50,
49/33, 49/50,
50/33,
51/74, 51/58, 51/47, 51/66,
52/53, 52/44,
53/44,
54/53, 54/52,
55/53, 55/54,
56/57, 56/52,
57/72, 57/54,
58/57, 58/56,
60/63, 60/59,
61/59, 61/60, 61/62,
62/60, 62/63, 62/64,
63/71, 63/70,
64/65, 64/61,
65/69, 65/67,
66/65, 66/73, 66/64,
67/68, 67/59,
68/12, 68/59,
69/12, 69/68, 69/67,
70/71, 70/72,
71/55, 71/72,
72/55,
73/70, 73/57,
74/73, 74/57}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,74}
\fill[blue] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[Green,very thick] (p-8) -- (p-7);
\draw[Green,very thick] (p-29) -- (p-27);
\draw[Green,very thick] (p-47) -- (p-45);
\draw[Green,very thick] (p-66) -- (p-64);
\draw[Green,very thick] (p-14) -- (p-8);
\draw[Green,very thick] (p-14) -- (p-29);
\draw[Green,very thick] (p-51) -- (p-47);
\draw[Green,very thick] (p-51) -- (p-66);
\draw[LimeGreen,very thick] (p-4) -- (p-6);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
1/353.28/442.24/0.4/Blue,
5/322.24/457.76/0.4/Green,
18/277.76/382.24/0.4/Orange,
26/262.24/337.76/0.4/Violet,
22/217.76/366.72/0.4/Teal,
33/186.72/293.28/0.4/Lime,
40/173.28/262.24/0.4/LightBlue,
44/142.24/277.76/0.4/LightCoral,
55/97.76/202.24/0.4/LightCyan}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/292,
2/172,
3/52,
4/52,
5/172,
6/52,
7/308,
8/68,
9/83,
10/323,
11/23,
12/217,
13/93,
14/295,
15/308,
16/128,
17/68,
18/128,
19/248,
20/128,
21/8,
22/68,
23/188,
24/8,
25/188,
26/188,
27/308,
28/52,
29/292,
30/217,
31/157,
32/37,
33/37,
34/273,
35/352,
36/112,
37/292,
38/112,
39/352,
40/23,
41/352,
42/172,
43/352,
44/68,
45/232,
46/128,
47/248,
48/23,
49/23,
50/263,
51/115,
52/188,
53/68,
54/248,
55/308,
56/68,
57/308,
58/188,
59/248,
60/248,
61/128,
62/8,
63/292,
64/128,
65/232,
66/112,
67/37,
68/277,
69/217,
70/172,
71/352,
72/112,
73/292,
74/172}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/d7412f6100ef3c7be9b8363cbdea4a1f.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1897-2</Bildtext>
%<Ausrichten von=\"1\" nach=\"2\"/>
%<Winkel size=\"18\" color=\"blue\" id=\"blauerWinkel\" value=\"88.95502437185986\"/>
%<Winkel size=\"18\" color=\"green\" id=\"gruenerWinkel\" value=\"135.5224878140701\"/>
%<Winkel size=\"18\" color=\"orange\" id=\"orangerWinkel\" value=\"104.4775121859299\"/>
%<Winkel size=\"18\" color=\"violet\" id=\"vierterWinkel\" value=\"75.5224878140701\"/>
%<Winkel size=\"18\" color=\"teal\" id=\"fuenfterWinkel\" value=\"148.95502437185988\"/>
%<Winkel size=\"18\" color=\"lime\" id=\"sechsterWinkel\" value=\"106.56746344221018\"/>
%<Winkel size=\"18\" color=\"LightBlue\" id=\"siebenterWinkel\" value=\"88.95502437185979\"/>
%<Winkel size=\"18\" color=\"LightCoral\" id=\"achterWinkel\" value=\"135.52248781407013\"/>
%<Winkel size=\"18\" color=\"LightCyan\" id=\"neunterWinkel\" value=\"104.47751218592983\"/>
%<Feinjustieren Anzahl=\"9,9\"/>
%<Rechenweg>
%P[12]=[81.19895302251368,-23.620797303099163]; P[10]=[31.54207889274421,-17.773160886543323]; D=ab(12,10); A(10,12); N(11,10,12); N(9,10,11); N(1,10,9); M(3,1,10,blauerWinkel); N(2,1,3); N(4,2,3); N(5,2,4); M(16,5,2,gruenerWinkel); N(15,16,5); N(17,16,15); N(18,16,17); M(37,18,16,orangerWinkel); N(36,18,37); N(35,36,37); N(26,36,35); M(25,26,36,vierterWinkel); N(23,26,25); N(24,23,25); N(22,23,24); M(31,22,23,fuenfterWinkel); N(30,31,22); N(32,31,30); N(33,31,32); M(50,33,31,sechsterWinkel); N(49,33,50); N(48,49,50); N(40,49,48); M(42,40,49,siebenterWinkel); N(41,40,42); N(43,41,42); N(44,41,43); M(53,44,41,achterWinkel); N(52,53,44); N(54,53,52); N(55,53,54); M(72,55,53,neunterWinkel); N(71,55,72); N(70,71,72); N(63,71,70); Q(59,63,12,2*D,2*D); A(59,63); A(59,12); H(68,12,59,2); A(68,12); L(69,12,68); H(60,63,59,2); A(60,63); L(62,60,63); A(60,59); L(61,59,60); A(61,62); A(68,59); L(67,68,59); A(69,67); N(7,9,11); N(20,37,17); N(28,32,30); N(38,35,20); N(46,48,50); N(57,72,54); N(65,69,67); N(73,70,57); N(6,3,7); N(19,20,15); N(27,28,24); N(45,42,46); N(56,57,52); N(64,65,61); N(8,19,6); N(21,20,19); N(29,28,38); N(39,38,20); N(47,56,46); N(58,57,56); N(66,65,73); N(74,73,57); N(14,39,21); N(51,74,58); N(13,51,14); N(34,14,51);
%A(8,7); R(8,7,\"green\");
%A(29,27); R(29,27,\"green\");
%A(47,45); R(47,45,\"green\");
%A(66,64); R(66,64,\"green\");
%A(14,8); R(14,8,\"green\");
%A(14,29); R(14,29,\"green\");
%A(51,47); R(51,47,\"green\");
%A(51,66); R(51,66,\"green\"); RA(4,6); A(62,64); A(43,45); A(25,27);
%</Rechenweg>
%
%<Knopf id=\"Stopp_alleWinkel\" color=\"LightGrey\"/>
%
%<Knopf id=\"Start_blauerWinkel\" color=\"blue\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#blauerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_blauerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_gruenerWinkel\" color=\"green\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#gruenerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_gruenerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_orangerWinkel\" color=\"orange\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#orangerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_orangerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_vierterWinkel\" color=\"violet\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#vierterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_vierterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_fuenfterWinkel\" color=\"teal\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#fuenfterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_fuenfterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_sechsterWinkel\" color=\"lime\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#sechsterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_sechsterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_siebenterWinkel\" color=\"LightBlue\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#siebenterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_siebenterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_achterWinkel\" color=\"LightCoral\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#achterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_achterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_neunterWinkel\" color=\"LightCyan\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#neunterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_neunterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LightBlue}{rgb}{0.68,0.84,0.90}
\definecolor{LightCoral}{rgb}{0.94,0.50,0.50}
\definecolor{LightCyan}{rgb}{0.88,1.00,1.00}
\definecolor{Lime}{rgb}{0.00,1.00,0.00}
\definecolor{LimeGreen}{rgb}{0.20,0.80,0.20}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
\definecolor{Teal}{rgb}{0.00,0.50,0.50}
\definecolor{Violet}{rgb}{0.93,0.51,0.93}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.85/0.23,
2/1.06/0.85,
3/1.99/1.22,
4/1.20/1.84,
5/0.27/1.46,
6/2.12/2.22,
7/3.05/1.84,
8/2.91/2.83,
9/2.45/1.04,
10/2.84/0.12,
11/3.44/0.92,
12/3.84/0.00,
13/3.84/2.45,
14/3.70/3.44,
15/1.06/2.07,
16/0.14/2.45,
17/0.93/3.06,
18/0.00/3.44,
19/1.99/2.45,
20/1.85/3.44,
21/2.78/3.06,
22/1.85/6.65,
23/1.06/6.03,
24/1.99/5.66,
25/1.20/5.04,
26/0.27/5.42,
27/2.12/4.67,
28/3.05/5.04,
29/2.91/4.05,
30/2.45/5.85,
31/2.84/6.76,
32/3.44/5.96,
33/3.84/6.88,
34/3.84/4.43,
35/1.06/4.81,
36/0.14/4.43,
37/0.93/3.82,
38/1.99/4.43,
39/2.78/3.82,
40/5.82/6.65,
41/6.61/6.03,
42/5.69/5.66,
43/6.48/5.04,
44/7.40/5.42,
45/5.55/4.67,
46/4.63/5.04,
47/4.76/4.05,
48/5.23/5.85,
49/4.83/6.76,
50/4.23/5.96,
51/3.97/3.44,
52/6.61/4.81,
53/7.54/4.43,
54/6.75/3.82,
55/7.68/3.44,
56/5.69/4.43,
57/5.82/3.44,
58/4.90/3.82,
59/5.82/0.23,
60/6.61/0.85,
61/5.69/1.22,
62/6.48/1.84,
63/7.40/1.46,
64/5.55/2.22,
65/4.63/1.84,
66/4.76/2.83,
67/5.23/1.04,
68/4.83/0.12,
69/4.23/0.92,
70/6.61/2.07,
71/7.54/2.45,
72/6.75/3.06,
73/5.69/2.45,
74/4.90/3.06}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
1/353.28/442.24/0.4/Blue,
5/322.24/457.76/0.4/Green,
18/277.76/382.24/0.4/Orange,
26/262.24/337.76/0.4/Violet,
22/217.76/366.72/0.4/Teal,
33/186.72/293.28/0.4/Lime,
40/173.28/262.24/0.4/LightBlue,
44/142.24/277.76/0.4/LightCoral,
55/97.76/202.24/0.4/LightCyan}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
1/10, 1/9,
2/1, 2/3,
3/1,
4/2, 4/3, 4/6,
5/2, 5/4,
6/3, 6/7,
7/9, 7/11,
8/19, 8/6, 8/7,
9/10, 9/11,
10/12,
11/10, 11/12,
13/51, 13/14,
14/39, 14/21, 14/8, 14/29,
15/16, 15/5,
16/5,
17/16, 17/15,
18/16, 18/17,
19/20, 19/15,
20/37, 20/17,
21/20, 21/19,
22/23, 22/24,
23/26, 23/25,
24/23, 24/25,
25/26, 25/27,
26/36, 26/35,
27/28, 27/24,
28/32, 28/30,
29/28, 29/38, 29/27,
30/31, 30/22,
31/22,
32/31, 32/30,
33/31, 33/32,
34/14, 34/51,
35/36, 35/37,
36/18, 36/37,
37/18,
38/35, 38/20,
39/38, 39/20,
40/49, 40/48,
41/40, 41/42,
42/40,
43/41, 43/42, 43/45,
44/41, 44/43,
45/42, 45/46,
46/48, 46/50,
47/56, 47/46, 47/45,
48/49, 48/50,
49/33, 49/50,
50/33,
51/74, 51/58, 51/47, 51/66,
52/53, 52/44,
53/44,
54/53, 54/52,
55/53, 55/54,
56/57, 56/52,
57/72, 57/54,
58/57, 58/56,
60/63, 60/59,
61/59, 61/60, 61/62,
62/60, 62/63, 62/64,
63/71, 63/70,
64/65, 64/61,
65/69, 65/67,
66/65, 66/73, 66/64,
67/68, 67/59,
68/12, 68/59,
69/12, 69/68, 69/67,
70/71, 70/72,
71/55, 71/72,
72/55,
73/70, 73/57,
74/73, 74/57}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,74}
\fill[blue] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[Green,very thick] (p-8) -- (p-7);
\draw[Green,very thick] (p-29) -- (p-27);
\draw[Green,very thick] (p-47) -- (p-45);
\draw[Green,very thick] (p-66) -- (p-64);
\draw[Green,very thick] (p-14) -- (p-8);
\draw[Green,very thick] (p-14) -- (p-29);
\draw[Green,very thick] (p-51) -- (p-47);
\draw[Green,very thick] (p-51) -- (p-66);
\draw[LimeGreen,very thick] (p-4) -- (p-6);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
1/353.28/442.24/0.4/Blue,
5/322.24/457.76/0.4/Green,
18/277.76/382.24/0.4/Orange,
26/262.24/337.76/0.4/Violet,
22/217.76/366.72/0.4/Teal,
33/186.72/293.28/0.4/Lime,
40/173.28/262.24/0.4/LightBlue,
44/142.24/277.76/0.4/LightCoral,
55/97.76/202.24/0.4/LightCyan}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/292,
2/172,
3/52,
4/52,
5/172,
6/52,
7/308,
8/68,
9/83,
10/323,
11/23,
12/217,
13/93,
14/295,
15/308,
16/128,
17/68,
18/128,
19/248,
20/128,
21/8,
22/68,
23/188,
24/8,
25/188,
26/188,
27/308,
28/52,
29/292,
30/217,
31/157,
32/37,
33/37,
34/273,
35/352,
36/112,
37/292,
38/112,
39/352,
40/23,
41/352,
42/172,
43/352,
44/68,
45/232,
46/128,
47/248,
48/23,
49/23,
50/263,
51/115,
52/188,
53/68,
54/248,
55/308,
56/68,
57/308,
58/188,
59/248,
60/248,
61/128,
62/8,
63/292,
64/128,
65/232,
66/112,
67/37,
68/277,
69/217,
70/172,
71/352,
72/112,
73/292,
74/172}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
ohne 8-7:
74 Knoten, 8×Grad 3, 62×Grad 4, 4×Grad 6, 0 Überschneidungen
148 Kanten, minimal 0.99999999999995581312, maximal 1.00000000000017252866
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1894-3</Bildtext>
%<Ausrichten von="1" nach="2"/>
%<Winkel size="18" color="blue" id="blauerWinkel" value="88.95502437185989"/>
%<Winkel size="18" color="green" id="gruenerWinkel" value="135.52248781407013"/>
%<Winkel size="18" color="orange" id="orangerWinkel" value="104.47751218592992"/>
%<Winkel size="18" color="violet" id="vierterWinkel" value="75.52248781407"/>
%<Winkel size="18" color="teal" id="fuenfterWinkel" value="148.95502437185982"/>
%<Winkel size="18" color="lime" id="sechsterWinkel" value="106.56746344221033"/>
%<Winkel size="18" color="LightBlue" id="siebenterWinkel" value="88.9550243718598"/>
%<Winkel size="18" color="LightCoral" id="achterWinkel" value="135.52248781407002"/>
%<Winkel size="18" color="LightCyan" id="neunterWinkel" value="104.47751218592998"/>
%<Feinjustieren Anzahl="8,8"/>
%<Rechenweg>
%P[12]=[81.19895302251368,-23.620797303099163]; P[10]=[31.54207889274421,-17.773160886543323]; D=ab(12,10); A(10,12); N(11,10,12); N(9,10,11); N(1,10,9); M(3,1,10,blauerWinkel); N(2,1,3); N(4,2,3); N(5,2,4); M(16,5,2,gruenerWinkel); N(15,16,5); N(17,16,15); N(18,16,17); M(37,18,16,orangerWinkel); N(36,18,37); N(35,36,37); N(26,36,35); M(25,26,36,vierterWinkel); N(23,26,25); N(24,23,25); N(22,23,24); M(31,22,23,fuenfterWinkel); N(30,31,22); N(32,31,30); N(33,31,32); M(50,33,31,sechsterWinkel); N(49,33,50); N(48,49,50); N(40,49,48); M(42,40,49,siebenterWinkel); N(41,40,42); N(43,41,42); N(44,41,43); M(53,44,41,achterWinkel); N(52,53,44); N(54,53,52); N(55,53,54); M(72,55,53,neunterWinkel); N(71,55,72); N(70,71,72); N(63,71,70); Q(59,63,12,2*D,2*D); A(59,63); A(59,12); H(68,12,59,2); A(68,12); L(69,12,68); H(60,63,59,2); A(60,63); L(62,60,63); A(60,59); L(61,59,60); A(61,62); A(68,59); L(67,68,59); A(69,67); N(7,9,11); N(20,37,17); N(28,32,30); N(38,35,20); N(46,48,50); N(57,72,54); N(65,69,67); N(73,70,57); N(6,3,7); N(19,20,15); N(27,28,24); N(45,42,46); N(56,57,52); N(64,65,61); N(8,19,6); N(21,20,19); N(29,27,38); N(39,38,20); N(47,56,45); N(58,57,56); N(66,64,73); N(74,73,57); N(13,66,8); N(14,39,21); N(34,29,47); N(51,74,58);
%A(14,8); R(14,8,"green");
%A(14,13); R(14,13,"green");
%A(14,29); R(14,29,"green");
%A(34,14); R(34,14,"green");
%A(51,13); R(51,13,"green");
%A(51,47); R(51,47,"green");
%A(51,34); R(51,34,"green");
%A(51,66); R(51,66,"green"); RA(4,6); A(62,64); A(43,45); A(25,27);
%</Rechenweg>
%
%<Knopf id="Stopp_alleWinkel" color="LightGrey"/>
%
%<Knopf id="Start_blauerWinkel" color="blue"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#blauerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_blauerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_gruenerWinkel" color="green"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#gruenerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_gruenerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_orangerWinkel" color="orange"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#orangerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_orangerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_vierterWinkel" color="violet"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#vierterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_vierterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_fuenfterWinkel" color="teal"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#fuenfterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_fuenfterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_sechsterWinkel" color="lime"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#sechsterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_sechsterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_siebenterWinkel" color="LightBlue"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#siebenterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_siebenterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_achterWinkel" color="LightCoral"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#achterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_achterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_neunterWinkel" color="LightCyan"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#neunterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_neunterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LightBlue}{rgb}{0.68,0.84,0.90}
\definecolor{LightCoral}{rgb}{0.94,0.50,0.50}
\definecolor{LightCyan}{rgb}{0.88,1.00,1.00}
\definecolor{Lime}{rgb}{0.00,1.00,0.00}
\definecolor{LimeGreen}{rgb}{0.20,0.80,0.20}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
\definecolor{Teal}{rgb}{0.00,0.50,0.50}
\definecolor{Violet}{rgb}{0.93,0.51,0.93}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.85/0.23,
2/1.06/0.85,
3/1.99/1.22,
4/1.20/1.84,
5/0.27/1.46,
6/2.12/2.22,
7/3.05/1.84,
8/2.91/2.83,
9/2.45/1.04,
10/2.84/0.12,
11/3.44/0.92,
12/3.84/0.00,
13/3.84/2.45,
14/3.70/3.44,
15/1.06/2.07,
16/0.14/2.45,
17/0.93/3.06,
18/0.00/3.44,
19/1.99/2.45,
20/1.85/3.44,
21/2.78/3.06,
22/1.85/6.65,
23/1.06/6.03,
24/1.99/5.66,
25/1.20/5.04,
26/0.27/5.42,
27/2.12/4.67,
28/3.05/5.04,
29/2.91/4.05,
30/2.45/5.85,
31/2.84/6.76,
32/3.44/5.96,
33/3.84/6.88,
34/3.84/4.43,
35/1.06/4.81,
36/0.14/4.43,
37/0.93/3.82,
38/1.99/4.43,
39/2.78/3.82,
40/5.82/6.65,
41/6.61/6.03,
42/5.69/5.66,
43/6.48/5.04,
44/7.40/5.42,
45/5.55/4.67,
46/4.63/5.04,
47/4.76/4.05,
48/5.23/5.85,
49/4.83/6.76,
50/4.23/5.96,
51/3.97/3.44,
52/6.61/4.81,
53/7.54/4.43,
54/6.75/3.82,
55/7.68/3.44,
56/5.69/4.43,
57/5.82/3.44,
58/4.90/3.82,
59/5.82/0.23,
60/6.61/0.85,
61/5.69/1.22,
62/6.48/1.84,
63/7.40/1.46,
64/5.55/2.22,
65/4.63/1.84,
66/4.76/2.83,
67/5.23/1.04,
68/4.83/0.12,
69/4.23/0.92,
70/6.61/2.07,
71/7.54/2.45,
72/6.75/3.06,
73/5.69/2.45,
74/4.90/3.06}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
1/353.28/442.24/0.4/Blue,
5/322.24/457.76/0.4/Green,
18/277.76/382.24/0.4/Orange,
26/262.24/337.76/0.4/Violet,
22/217.76/366.72/0.4/Teal,
33/186.72/293.28/0.4/Lime,
40/173.28/262.24/0.4/LightBlue,
44/142.24/277.76/0.4/LightCoral,
55/97.76/202.24/0.4/LightCyan}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
1/10, 1/9,
2/1, 2/3,
3/1,
4/2, 4/3, 4/6,
5/2, 5/4,
6/3, 6/7,
7/9, 7/11,
8/19, 8/6,
9/10, 9/11,
10/12,
11/10, 11/12,
13/66, 13/8,
14/39, 14/21, 14/8, 14/13, 14/29,
15/16, 15/5,
16/5,
17/16, 17/15,
18/16, 18/17,
19/20, 19/15,
20/37, 20/17,
21/20, 21/19,
22/23, 22/24,
23/26, 23/25,
24/23, 24/25,
25/26, 25/27,
26/36, 26/35,
27/28, 27/24,
28/32, 28/30,
29/27, 29/38,
30/31, 30/22,
31/22,
32/31, 32/30,
33/31, 33/32,
34/29, 34/47, 34/14,
35/36, 35/37,
36/18, 36/37,
37/18,
38/35, 38/20,
39/38, 39/20,
40/49, 40/48,
41/40, 41/42,
42/40,
43/41, 43/42, 43/45,
44/41, 44/43,
45/42, 45/46,
46/48, 46/50,
47/56, 47/45,
48/49, 48/50,
49/33, 49/50,
50/33,
51/74, 51/58, 51/13, 51/47, 51/34, 51/66,
52/53, 52/44,
53/44,
54/53, 54/52,
55/53, 55/54,
56/57, 56/52,
57/72, 57/54,
58/57, 58/56,
60/63, 60/59,
61/59, 61/60, 61/62,
62/60, 62/63, 62/64,
63/71, 63/70,
64/65, 64/61,
65/69, 65/67,
66/64, 66/73,
67/68, 67/59,
68/12, 68/59,
69/12, 69/68, 69/67,
70/71, 70/72,
71/55, 71/72,
72/55,
73/70, 73/57,
74/73, 74/57}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,74}
\fill[blue] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[Green,very thick] (p-14) -- (p-8);
\draw[Green,very thick] (p-14) -- (p-13);
\draw[Green,very thick] (p-14) -- (p-29);
\draw[Green,very thick] (p-34) -- (p-14);
\draw[Green,very thick] (p-51) -- (p-13);
\draw[Green,very thick] (p-51) -- (p-47);
\draw[Green,very thick] (p-51) -- (p-34);
\draw[Green,very thick] (p-51) -- (p-66);
\draw[LimeGreen,very thick] (p-4) -- (p-6);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
1/353.28/442.24/0.4/Blue,
5/322.24/457.76/0.4/Green,
18/277.76/382.24/0.4/Orange,
26/262.24/337.76/0.4/Violet,
22/217.76/366.72/0.4/Teal,
33/186.72/293.28/0.4/Lime,
40/173.28/262.24/0.4/LightBlue,
44/142.24/277.76/0.4/LightCoral,
55/97.76/202.24/0.4/LightCyan}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/292,
2/172,
3/352,
4/172,
5/172,
6/52,
7/83,
8/188,
9/83,
10/323,
11/23,
12/217,
13/308,
14/68,
15/308,
16/188,
17/68,
18/128,
19/248,
20/232,
21/8,
22/68,
23/128,
24/68,
25/308,
26/112,
27/308,
28/277,
29/172,
30/277,
31/97,
32/277,
33/143,
34/128,
35/52,
36/172,
37/352,
38/112,
39/352,
40/23,
41/352,
42/112,
43/232,
44/68,
45/232,
46/263,
47/8,
48/23,
49/23,
50/263,
51/112,
52/128,
53/8,
54/188,
55/308,
56/68,
57/52,
58/188,
59/248,
60/8,
61/248,
62/68,
63/292,
64/128,
65/97,
66/352,
67/337,
68/277,
69/157,
70/172,
71/292,
72/112,
73/292,
74/172}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/9a772f6f99718b1d4c2242a5159e643e.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1894-3</Bildtext>
%<Ausrichten von=\"1\" nach=\"2\"/>
%<Winkel size=\"18\" color=\"blue\" id=\"blauerWinkel\" value=\"88.95502437185989\"/>
%<Winkel size=\"18\" color=\"green\" id=\"gruenerWinkel\" value=\"135.52248781407013\"/>
%<Winkel size=\"18\" color=\"orange\" id=\"orangerWinkel\" value=\"104.47751218592992\"/>
%<Winkel size=\"18\" color=\"violet\" id=\"vierterWinkel\" value=\"75.52248781407\"/>
%<Winkel size=\"18\" color=\"teal\" id=\"fuenfterWinkel\" value=\"148.95502437185982\"/>
%<Winkel size=\"18\" color=\"lime\" id=\"sechsterWinkel\" value=\"106.56746344221033\"/>
%<Winkel size=\"18\" color=\"LightBlue\" id=\"siebenterWinkel\" value=\"88.9550243718598\"/>
%<Winkel size=\"18\" color=\"LightCoral\" id=\"achterWinkel\" value=\"135.52248781407002\"/>
%<Winkel size=\"18\" color=\"LightCyan\" id=\"neunterWinkel\" value=\"104.47751218592998\"/>
%<Feinjustieren Anzahl=\"8,8\"/>
%<Rechenweg>
%P[12]=[81.19895302251368,-23.620797303099163]; P[10]=[31.54207889274421,-17.773160886543323]; D=ab(12,10); A(10,12); N(11,10,12); N(9,10,11); N(1,10,9); M(3,1,10,blauerWinkel); N(2,1,3); N(4,2,3); N(5,2,4); M(16,5,2,gruenerWinkel); N(15,16,5); N(17,16,15); N(18,16,17); M(37,18,16,orangerWinkel); N(36,18,37); N(35,36,37); N(26,36,35); M(25,26,36,vierterWinkel); N(23,26,25); N(24,23,25); N(22,23,24); M(31,22,23,fuenfterWinkel); N(30,31,22); N(32,31,30); N(33,31,32); M(50,33,31,sechsterWinkel); N(49,33,50); N(48,49,50); N(40,49,48); M(42,40,49,siebenterWinkel); N(41,40,42); N(43,41,42); N(44,41,43); M(53,44,41,achterWinkel); N(52,53,44); N(54,53,52); N(55,53,54); M(72,55,53,neunterWinkel); N(71,55,72); N(70,71,72); N(63,71,70); Q(59,63,12,2*D,2*D); A(59,63); A(59,12); H(68,12,59,2); A(68,12); L(69,12,68); H(60,63,59,2); A(60,63); L(62,60,63); A(60,59); L(61,59,60); A(61,62); A(68,59); L(67,68,59); A(69,67); N(7,9,11); N(20,37,17); N(28,32,30); N(38,35,20); N(46,48,50); N(57,72,54); N(65,69,67); N(73,70,57); N(6,3,7); N(19,20,15); N(27,28,24); N(45,42,46); N(56,57,52); N(64,65,61); N(8,19,6); N(21,20,19); N(29,27,38); N(39,38,20); N(47,56,45); N(58,57,56); N(66,64,73); N(74,73,57); N(13,66,8); N(14,39,21); N(34,29,47); N(51,74,58);
%A(14,8); R(14,8,\"green\");
%A(14,13); R(14,13,\"green\");
%A(14,29); R(14,29,\"green\");
%A(34,14); R(34,14,\"green\");
%A(51,13); R(51,13,\"green\");
%A(51,47); R(51,47,\"green\");
%A(51,34); R(51,34,\"green\");
%A(51,66); R(51,66,\"green\"); RA(4,6); A(62,64); A(43,45); A(25,27);
%</Rechenweg>
%
%<Knopf id=\"Stopp_alleWinkel\" color=\"LightGrey\"/>
%
%<Knopf id=\"Start_blauerWinkel\" color=\"blue\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#blauerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_blauerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_gruenerWinkel\" color=\"green\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#gruenerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_gruenerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_orangerWinkel\" color=\"orange\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#orangerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_orangerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_vierterWinkel\" color=\"violet\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#vierterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_vierterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_fuenfterWinkel\" color=\"teal\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#fuenfterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_fuenfterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_sechsterWinkel\" color=\"lime\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#sechsterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_sechsterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_siebenterWinkel\" color=\"LightBlue\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#siebenterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_siebenterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_achterWinkel\" color=\"LightCoral\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#achterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_achterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_neunterWinkel\" color=\"LightCyan\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#neunterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_neunterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LightBlue}{rgb}{0.68,0.84,0.90}
\definecolor{LightCoral}{rgb}{0.94,0.50,0.50}
\definecolor{LightCyan}{rgb}{0.88,1.00,1.00}
\definecolor{Lime}{rgb}{0.00,1.00,0.00}
\definecolor{LimeGreen}{rgb}{0.20,0.80,0.20}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
\definecolor{Teal}{rgb}{0.00,0.50,0.50}
\definecolor{Violet}{rgb}{0.93,0.51,0.93}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.85/0.23,
2/1.06/0.85,
3/1.99/1.22,
4/1.20/1.84,
5/0.27/1.46,
6/2.12/2.22,
7/3.05/1.84,
8/2.91/2.83,
9/2.45/1.04,
10/2.84/0.12,
11/3.44/0.92,
12/3.84/0.00,
13/3.84/2.45,
14/3.70/3.44,
15/1.06/2.07,
16/0.14/2.45,
17/0.93/3.06,
18/0.00/3.44,
19/1.99/2.45,
20/1.85/3.44,
21/2.78/3.06,
22/1.85/6.65,
23/1.06/6.03,
24/1.99/5.66,
25/1.20/5.04,
26/0.27/5.42,
27/2.12/4.67,
28/3.05/5.04,
29/2.91/4.05,
30/2.45/5.85,
31/2.84/6.76,
32/3.44/5.96,
33/3.84/6.88,
34/3.84/4.43,
35/1.06/4.81,
36/0.14/4.43,
37/0.93/3.82,
38/1.99/4.43,
39/2.78/3.82,
40/5.82/6.65,
41/6.61/6.03,
42/5.69/5.66,
43/6.48/5.04,
44/7.40/5.42,
45/5.55/4.67,
46/4.63/5.04,
47/4.76/4.05,
48/5.23/5.85,
49/4.83/6.76,
50/4.23/5.96,
51/3.97/3.44,
52/6.61/4.81,
53/7.54/4.43,
54/6.75/3.82,
55/7.68/3.44,
56/5.69/4.43,
57/5.82/3.44,
58/4.90/3.82,
59/5.82/0.23,
60/6.61/0.85,
61/5.69/1.22,
62/6.48/1.84,
63/7.40/1.46,
64/5.55/2.22,
65/4.63/1.84,
66/4.76/2.83,
67/5.23/1.04,
68/4.83/0.12,
69/4.23/0.92,
70/6.61/2.07,
71/7.54/2.45,
72/6.75/3.06,
73/5.69/2.45,
74/4.90/3.06}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
1/353.28/442.24/0.4/Blue,
5/322.24/457.76/0.4/Green,
18/277.76/382.24/0.4/Orange,
26/262.24/337.76/0.4/Violet,
22/217.76/366.72/0.4/Teal,
33/186.72/293.28/0.4/Lime,
40/173.28/262.24/0.4/LightBlue,
44/142.24/277.76/0.4/LightCoral,
55/97.76/202.24/0.4/LightCyan}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
1/10, 1/9,
2/1, 2/3,
3/1,
4/2, 4/3, 4/6,
5/2, 5/4,
6/3, 6/7,
7/9, 7/11,
8/19, 8/6,
9/10, 9/11,
10/12,
11/10, 11/12,
13/66, 13/8,
14/39, 14/21, 14/8, 14/13, 14/29,
15/16, 15/5,
16/5,
17/16, 17/15,
18/16, 18/17,
19/20, 19/15,
20/37, 20/17,
21/20, 21/19,
22/23, 22/24,
23/26, 23/25,
24/23, 24/25,
25/26, 25/27,
26/36, 26/35,
27/28, 27/24,
28/32, 28/30,
29/27, 29/38,
30/31, 30/22,
31/22,
32/31, 32/30,
33/31, 33/32,
34/29, 34/47, 34/14,
35/36, 35/37,
36/18, 36/37,
37/18,
38/35, 38/20,
39/38, 39/20,
40/49, 40/48,
41/40, 41/42,
42/40,
43/41, 43/42, 43/45,
44/41, 44/43,
45/42, 45/46,
46/48, 46/50,
47/56, 47/45,
48/49, 48/50,
49/33, 49/50,
50/33,
51/74, 51/58, 51/13, 51/47, 51/34, 51/66,
52/53, 52/44,
53/44,
54/53, 54/52,
55/53, 55/54,
56/57, 56/52,
57/72, 57/54,
58/57, 58/56,
60/63, 60/59,
61/59, 61/60, 61/62,
62/60, 62/63, 62/64,
63/71, 63/70,
64/65, 64/61,
65/69, 65/67,
66/64, 66/73,
67/68, 67/59,
68/12, 68/59,
69/12, 69/68, 69/67,
70/71, 70/72,
71/55, 71/72,
72/55,
73/70, 73/57,
74/73, 74/57}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,74}
\fill[blue] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[Green,very thick] (p-14) -- (p-8);
\draw[Green,very thick] (p-14) -- (p-13);
\draw[Green,very thick] (p-14) -- (p-29);
\draw[Green,very thick] (p-34) -- (p-14);
\draw[Green,very thick] (p-51) -- (p-13);
\draw[Green,very thick] (p-51) -- (p-47);
\draw[Green,very thick] (p-51) -- (p-34);
\draw[Green,very thick] (p-51) -- (p-66);
\draw[LimeGreen,very thick] (p-4) -- (p-6);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
1/353.28/442.24/0.4/Blue,
5/322.24/457.76/0.4/Green,
18/277.76/382.24/0.4/Orange,
26/262.24/337.76/0.4/Violet,
22/217.76/366.72/0.4/Teal,
33/186.72/293.28/0.4/Lime,
40/173.28/262.24/0.4/LightBlue,
44/142.24/277.76/0.4/LightCoral,
55/97.76/202.24/0.4/LightCyan}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/292,
2/172,
3/352,
4/172,
5/172,
6/52,
7/83,
8/188,
9/83,
10/323,
11/23,
12/217,
13/308,
14/68,
15/308,
16/188,
17/68,
18/128,
19/248,
20/232,
21/8,
22/68,
23/128,
24/68,
25/308,
26/112,
27/308,
28/277,
29/172,
30/277,
31/97,
32/277,
33/143,
34/128,
35/52,
36/172,
37/352,
38/112,
39/352,
40/23,
41/352,
42/112,
43/232,
44/68,
45/232,
46/263,
47/8,
48/23,
49/23,
50/263,
51/112,
52/128,
53/8,
54/188,
55/308,
56/68,
57/52,
58/188,
59/248,
60/8,
61/248,
62/68,
63/292,
64/128,
65/97,
66/352,
67/337,
68/277,
69/157,
70/172,
71/292,
72/112,
73/292,
74/172}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
ohne 8-6:
74 Knoten, 8×Grad 3, 62×Grad 4, 4×Grad 6, 0 Überschneidungen
148 Kanten, minimal 0.99999999999998567812, maximal 1.00000000000000222045
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1894-4</Bildtext>
%<Ausrichten von="1" nach="2"/>
%<Winkel size="18" color="blue" id="blauerWinkel" value="88.95502437185985"/>
%<Winkel size="18" color="green" id="gruenerWinkel" value="135.5224878140699"/>
%<Winkel size="18" color="orange" id="orangerWinkel" value="104.47751218593022"/>
%<Winkel size="18" color="violet" id="vierterWinkel" value="75.52248781407015"/>
%<Winkel size="18" color="teal" id="fuenfterWinkel" value="148.95502437185937"/>
%<Winkel size="18" color="lime" id="sechsterWinkel" value="106.56746344221077"/>
%<Winkel size="18" color="LightBlue" id="siebenterWinkel" value="88.95502437185964"/>
%<Winkel size="18" color="LightCoral" id="achterWinkel" value="135.52248781407"/>
%<Winkel size="18" color="LightCyan" id="neunterWinkel" value="104.4775121859302"/>
%<Feinjustieren Anzahl="9,9"/>
%<Rechenweg>
%P[12]=[31.198953022513678,-23.620797303099163]; P[10]=[-18.45792110725579,-17.773160886543323]; D=ab(12,10); A(10,12); N(11,10,12); N(9,10,11); N(1,10,9); M(3,1,10,blauerWinkel); N(2,1,3); N(4,2,3); N(5,2,4); M(16,5,2,gruenerWinkel); N(15,16,5); N(17,16,15); N(18,16,17); M(37,18,16,orangerWinkel); N(36,18,37); N(35,36,37); N(26,36,35); M(25,26,36,vierterWinkel); N(23,26,25); N(24,23,25); N(22,23,24); M(31,22,23,fuenfterWinkel); N(30,31,22); N(32,31,30); N(33,31,32); M(50,33,31,sechsterWinkel); N(49,33,50); N(48,49,50); N(40,49,48); M(42,40,49,siebenterWinkel); N(41,40,42); N(43,41,42); N(44,41,43); M(53,44,41,achterWinkel); N(52,53,44); N(54,53,52); N(55,53,54); M(72,55,53,neunterWinkel); N(71,55,72); N(70,71,72); N(63,71,70); Q(59,63,12,2*D,2*D); A(59,63); A(59,12); H(68,12,59,2); A(68,12); L(69,12,68); H(60,63,59,2); A(60,63); L(62,60,63); A(60,59); L(61,59,60); A(61,62); A(68,59); L(67,68,59); A(69,67); N(7,9,11); N(20,37,17); N(28,32,30); N(38,35,20); N(46,48,50); N(57,72,54); N(65,69,67); N(73,70,57); N(6,3,7); N(19,20,15); N(27,28,24); N(45,42,46); N(56,57,52); N(64,65,61); N(8,19,7); N(21,20,19); N(29,28,38); N(39,38,20); N(47,56,46); N(58,57,56); N(66,65,73); N(74,73,57); N(13,66,8); N(14,39,21); N(34,29,47); N(51,74,58);
%A(14,8); R(14,8,"green");
%A(14,13); R(14,13,"green");
%A(14,29); R(14,29,"green");
%A(34,14); R(34,14,"green");
%A(51,13); R(51,13,"green");
%A(51,47); R(51,47,"green");
%A(51,34); R(51,34,"green");
%A(51,66); R(51,66,"green"); RA(4,6); A(62,64); A(43,45); A(25,27);
%</Rechenweg>
%
%<Knopf id="Stopp_alleWinkel" color="LightGrey"/>
%
%<Knopf id="Start_blauerWinkel" color="blue"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#blauerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_blauerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_gruenerWinkel" color="green"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#gruenerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_gruenerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_orangerWinkel" color="orange"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#orangerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_orangerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_vierterWinkel" color="violet"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#vierterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_vierterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_fuenfterWinkel" color="teal"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#fuenfterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_fuenfterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_sechsterWinkel" color="lime"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#sechsterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_sechsterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_siebenterWinkel" color="LightBlue"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#siebenterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_siebenterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_achterWinkel" color="LightCoral"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#achterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_achterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_neunterWinkel" color="LightCyan"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#neunterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_neunterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LightBlue}{rgb}{0.68,0.84,0.90}
\definecolor{LightCoral}{rgb}{0.94,0.50,0.50}
\definecolor{LightCyan}{rgb}{0.88,1.00,1.00}
\definecolor{Lime}{rgb}{0.00,1.00,0.00}
\definecolor{LimeGreen}{rgb}{0.20,0.80,0.20}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
\definecolor{Teal}{rgb}{0.00,0.50,0.50}
\definecolor{Violet}{rgb}{0.93,0.51,0.93}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.85/0.23,
2/1.06/0.85,
3/1.99/1.22,
4/1.20/1.84,
5/0.27/1.46,
6/2.12/2.22,
7/3.05/1.84,
8/2.91/2.83,
9/2.45/1.04,
10/2.84/0.12,
11/3.44/0.92,
12/3.84/0.00,
13/3.84/2.45,
14/3.70/3.44,
15/1.06/2.07,
16/0.14/2.45,
17/0.93/3.06,
18/0.00/3.44,
19/1.99/2.45,
20/1.85/3.44,
21/2.78/3.06,
22/1.85/6.65,
23/1.06/6.03,
24/1.99/5.66,
25/1.20/5.04,
26/0.27/5.42,
27/2.12/4.67,
28/3.05/5.04,
29/2.91/4.05,
30/2.45/5.85,
31/2.84/6.76,
32/3.44/5.96,
33/3.84/6.88,
34/3.84/4.43,
35/1.06/4.81,
36/0.14/4.43,
37/0.93/3.82,
38/1.99/4.43,
39/2.78/3.82,
40/5.82/6.65,
41/6.61/6.03,
42/5.69/5.66,
43/6.48/5.04,
44/7.40/5.42,
45/5.55/4.67,
46/4.63/5.04,
47/4.76/4.05,
48/5.23/5.85,
49/4.83/6.76,
50/4.23/5.96,
51/3.97/3.44,
52/6.61/4.81,
53/7.54/4.43,
54/6.75/3.82,
55/7.68/3.44,
56/5.69/4.43,
57/5.82/3.44,
58/4.90/3.82,
59/5.82/0.23,
60/6.61/0.85,
61/5.69/1.22,
62/6.48/1.84,
63/7.40/1.46,
64/5.55/2.22,
65/4.63/1.84,
66/4.76/2.83,
67/5.23/1.04,
68/4.83/0.12,
69/4.23/0.92,
70/6.61/2.07,
71/7.54/2.45,
72/6.75/3.06,
73/5.69/2.45,
74/4.90/3.06}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
1/353.28/442.24/0.4/Blue,
5/322.24/457.76/0.4/Green,
18/277.76/382.24/0.4/Orange,
26/262.24/337.76/0.4/Violet,
22/217.76/366.72/0.4/Teal,
33/186.72/293.28/0.4/Lime,
40/173.28/262.24/0.4/LightBlue,
44/142.24/277.76/0.4/LightCoral,
55/97.76/202.24/0.4/LightCyan}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
1/10, 1/9,
2/1, 2/3,
3/1,
4/2, 4/3, 4/6,
5/2, 5/4,
6/3, 6/7,
7/9, 7/11,
8/19, 8/7,
9/10, 9/11,
10/12,
11/10, 11/12,
13/66, 13/8,
14/39, 14/21, 14/8, 14/13, 14/29,
15/16, 15/5,
16/5,
17/16, 17/15,
18/16, 18/17,
19/20, 19/15,
20/37, 20/17,
21/20, 21/19,
22/23, 22/24,
23/26, 23/25,
24/23, 24/25,
25/26, 25/27,
26/36, 26/35,
27/28, 27/24,
28/32, 28/30,
29/28, 29/38,
30/31, 30/22,
31/22,
32/31, 32/30,
33/31, 33/32,
34/29, 34/47, 34/14,
35/36, 35/37,
36/18, 36/37,
37/18,
38/35, 38/20,
39/38, 39/20,
40/49, 40/48,
41/40, 41/42,
42/40,
43/41, 43/42, 43/45,
44/41, 44/43,
45/42, 45/46,
46/48, 46/50,
47/56, 47/46,
48/49, 48/50,
49/33, 49/50,
50/33,
51/74, 51/58, 51/13, 51/47, 51/34, 51/66,
52/53, 52/44,
53/44,
54/53, 54/52,
55/53, 55/54,
56/57, 56/52,
57/72, 57/54,
58/57, 58/56,
60/63, 60/59,
61/59, 61/60, 61/62,
62/60, 62/63, 62/64,
63/71, 63/70,
64/65, 64/61,
65/69, 65/67,
66/65, 66/73,
67/68, 67/59,
68/12, 68/59,
69/12, 69/68, 69/67,
70/71, 70/72,
71/55, 71/72,
72/55,
73/70, 73/57,
74/73, 74/57}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,74}
\fill[blue] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[Green,very thick] (p-14) -- (p-8);
\draw[Green,very thick] (p-14) -- (p-13);
\draw[Green,very thick] (p-14) -- (p-29);
\draw[Green,very thick] (p-34) -- (p-14);
\draw[Green,very thick] (p-51) -- (p-13);
\draw[Green,very thick] (p-51) -- (p-47);
\draw[Green,very thick] (p-51) -- (p-34);
\draw[Green,very thick] (p-51) -- (p-66);
\draw[LimeGreen,very thick] (p-4) -- (p-6);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
1/353.28/442.24/0.4/Blue,
5/322.24/457.76/0.4/Green,
18/277.76/382.24/0.4/Orange,
26/262.24/337.76/0.4/Violet,
22/217.76/366.72/0.4/Teal,
33/186.72/293.28/0.4/Lime,
40/173.28/262.24/0.4/LightBlue,
44/142.24/277.76/0.4/LightCoral,
55/97.76/202.24/0.4/LightCyan}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/203,
2/292,
3/292,
4/52,
5/172,
6/52,
7/83,
8/188,
9/83,
10/323,
11/23,
12/217,
13/308,
14/292,
15/8,
16/128,
17/68,
18/232,
19/248,
20/128,
21/8,
22/68,
23/68,
24/68,
25/308,
26/112,
27/308,
28/277,
29/172,
30/157,
31/37,
32/337,
33/143,
34/52,
35/352,
36/172,
37/352,
38/112,
39/352,
40/112,
41/352,
42/112,
43/292,
44/352,
45/232,
46/263,
47/8,
48/323,
49/83,
50/143,
51/248,
52/128,
53/68,
54/248,
55/308,
56/68,
57/308,
58/188,
59/337,
60/8,
61/128,
62/8,
63/292,
64/128,
65/97,
66/352,
67/37,
68/277,
69/97,
70/172,
71/292,
72/112,
73/292,
74/172}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/1f078023c889906c9d3f055cc501dfa0.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1894-4</Bildtext>
%<Ausrichten von=\"1\" nach=\"2\"/>
%<Winkel size=\"18\" color=\"blue\" id=\"blauerWinkel\" value=\"88.95502437185985\"/>
%<Winkel size=\"18\" color=\"green\" id=\"gruenerWinkel\" value=\"135.5224878140699\"/>
%<Winkel size=\"18\" color=\"orange\" id=\"orangerWinkel\" value=\"104.47751218593022\"/>
%<Winkel size=\"18\" color=\"violet\" id=\"vierterWinkel\" value=\"75.52248781407015\"/>
%<Winkel size=\"18\" color=\"teal\" id=\"fuenfterWinkel\" value=\"148.95502437185937\"/>
%<Winkel size=\"18\" color=\"lime\" id=\"sechsterWinkel\" value=\"106.56746344221077\"/>
%<Winkel size=\"18\" color=\"LightBlue\" id=\"siebenterWinkel\" value=\"88.95502437185964\"/>
%<Winkel size=\"18\" color=\"LightCoral\" id=\"achterWinkel\" value=\"135.52248781407\"/>
%<Winkel size=\"18\" color=\"LightCyan\" id=\"neunterWinkel\" value=\"104.4775121859302\"/>
%<Feinjustieren Anzahl=\"9,9\"/>
%<Rechenweg>
%P[12]=[31.198953022513678,-23.620797303099163]; P[10]=[-18.45792110725579,-17.773160886543323]; D=ab(12,10); A(10,12); N(11,10,12); N(9,10,11); N(1,10,9); M(3,1,10,blauerWinkel); N(2,1,3); N(4,2,3); N(5,2,4); M(16,5,2,gruenerWinkel); N(15,16,5); N(17,16,15); N(18,16,17); M(37,18,16,orangerWinkel); N(36,18,37); N(35,36,37); N(26,36,35); M(25,26,36,vierterWinkel); N(23,26,25); N(24,23,25); N(22,23,24); M(31,22,23,fuenfterWinkel); N(30,31,22); N(32,31,30); N(33,31,32); M(50,33,31,sechsterWinkel); N(49,33,50); N(48,49,50); N(40,49,48); M(42,40,49,siebenterWinkel); N(41,40,42); N(43,41,42); N(44,41,43); M(53,44,41,achterWinkel); N(52,53,44); N(54,53,52); N(55,53,54); M(72,55,53,neunterWinkel); N(71,55,72); N(70,71,72); N(63,71,70); Q(59,63,12,2*D,2*D); A(59,63); A(59,12); H(68,12,59,2); A(68,12); L(69,12,68); H(60,63,59,2); A(60,63); L(62,60,63); A(60,59); L(61,59,60); A(61,62); A(68,59); L(67,68,59); A(69,67); N(7,9,11); N(20,37,17); N(28,32,30); N(38,35,20); N(46,48,50); N(57,72,54); N(65,69,67); N(73,70,57); N(6,3,7); N(19,20,15); N(27,28,24); N(45,42,46); N(56,57,52); N(64,65,61); N(8,19,7); N(21,20,19); N(29,28,38); N(39,38,20); N(47,56,46); N(58,57,56); N(66,65,73); N(74,73,57); N(13,66,8); N(14,39,21); N(34,29,47); N(51,74,58);
%A(14,8); R(14,8,\"green\");
%A(14,13); R(14,13,\"green\");
%A(14,29); R(14,29,\"green\");
%A(34,14); R(34,14,\"green\");
%A(51,13); R(51,13,\"green\");
%A(51,47); R(51,47,\"green\");
%A(51,34); R(51,34,\"green\");
%A(51,66); R(51,66,\"green\"); RA(4,6); A(62,64); A(43,45); A(25,27);
%</Rechenweg>
%
%<Knopf id=\"Stopp_alleWinkel\" color=\"LightGrey\"/>
%
%<Knopf id=\"Start_blauerWinkel\" color=\"blue\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#blauerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_blauerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_gruenerWinkel\" color=\"green\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#gruenerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_gruenerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_orangerWinkel\" color=\"orange\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#orangerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_orangerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_vierterWinkel\" color=\"violet\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#vierterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_vierterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_fuenfterWinkel\" color=\"teal\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#fuenfterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_fuenfterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_sechsterWinkel\" color=\"lime\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#sechsterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_sechsterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_siebenterWinkel\" color=\"LightBlue\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#siebenterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_siebenterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_achterWinkel\" color=\"LightCoral\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#achterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_achterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_neunterWinkel\" color=\"LightCyan\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#neunterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_neunterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LightBlue}{rgb}{0.68,0.84,0.90}
\definecolor{LightCoral}{rgb}{0.94,0.50,0.50}
\definecolor{LightCyan}{rgb}{0.88,1.00,1.00}
\definecolor{Lime}{rgb}{0.00,1.00,0.00}
\definecolor{LimeGreen}{rgb}{0.20,0.80,0.20}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
\definecolor{Teal}{rgb}{0.00,0.50,0.50}
\definecolor{Violet}{rgb}{0.93,0.51,0.93}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.85/0.23,
2/1.06/0.85,
3/1.99/1.22,
4/1.20/1.84,
5/0.27/1.46,
6/2.12/2.22,
7/3.05/1.84,
8/2.91/2.83,
9/2.45/1.04,
10/2.84/0.12,
11/3.44/0.92,
12/3.84/0.00,
13/3.84/2.45,
14/3.70/3.44,
15/1.06/2.07,
16/0.14/2.45,
17/0.93/3.06,
18/0.00/3.44,
19/1.99/2.45,
20/1.85/3.44,
21/2.78/3.06,
22/1.85/6.65,
23/1.06/6.03,
24/1.99/5.66,
25/1.20/5.04,
26/0.27/5.42,
27/2.12/4.67,
28/3.05/5.04,
29/2.91/4.05,
30/2.45/5.85,
31/2.84/6.76,
32/3.44/5.96,
33/3.84/6.88,
34/3.84/4.43,
35/1.06/4.81,
36/0.14/4.43,
37/0.93/3.82,
38/1.99/4.43,
39/2.78/3.82,
40/5.82/6.65,
41/6.61/6.03,
42/5.69/5.66,
43/6.48/5.04,
44/7.40/5.42,
45/5.55/4.67,
46/4.63/5.04,
47/4.76/4.05,
48/5.23/5.85,
49/4.83/6.76,
50/4.23/5.96,
51/3.97/3.44,
52/6.61/4.81,
53/7.54/4.43,
54/6.75/3.82,
55/7.68/3.44,
56/5.69/4.43,
57/5.82/3.44,
58/4.90/3.82,
59/5.82/0.23,
60/6.61/0.85,
61/5.69/1.22,
62/6.48/1.84,
63/7.40/1.46,
64/5.55/2.22,
65/4.63/1.84,
66/4.76/2.83,
67/5.23/1.04,
68/4.83/0.12,
69/4.23/0.92,
70/6.61/2.07,
71/7.54/2.45,
72/6.75/3.06,
73/5.69/2.45,
74/4.90/3.06}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
1/353.28/442.24/0.4/Blue,
5/322.24/457.76/0.4/Green,
18/277.76/382.24/0.4/Orange,
26/262.24/337.76/0.4/Violet,
22/217.76/366.72/0.4/Teal,
33/186.72/293.28/0.4/Lime,
40/173.28/262.24/0.4/LightBlue,
44/142.24/277.76/0.4/LightCoral,
55/97.76/202.24/0.4/LightCyan}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
1/10, 1/9,
2/1, 2/3,
3/1,
4/2, 4/3, 4/6,
5/2, 5/4,
6/3, 6/7,
7/9, 7/11,
8/19, 8/7,
9/10, 9/11,
10/12,
11/10, 11/12,
13/66, 13/8,
14/39, 14/21, 14/8, 14/13, 14/29,
15/16, 15/5,
16/5,
17/16, 17/15,
18/16, 18/17,
19/20, 19/15,
20/37, 20/17,
21/20, 21/19,
22/23, 22/24,
23/26, 23/25,
24/23, 24/25,
25/26, 25/27,
26/36, 26/35,
27/28, 27/24,
28/32, 28/30,
29/28, 29/38,
30/31, 30/22,
31/22,
32/31, 32/30,
33/31, 33/32,
34/29, 34/47, 34/14,
35/36, 35/37,
36/18, 36/37,
37/18,
38/35, 38/20,
39/38, 39/20,
40/49, 40/48,
41/40, 41/42,
42/40,
43/41, 43/42, 43/45,
44/41, 44/43,
45/42, 45/46,
46/48, 46/50,
47/56, 47/46,
48/49, 48/50,
49/33, 49/50,
50/33,
51/74, 51/58, 51/13, 51/47, 51/34, 51/66,
52/53, 52/44,
53/44,
54/53, 54/52,
55/53, 55/54,
56/57, 56/52,
57/72, 57/54,
58/57, 58/56,
60/63, 60/59,
61/59, 61/60, 61/62,
62/60, 62/63, 62/64,
63/71, 63/70,
64/65, 64/61,
65/69, 65/67,
66/65, 66/73,
67/68, 67/59,
68/12, 68/59,
69/12, 69/68, 69/67,
70/71, 70/72,
71/55, 71/72,
72/55,
73/70, 73/57,
74/73, 74/57}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,74}
\fill[blue] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[Green,very thick] (p-14) -- (p-8);
\draw[Green,very thick] (p-14) -- (p-13);
\draw[Green,very thick] (p-14) -- (p-29);
\draw[Green,very thick] (p-34) -- (p-14);
\draw[Green,very thick] (p-51) -- (p-13);
\draw[Green,very thick] (p-51) -- (p-47);
\draw[Green,very thick] (p-51) -- (p-34);
\draw[Green,very thick] (p-51) -- (p-66);
\draw[LimeGreen,very thick] (p-4) -- (p-6);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
1/353.28/442.24/0.4/Blue,
5/322.24/457.76/0.4/Green,
18/277.76/382.24/0.4/Orange,
26/262.24/337.76/0.4/Violet,
22/217.76/366.72/0.4/Teal,
33/186.72/293.28/0.4/Lime,
40/173.28/262.24/0.4/LightBlue,
44/142.24/277.76/0.4/LightCoral,
55/97.76/202.24/0.4/LightCyan}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/203,
2/292,
3/292,
4/52,
5/172,
6/52,
7/83,
8/188,
9/83,
10/323,
11/23,
12/217,
13/308,
14/292,
15/8,
16/128,
17/68,
18/232,
19/248,
20/128,
21/8,
22/68,
23/68,
24/68,
25/308,
26/112,
27/308,
28/277,
29/172,
30/157,
31/37,
32/337,
33/143,
34/52,
35/352,
36/172,
37/352,
38/112,
39/352,
40/112,
41/352,
42/112,
43/292,
44/352,
45/232,
46/263,
47/8,
48/323,
49/83,
50/143,
51/248,
52/128,
53/68,
54/248,
55/308,
56/68,
57/308,
58/188,
59/337,
60/8,
61/128,
62/8,
63/292,
64/128,
65/97,
66/352,
67/37,
68/277,
69/97,
70/172,
71/292,
72/112,
73/292,
74/172}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
|
Profil
Quote
Link |
StefanVogel
Senior
Dabei seit: 26.11.2005
Mitteilungen: 3446
Aus: Raun
| Beitrag No.1898, eingetragen 2020-01-25 20:05
|
2020-01-19 08:44 - StefanVogel in Beitrag No. 1892 schreibt:
Wenn ich aber den blauen Winkel um -0.01° verändere und dann den Graph mit Button Feinjustieren(3) wieder zurechtziehe, so wird nicht mehr der Ausgangswert 90° erreicht:
blauerWinkel = 89.99483124096407
gruenerWinkel = 90.00516875903601
orangerWinkel = 89.99483124096504
ein Zeichen für Beweglichkeit des Graphen. Das Ergebnis lässt auch vermuten, das gruenerWinkel=180°-blauerWinkel und orangerWinkel=blauerWinkel ist.
Diese Abhhängigkeit ist auch aus der Matrix ablesbar, welche beim Feinjustieren verwendet wird (ist im Streichholzprogramm beschrieben):
-1.7453327028071897e-7,-3.7606695291181325e-7,-2.0153348168072682e-7
4.3633292889921904e-7, 3.3556678469270906e-7,-1.0076635215128249e-7
-1.308999086901963e-7 ,-2.3166669071983392e-7,-1.0076669032521579e-7 |
Die drei Spalten der Matrix sind nahezu linear abhängig. Erste Spalte minus zweite Spalte plus dritte Spalte ergibt Null. Das bedeutet wieder die gleiche Abhängigkeit für die Winkeländerung. Wenn blauerWinkel um 1' vergrößert wird und gruenerWinkel um 1' verkleinert und orangerWinkel um 1' vergrößert, bleiben die Kantenlängen unverändert. Der Graph ist beweglich. Das kann ohne Probieren gleich mit aus der Matrix herausgelesen werden und es stellt sich hier die berechtigte Frage, warum nicht gleich so. Das kann ich nur mit Ausreden versuchen zu beantworten. Bei Graphen mit nur einem beweglichen Winkel gibt es keinen solchen Zusammenhang. Symmetrische Eingabe des Graphen schränkt die Beweglichkeit ein und da funktioniert das nicht. Buttons für neue Eingabe ohne Symmetriebedingungen gab es anfangs nur solche, wo dann 10 oder 20 bewegliche Winkel entstehen mit entsprechend großer Matrix. Damit in javascript weiter rechnen ist nicht gerade verlockend. Deshalb hatte ich lieber das extra GAP-Programm verwendet. Doch inzwischen scheint Button neue Eingabe "wenig Winkel" (der aber auch nicht immer funktioniert) eine echte Alternative zu bieten, nur eine 3x3 Matrix statt 20*20 nach neuer Eingabe mit mehr Winkeln oder 100*100 im extra GAP-Programm. Das schreibe ich jetzt nochmal genau auf.
Mit drei beweglichen Winkeln \(\alpha, \beta, \gamma\) werden drei Kantenlängen \(a, b, c\) eingestellt. Die Kantenlängen sind Funktionen der Winkel
\(a = a(\alpha, \beta, \gamma)\),
\(b = b(\alpha, \beta, \gamma)\),
\(c = c(\alpha, \beta, \gamma)\).
Wie die Funktionen ungefähr aussehen, siehe die Berechnung von x im Beweis von Slash. Meistens liegen dann noch mehr Knoten und Kanten dazwischen.
Bei einem beweglichen Graph lassen sich die Winkel abhängig von einem Bahnparameter t (zum Beispiel Zeit t) verändern
\(\alpha = \alpha(t)\),
\(\beta = \beta(t)\),
\(\gamma = \gamma(t)\),
ohne dass sich dabei die Kantenlängen ändern
\(\begin{pmatrix}
a(\alpha(t), \beta(t), \gamma(t)) \\
b(\alpha(t), \beta(t), \gamma(t)) \\
c(\alpha(t), \beta(t), \gamma(t)) \\
\end{pmatrix} = \mathbb{const}\).
Bei einer konstanten Funktion jedoch sind sämtliche Ableitungen Null. Für die erste Ableitung mit mehrdimensionaler Kettenregel ausgerechnet bedeutet das
\(\displaystyle \begin{pmatrix}
\dfrac{\partial{a}}{\partial{\alpha}} && \dfrac{\partial{a}}{\partial{\beta}} && \dfrac{\partial{a}}{\partial{\gamma}} \\
\dfrac{\partial{b}}{\partial{\alpha}} && \dfrac{\partial{b}}{\partial{\beta}} && \dfrac{\partial{b}}{\partial{\gamma}} \\
\dfrac{\partial{c}}{\partial{\alpha}} && \dfrac{\partial{c}}{\partial{\beta}} && \dfrac{\partial{c}}{\partial{\gamma}} \\
\end{pmatrix} \begin{pmatrix}
\dfrac{\mathrm{d}\alpha}{\mathrm{d}t} \\
\dfrac{\mathrm{d}\beta}{\mathrm{d}t} \\
\dfrac{\mathrm{d}\gamma}{\mathrm{d}t} \\
\end{pmatrix} = 0\).
Dafür gibt es nur von Null verschiedene Lösungen, wenn die Spalten der Matrix linear abhängig sind und die Linearfaktoren erscheinen dann nochmal in der Lösung.
Gleiches gilt für die höheren Ableitungen. Die müssen gleich Null gesetzt ebenfalls alle diese Lösungen haben.
An der Stelle löst sich auch das mit der falschen Beweglichkeit auf, Beitrag No.785/787. Der Graph ist nicht mehr statisch bestimmt, wenn die erste Ableitung Null ist, aber erst wirklich beweglich, wenn auch die höheren Ableitungen Null sind. Das herauszufinden hat das extra GAP-Programm nicht geschafft.
Ob sich das konkret alles mit ausreichender Genauigkeit rechnen lässt, muss sich noch herausstellen. Die Matrix am Anfang des Beitrages ist eine Näherung für die Matrix in der ersten Ableitung, zusammengestellt aus der Änderung der Kantenlängen bei geringfügiger Variation der Winkel, und da ist ja die lineare Abhängigkeit ganz gut erkennbar.
[Die Antwort wurde nach Beitrag No.1895 begonnen.]
|
Profil
Quote
Link |
StefanVogel
Senior
Dabei seit: 26.11.2005
Mitteilungen: 3446
Aus: Raun
| Beitrag No.1899, eingetragen 2020-01-26 08:00
|
Eine kleine Hürde noch: Aus Graph #1892-1 erhalte ich nach Button neue Eingabe "egal wie" folgende Eingabe
88 Knoten, 4×Grad 3, 80×Grad 4, 2×Grad 5, 2×Grad 7, 0 Überschneidungen
178 Kanten, minimal 0.99999999999960054176, maximal 1.00000000000029820590
einzustellende Kanten, Abstände und Winkel:
|P50-P88|=1.00000000000005773160
|P80-P81|=0.99999999999997546407
|P47-P49|=0.99999999999993238742
|P33-P35|=0.99999999999984556798
|P29-P31|=1.00000000000003330669
|P14-P16|=0.99999999999960054176
|P15-P16|=0.99999999999966382447
|P15-P17|=1.00000000000029820590
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>Automatisch generierte Eingabe zu: #1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78);</Bildtext>
%<Ausrichten von="1" nach="2"/>
%<Winkel size="18" color="blue" id="blauerWinkel" value="270.000000021423"/>
%<Winkel size="18" color="green" id="gruenerWinkel" value="180.0000000000004"/>
%<Winkel size="18" color="orange" id="orangerWinkel" value="270.000000021423"/>
%<Feinjustieren Anzahl="8,3"/>
%<Rechenweg>
%P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(2,1); N(3,1,2); N(4,3,2); N(5,4,2); M(38,5,4,blauerWinkel); N(36,5,38); N(8,4,36); N(37,8,36); N(40,37,38); N(43,37,40); N(44,40,38); N(46,43,44); N(72,46,44); N(74,8,43); N(75,8,74); N(7,3,8); N(71,46,72); N(73,7,8); N(76,73,75); N(77,73,76); N(6,1,7); N(9,1,6); N(10,9,6); N(11,9,10); N(69,71,72); M(84,74,8,gruenerWinkel); N(70,84,71); N(83,75,84); N(85,84,70); N(68,70,69); N(67,68,69); N(66,68,67); N(64,66,67); N(65,85,66); N(63,65,64); N(62,63,64); N(61,63,62); N(59,61,62); N(60,65,61); N(58,60,59); N(57,58,59); N(56,58,57); N(54,56,57); N(55,60,56); N(87,85,55); N(53,55,54); N(86,83,87); N(88,86,87); N(52,53,54); N(82,83,86); N(51,53,52); N(79,76,82); N(81,82,86); N(42,81,88); N(49,51,52); N(50,51,42); N(78,77,79); N(80,79,42); N(48,50,49); N(45,42,48); N(47,45,48); N(41,45,47); N(39,42,41); N(34,39,41); N(35,42,39); N(32,80,35); N(33,32,34); N(27,78,32); N(31,33,34); N(30,32,31); N(28,27,30); N(29,28,30); N(26,28,29); N(25,27,26); N(24,25,26); N(23,25,24); N(21,23,24); M(22,23,25,orangerWinkel); N(20,22,21); N(19,20,21); N(18,20,19); N(16,18,19); N(17,22,18); N(12,17,10); N(13,11,12); N(14,11,13); N(15,14,13);
%A(50,88); R(50,88,"green");
%A(80,81); R(80,81,"green");
%A(47,49); R(47,49,"green");
%A(33,35); R(33,35,"green");
%A(29,31); R(29,31,"green");
%A(14,16); R(14,16,"green");
%A(15,16); R(15,16,"green");
%A(15,17); R(15,17,"green");
%</Rechenweg>
%
%<Knopf id="Stopp_alleWinkel" color="LightGrey"/>
%
%<Knopf id="Start_blauerWinkel" color="blue"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#blauerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_blauerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_gruenerWinkel" color="green"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#gruenerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_gruenerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_orangerWinkel" color="orange"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#orangerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_orangerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/2.73/0.00,
2/3.73/0.00,
3/3.23/0.87,
4/4.23/0.87,
5/4.73/0.00,
6/2.73/1.00,
7/3.23/1.87,
8/4.23/1.87,
9/1.87/0.50,
10/1.87/1.50,
11/1.00/1.00,
12/2.37/2.37,
13/1.50/1.87,
14/0.50/1.87,
15/1.00/2.73,
16/0.00/2.73,
17/1.87/3.23,
18/0.87/3.23,
19/0.00/3.73,
20/0.87/4.23,
21/0.00/4.73,
22/1.87/4.23,
23/1.00/4.73,
24/0.50/5.60,
25/1.50/5.60,
26/1.00/6.46,
27/2.37/5.10,
28/1.87/5.96,
29/1.87/6.96,
30/2.73/6.46,
31/2.73/7.46,
32/3.23/5.60,
33/3.23/6.60,
34/3.73/7.46,
35/4.10/6.10,
36/4.73/1.00,
37/5.23/1.87,
38/5.60/0.50,
39/4.60/6.96,
40/6.10/1.37,
41/4.60/7.96,
42/5.10/6.10,
43/6.10/2.37,
44/6.60/0.50,
45/5.10/7.10,
46/6.60/1.50,
47/5.60/7.96,
48/6.10/7.10,
49/6.60/7.96,
50/6.10/6.10,
51/6.60/6.96,
52/7.46/7.46,
53/7.46/6.46,
54/8.33/6.96,
55/6.96/5.60,
56/7.83/6.10,
57/8.83/6.10,
58/8.33/5.23,
59/9.33/5.23,
60/7.46/4.73,
61/8.46/4.73,
62/9.33/4.23,
63/8.46/3.73,
64/9.33/3.23,
65/7.46/3.73,
66/8.33/3.23,
67/8.83/2.37,
68/7.83/2.37,
69/8.33/1.50,
70/6.96/2.87,
71/7.46/2.00,
72/7.46/1.00,
73/3.73/2.73,
74/5.10/2.37,
75/4.23/2.87,
76/3.73/3.73,
77/2.87/3.23,
78/2.87/4.23,
79/3.73/4.73,
80/4.23/5.60,
81/5.10/5.10,
82/4.60/4.23,
83/5.10/3.37,
84/5.96/2.87,
85/6.46/3.73,
86/5.60/4.23,
87/6.46/4.73,
88/5.60/5.23}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
5/120.00/390.00/0.4/Blue,
74/210.00/390.00/0.4/Green,
23/60.00/330.00/0.4/Orange}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
2/1,
3/1, 3/2,
4/3, 4/2,
5/4, 5/2,
6/1, 6/7,
7/3, 7/8,
8/4, 8/36,
9/1, 9/6,
10/9, 10/6,
11/9, 11/10,
12/17, 12/10,
13/11, 13/12,
14/11, 14/13, 14/16,
15/14, 15/13, 15/16, 15/17,
16/18, 16/19,
17/22, 17/18,
18/20, 18/19,
19/20, 19/21,
20/22, 20/21,
21/23, 21/24,
22/23,
23/25, 23/24,
24/25, 24/26,
25/27, 25/26,
26/28, 26/29,
27/78, 27/32,
28/27, 28/30,
29/28, 29/30, 29/31,
30/32, 30/31,
31/33, 31/34,
32/80, 32/35,
33/32, 33/34, 33/35,
34/39, 34/41,
35/42, 35/39,
36/5, 36/38,
37/8, 37/36,
38/5,
39/42, 39/41,
40/37, 40/38,
41/45, 41/47,
42/81, 42/88,
43/37, 43/40,
44/40, 44/38,
45/42, 45/48,
46/43, 46/44,
47/45, 47/48, 47/49,
48/50, 48/49,
49/51, 49/52,
50/51, 50/42, 50/88,
51/53, 51/52,
52/53, 52/54,
53/55, 53/54,
54/56, 54/57,
55/60, 55/56,
56/58, 56/57,
57/58, 57/59,
58/60, 58/59,
59/61, 59/62,
60/65, 60/61,
61/63, 61/62,
62/63, 62/64,
63/65, 63/64,
64/66, 64/67,
65/85, 65/66,
66/68, 66/67,
67/68, 67/69,
68/70, 68/69,
69/71, 69/72,
70/84, 70/71,
71/46, 71/72,
72/46, 72/44,
73/7, 73/8,
74/8, 74/43,
75/8, 75/74,
76/73, 76/75,
77/73, 77/76,
78/77, 78/79,
79/76, 79/82,
80/79, 80/42, 80/81,
81/82, 81/86,
82/83, 82/86,
83/75, 83/84,
84/74,
85/84, 85/70,
86/83, 86/87,
87/85, 87/55,
88/86, 88/87}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,88}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[Green,very thick] (p-50) -- (p-88);
\draw[Green,very thick] (p-80) -- (p-81);
\draw[Green,very thick] (p-47) -- (p-49);
\draw[Green,very thick] (p-33) -- (p-35);
\draw[Green,very thick] (p-29) -- (p-31);
\draw[Green,very thick] (p-14) -- (p-16);
\draw[Green,very thick] (p-15) -- (p-16);
\draw[Green,very thick] (p-15) -- (p-17);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
5/120.00/390.00/0.4/Blue,
74/210.00/390.00/0.4/Green,
23/60.00/330.00/0.4/Orange}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/210,
2/330,
3/150,
4/30,
5/330,
6/360,
7/210,
8/330,
9/180,
10/60,
11/180,
12/348,
13/30,
14/150,
15/30,
16/150,
17/317,
18/360,
19/240,
20/60,
21/120,
22/47,
23/330,
24/210,
25/30,
26/90,
27/167,
28/240,
29/180,
30/360,
31/60,
32/240,
33/270,
34/30,
35/210,
36/120,
37/30,
38/360,
39/300,
40/90,
41/60,
42/60,
43/60,
44/240,
45/270,
46/180,
47/30,
48/270,
49/120,
50/30,
51/240,
52/60,
53/240,
54/360,
55/93,
56/210,
57/330,
58/210,
59/60,
60/137,
61/120,
62/360,
63/180,
64/300,
65/227,
66/90,
67/270,
68/150,
69/360,
70/330,
71/60,
72/360,
73/300,
74/360,
75/120,
76/60,
77/180,
78/257,
79/62,
80/180,
81/90,
82/150,
83/270,
84/210,
85/90,
86/240,
87/360,
88/270}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/650c866fdbc638d0512a04cf87d5a032.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>Automatisch generierte Eingabe zu: #1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78);</Bildtext>
%<Ausrichten von=\"1\" nach=\"2\"/>
%<Winkel size=\"18\" color=\"blue\" id=\"blauerWinkel\" value=\"270.000000021423\"/>
%<Winkel size=\"18\" color=\"green\" id=\"gruenerWinkel\" value=\"180.0000000000004\"/>
%<Winkel size=\"18\" color=\"orange\" id=\"orangerWinkel\" value=\"270.000000021423\"/>
%<Feinjustieren Anzahl=\"8,3\"/>
%<Rechenweg>
%P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(2,1); N(3,1,2); N(4,3,2); N(5,4,2); M(38,5,4,blauerWinkel); N(36,5,38); N(8,4,36); N(37,8,36); N(40,37,38); N(43,37,40); N(44,40,38); N(46,43,44); N(72,46,44); N(74,8,43); N(75,8,74); N(7,3,8); N(71,46,72); N(73,7,8); N(76,73,75); N(77,73,76); N(6,1,7); N(9,1,6); N(10,9,6); N(11,9,10); N(69,71,72); M(84,74,8,gruenerWinkel); N(70,84,71); N(83,75,84); N(85,84,70); N(68,70,69); N(67,68,69); N(66,68,67); N(64,66,67); N(65,85,66); N(63,65,64); N(62,63,64); N(61,63,62); N(59,61,62); N(60,65,61); N(58,60,59); N(57,58,59); N(56,58,57); N(54,56,57); N(55,60,56); N(87,85,55); N(53,55,54); N(86,83,87); N(88,86,87); N(52,53,54); N(82,83,86); N(51,53,52); N(79,76,82); N(81,82,86); N(42,81,88); N(49,51,52); N(50,51,42); N(78,77,79); N(80,79,42); N(48,50,49); N(45,42,48); N(47,45,48); N(41,45,47); N(39,42,41); N(34,39,41); N(35,42,39); N(32,80,35); N(33,32,34); N(27,78,32); N(31,33,34); N(30,32,31); N(28,27,30); N(29,28,30); N(26,28,29); N(25,27,26); N(24,25,26); N(23,25,24); N(21,23,24); M(22,23,25,orangerWinkel); N(20,22,21); N(19,20,21); N(18,20,19); N(16,18,19); N(17,22,18); N(12,17,10); N(13,11,12); N(14,11,13); N(15,14,13);
%A(50,88); R(50,88,\"green\");
%A(80,81); R(80,81,\"green\");
%A(47,49); R(47,49,\"green\");
%A(33,35); R(33,35,\"green\");
%A(29,31); R(29,31,\"green\");
%A(14,16); R(14,16,\"green\");
%A(15,16); R(15,16,\"green\");
%A(15,17); R(15,17,\"green\");
%</Rechenweg>
%
%<Knopf id=\"Stopp_alleWinkel\" color=\"LightGrey\"/>
%
%<Knopf id=\"Start_blauerWinkel\" color=\"blue\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#blauerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_blauerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_gruenerWinkel\" color=\"green\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#gruenerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_gruenerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_orangerWinkel\" color=\"orange\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#orangerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_orangerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/2.73/0.00,
2/3.73/0.00,
3/3.23/0.87,
4/4.23/0.87,
5/4.73/0.00,
6/2.73/1.00,
7/3.23/1.87,
8/4.23/1.87,
9/1.87/0.50,
10/1.87/1.50,
11/1.00/1.00,
12/2.37/2.37,
13/1.50/1.87,
14/0.50/1.87,
15/1.00/2.73,
16/0.00/2.73,
17/1.87/3.23,
18/0.87/3.23,
19/0.00/3.73,
20/0.87/4.23,
21/0.00/4.73,
22/1.87/4.23,
23/1.00/4.73,
24/0.50/5.60,
25/1.50/5.60,
26/1.00/6.46,
27/2.37/5.10,
28/1.87/5.96,
29/1.87/6.96,
30/2.73/6.46,
31/2.73/7.46,
32/3.23/5.60,
33/3.23/6.60,
34/3.73/7.46,
35/4.10/6.10,
36/4.73/1.00,
37/5.23/1.87,
38/5.60/0.50,
39/4.60/6.96,
40/6.10/1.37,
41/4.60/7.96,
42/5.10/6.10,
43/6.10/2.37,
44/6.60/0.50,
45/5.10/7.10,
46/6.60/1.50,
47/5.60/7.96,
48/6.10/7.10,
49/6.60/7.96,
50/6.10/6.10,
51/6.60/6.96,
52/7.46/7.46,
53/7.46/6.46,
54/8.33/6.96,
55/6.96/5.60,
56/7.83/6.10,
57/8.83/6.10,
58/8.33/5.23,
59/9.33/5.23,
60/7.46/4.73,
61/8.46/4.73,
62/9.33/4.23,
63/8.46/3.73,
64/9.33/3.23,
65/7.46/3.73,
66/8.33/3.23,
67/8.83/2.37,
68/7.83/2.37,
69/8.33/1.50,
70/6.96/2.87,
71/7.46/2.00,
72/7.46/1.00,
73/3.73/2.73,
74/5.10/2.37,
75/4.23/2.87,
76/3.73/3.73,
77/2.87/3.23,
78/2.87/4.23,
79/3.73/4.73,
80/4.23/5.60,
81/5.10/5.10,
82/4.60/4.23,
83/5.10/3.37,
84/5.96/2.87,
85/6.46/3.73,
86/5.60/4.23,
87/6.46/4.73,
88/5.60/5.23}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
5/120.00/390.00/0.4/Blue,
74/210.00/390.00/0.4/Green,
23/60.00/330.00/0.4/Orange}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
2/1,
3/1, 3/2,
4/3, 4/2,
5/4, 5/2,
6/1, 6/7,
7/3, 7/8,
8/4, 8/36,
9/1, 9/6,
10/9, 10/6,
11/9, 11/10,
12/17, 12/10,
13/11, 13/12,
14/11, 14/13, 14/16,
15/14, 15/13, 15/16, 15/17,
16/18, 16/19,
17/22, 17/18,
18/20, 18/19,
19/20, 19/21,
20/22, 20/21,
21/23, 21/24,
22/23,
23/25, 23/24,
24/25, 24/26,
25/27, 25/26,
26/28, 26/29,
27/78, 27/32,
28/27, 28/30,
29/28, 29/30, 29/31,
30/32, 30/31,
31/33, 31/34,
32/80, 32/35,
33/32, 33/34, 33/35,
34/39, 34/41,
35/42, 35/39,
36/5, 36/38,
37/8, 37/36,
38/5,
39/42, 39/41,
40/37, 40/38,
41/45, 41/47,
42/81, 42/88,
43/37, 43/40,
44/40, 44/38,
45/42, 45/48,
46/43, 46/44,
47/45, 47/48, 47/49,
48/50, 48/49,
49/51, 49/52,
50/51, 50/42, 50/88,
51/53, 51/52,
52/53, 52/54,
53/55, 53/54,
54/56, 54/57,
55/60, 55/56,
56/58, 56/57,
57/58, 57/59,
58/60, 58/59,
59/61, 59/62,
60/65, 60/61,
61/63, 61/62,
62/63, 62/64,
63/65, 63/64,
64/66, 64/67,
65/85, 65/66,
66/68, 66/67,
67/68, 67/69,
68/70, 68/69,
69/71, 69/72,
70/84, 70/71,
71/46, 71/72,
72/46, 72/44,
73/7, 73/8,
74/8, 74/43,
75/8, 75/74,
76/73, 76/75,
77/73, 77/76,
78/77, 78/79,
79/76, 79/82,
80/79, 80/42, 80/81,
81/82, 81/86,
82/83, 82/86,
83/75, 83/84,
84/74,
85/84, 85/70,
86/83, 86/87,
87/85, 87/55,
88/86, 88/87}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,88}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[Green,very thick] (p-50) -- (p-88);
\draw[Green,very thick] (p-80) -- (p-81);
\draw[Green,very thick] (p-47) -- (p-49);
\draw[Green,very thick] (p-33) -- (p-35);
\draw[Green,very thick] (p-29) -- (p-31);
\draw[Green,very thick] (p-14) -- (p-16);
\draw[Green,very thick] (p-15) -- (p-16);
\draw[Green,very thick] (p-15) -- (p-17);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
5/120.00/390.00/0.4/Blue,
74/210.00/390.00/0.4/Green,
23/60.00/330.00/0.4/Orange}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/210,
2/330,
3/150,
4/30,
5/330,
6/360,
7/210,
8/330,
9/180,
10/60,
11/180,
12/348,
13/30,
14/150,
15/30,
16/150,
17/317,
18/360,
19/240,
20/60,
21/120,
22/47,
23/330,
24/210,
25/30,
26/90,
27/167,
28/240,
29/180,
30/360,
31/60,
32/240,
33/270,
34/30,
35/210,
36/120,
37/30,
38/360,
39/300,
40/90,
41/60,
42/60,
43/60,
44/240,
45/270,
46/180,
47/30,
48/270,
49/120,
50/30,
51/240,
52/60,
53/240,
54/360,
55/93,
56/210,
57/330,
58/210,
59/60,
60/137,
61/120,
62/360,
63/180,
64/300,
65/227,
66/90,
67/270,
68/150,
69/360,
70/330,
71/60,
72/360,
73/300,
74/360,
75/120,
76/60,
77/180,
78/257,
79/62,
80/180,
81/90,
82/150,
83/270,
84/210,
85/90,
86/240,
87/360,
88/270}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
Darin verwendet Button "Feinjustieren(3)" folgende näherungsweise Ableitungsmatrix
4.440892098500626e-15 , -0.0000015708025822291916, 0
-5.10702591327572e-15 , 5.038299732973428e-7 , 0
3.9968028886505635e-15, 0.0000018325966834042973, 0 |
Die dritte Spalte ist komplett Null, ich könnte also den dritten (orangen) Winkel alleine verstellen ohne dass sich die Kantenlängen ändern. Für die ersten drei Einsetzkanten stimmt das auch, allerdings ändern sich die letzten drei Einsetzkanten P14-P16, P15-P16, P15-P17. Für Button Feinjustieren müsste ich eigentlich diese letzten drei Einsetzkanten an den Anfang setzen und damit die Ableitungsmatrix bilden. Wie man solche Kanten herausfinden kann, dazu gab es schonmal Überlegungen in Beitrag No.630 letzter Absatz ab "Bei Button...". Die auszuwählenden Einsetzkanten sind dort als Anfügekanten bezeichnet. Ziemlich kompliziert das alles, es geht einfacher. Ich muss die Ableitungsmatrix nicht aus den drei Winkeln und den ersten drei Einsetzkanten bilden, sondern aus allen Winkeln und allen Einsetzkanten. Dann sieht die Matrix so aus
4.440892098500626e-15, -0.0000015708025822291916, 0
-5.10702591327572e-15, 5.038299732973428e-7, 0
3.9968028886505635e-15, 0.0000018325966834042973, 0
-2.1649348980190553e-14, 0.000003728382380385753, 0
1.3100631690576847e-14,-5.794182773577461e-7, 0
-1.7453302114667224e-7, 0.000009126448137664056, 1.7453285150459408e-7
-3.4906585666405476e-7, 0.000008188297134559264, 3.490659944427321e-7
3.0229989467223106e-7, -0.0000074187649146129075, -3.0230001990538824e-7 |
Die Einträge ...e-14 und ...-e-15 betrachte ich als Null. Dann besteht die lineare Abhängigkeit jetzt aus der Gleichung 1 * erste Spalte + 0 * zweite Spalte + 1 * dritte Spalte = 0. Auf die Winkel übertragen, wenn ich den ersten (blauen) Winkel ein wenig ändere, muss ich den zweiten (grünen) Winkel unverändert lassen und den dritten (orangen) Winkel genau wie den ersten ändern. Das übernehme ich in die Eingabe
88 Knoten, 4×Grad 3, 80×Grad 4, 2×Grad 5, 2×Grad 7, 0 Überschneidungen
178 Kanten, minimal 0.99999999999991695532, maximal 1.00000000000007682743
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>Automatisch generierte Eingabe zu: #1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78);</Bildtext>
%<Ausrichten von="1" nach="2"/>
%<Winkel size="18" color="blue" id="blauerWinkel" value="-90"/>
%<Winkel size="18" color="green" id="gruenerWinkel" value="-179.9999999999996"/>
%<Winkel size="18" color="orange" id="orangerWinkel" value="-90"/>
%<Feinjustieren Anzahl="8,3"/>
%<Rechenweg>
%P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(2,1); N(3,1,2); N(4,3,2); N(5,4,2); M(38,5,4,blauerWinkel); N(36,5,38); N(8,4,36); N(37,8,36); N(40,37,38); N(43,37,40); N(44,40,38); N(46,43,44); N(72,46,44); N(74,8,43); N(75,8,74); N(7,3,8); N(71,46,72); N(73,7,8); N(76,73,75); N(77,73,76); N(6,1,7); N(9,1,6); N(10,9,6); N(11,9,10); N(69,71,72); M(84,74,8,-180); N(70,84,71); N(83,75,84); N(85,84,70); N(68,70,69); N(67,68,69); N(66,68,67); N(64,66,67); N(65,85,66); N(63,65,64); N(62,63,64); N(61,63,62); N(59,61,62); N(60,65,61); N(58,60,59); N(57,58,59); N(56,58,57); N(54,56,57); N(55,60,56); N(87,85,55); N(53,55,54); N(86,83,87); N(88,86,87); N(52,53,54); N(82,83,86); N(51,53,52); N(79,76,82); N(81,82,86); N(42,81,88); N(49,51,52); N(50,51,42); N(78,77,79); N(80,79,42); N(48,50,49); N(45,42,48); N(47,45,48); N(41,45,47); N(39,42,41); N(34,39,41); N(35,42,39); N(32,80,35); N(33,32,34); N(27,78,32); N(31,33,34); N(30,32,31); N(28,27,30); N(29,28,30); N(26,28,29); N(25,27,26); N(24,25,26); N(23,25,24); N(21,23,24); M(22,23,25,blauerWinkel); N(20,22,21); N(19,20,21); N(18,20,19); N(16,18,19); N(17,22,18); N(12,17,10); N(13,11,12); N(14,11,13); N(15,14,13);
%A(50,88); R(50,88,"green");
%A(80,81); R(80,81,"green");
%A(47,49); R(47,49,"green");
%A(33,35); R(33,35,"green");
%A(29,31); R(29,31,"green");
%A(14,16); R(14,16,"green");
%A(15,16); R(15,16,"green");
%A(15,17); R(15,17,"green");
%</Rechenweg>
%
%<Knopf id="Stopp_alleWinkel" color="LightGrey"/>
%
%<Knopf id="Start_blauerWinkel" color="blue"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#blauerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_blauerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_gruenerWinkel" color="green"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#gruenerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_gruenerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_orangerWinkel" color="orange"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#orangerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_orangerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/2.73/0.00,
2/3.73/0.00,
3/3.23/0.87,
4/4.23/0.87,
5/4.73/0.00,
6/2.73/1.00,
7/3.23/1.87,
8/4.23/1.87,
9/1.87/0.50,
10/1.87/1.50,
11/1.00/1.00,
12/2.37/2.37,
13/1.50/1.87,
14/0.50/1.87,
15/1.00/2.73,
16/0.00/2.73,
17/1.87/3.23,
18/0.87/3.23,
19/0.00/3.73,
20/0.87/4.23,
21/0.00/4.73,
22/1.87/4.23,
23/1.00/4.73,
24/0.50/5.60,
25/1.50/5.60,
26/1.00/6.46,
27/2.37/5.10,
28/1.87/5.96,
29/1.87/6.96,
30/2.73/6.46,
31/2.73/7.46,
32/3.23/5.60,
33/3.23/6.60,
34/3.73/7.46,
35/4.10/6.10,
36/4.73/1.00,
37/5.23/1.87,
38/5.60/0.50,
39/4.60/6.96,
40/6.10/1.37,
41/4.60/7.96,
42/5.10/6.10,
43/6.10/2.37,
44/6.60/0.50,
45/5.10/7.10,
46/6.60/1.50,
47/5.60/7.96,
48/6.10/7.10,
49/6.60/7.96,
50/6.10/6.10,
51/6.60/6.96,
52/7.46/7.46,
53/7.46/6.46,
54/8.33/6.96,
55/6.96/5.60,
56/7.83/6.10,
57/8.83/6.10,
58/8.33/5.23,
59/9.33/5.23,
60/7.46/4.73,
61/8.46/4.73,
62/9.33/4.23,
63/8.46/3.73,
64/9.33/3.23,
65/7.46/3.73,
66/8.33/3.23,
67/8.83/2.37,
68/7.83/2.37,
69/8.33/1.50,
70/6.96/2.87,
71/7.46/2.00,
72/7.46/1.00,
73/3.73/2.73,
74/5.10/2.37,
75/4.23/2.87,
76/3.73/3.73,
77/2.87/3.23,
78/2.87/4.23,
79/3.73/4.73,
80/4.23/5.60,
81/5.10/5.10,
82/4.60/4.23,
83/5.10/3.37,
84/5.96/2.87,
85/6.46/3.73,
86/5.60/4.23,
87/6.46/4.73,
88/5.60/5.23}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
5/120.00/390.00/0.4/Blue,
23/60.00/330.00/0.4/Blue}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
2/1,
3/1, 3/2,
4/3, 4/2,
5/4, 5/2,
6/1, 6/7,
7/3, 7/8,
8/4, 8/36,
9/1, 9/6,
10/9, 10/6,
11/9, 11/10,
12/17, 12/10,
13/11, 13/12,
14/11, 14/13, 14/16,
15/14, 15/13, 15/16, 15/17,
16/18, 16/19,
17/22, 17/18,
18/20, 18/19,
19/20, 19/21,
20/22, 20/21,
21/23, 21/24,
22/23,
23/25, 23/24,
24/25, 24/26,
25/27, 25/26,
26/28, 26/29,
27/78, 27/32,
28/27, 28/30,
29/28, 29/30, 29/31,
30/32, 30/31,
31/33, 31/34,
32/80, 32/35,
33/32, 33/34, 33/35,
34/39, 34/41,
35/42, 35/39,
36/5, 36/38,
37/8, 37/36,
38/5,
39/42, 39/41,
40/37, 40/38,
41/45, 41/47,
42/81, 42/88,
43/37, 43/40,
44/40, 44/38,
45/42, 45/48,
46/43, 46/44,
47/45, 47/48, 47/49,
48/50, 48/49,
49/51, 49/52,
50/51, 50/42, 50/88,
51/53, 51/52,
52/53, 52/54,
53/55, 53/54,
54/56, 54/57,
55/60, 55/56,
56/58, 56/57,
57/58, 57/59,
58/60, 58/59,
59/61, 59/62,
60/65, 60/61,
61/63, 61/62,
62/63, 62/64,
63/65, 63/64,
64/66, 64/67,
65/85, 65/66,
66/68, 66/67,
67/68, 67/69,
68/70, 68/69,
69/71, 69/72,
70/84, 70/71,
71/46, 71/72,
72/46, 72/44,
73/7, 73/8,
74/8, 74/43,
75/8, 75/74,
76/73, 76/75,
77/73, 77/76,
78/77, 78/79,
79/76, 79/82,
80/79, 80/42, 80/81,
81/82, 81/86,
82/83, 82/86,
83/75, 83/84,
84/74,
85/84, 85/70,
86/83, 86/87,
87/85, 87/55,
88/86, 88/87}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,88}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[Green,very thick] (p-50) -- (p-88);
\draw[Green,very thick] (p-80) -- (p-81);
\draw[Green,very thick] (p-47) -- (p-49);
\draw[Green,very thick] (p-33) -- (p-35);
\draw[Green,very thick] (p-29) -- (p-31);
\draw[Green,very thick] (p-14) -- (p-16);
\draw[Green,very thick] (p-15) -- (p-16);
\draw[Green,very thick] (p-15) -- (p-17);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
5/120.00/390.00/0.4/Blue,
23/60.00/330.00/0.4/Blue}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/210,
2/330,
3/150,
4/30,
5/330,
6/360,
7/210,
8/330,
9/180,
10/60,
11/180,
12/347,
13/30,
14/270,
15/30,
16/240,
17/77,
18/360,
19/120,
20/360,
21/120,
22/48,
23/330,
24/90,
25/330,
26/90,
27/167,
28/300,
29/180,
30/360,
31/60,
32/240,
33/270,
34/30,
35/210,
36/120,
37/30,
38/360,
39/300,
40/90,
41/150,
42/60,
43/60,
44/240,
45/210,
46/180,
47/30,
48/270,
49/120,
50/30,
51/180,
52/60,
53/300,
54/90,
55/93,
56/210,
57/30,
58/210,
59/60,
60/257,
61/120,
62/300,
63/180,
64/30,
65/227,
66/90,
67/30,
68/150,
69/360,
70/330,
71/60,
72/360,
73/300,
74/360,
75/120,
76/60,
77/180,
78/257,
79/62,
80/180,
81/90,
82/150,
83/270,
84/210,
85/90,
86/330,
87/360,
88/270}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/5bd5e491d22c0c64548a69fce9c3a42e.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>Automatisch generierte Eingabe zu: #1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78);</Bildtext>
%<Ausrichten von=\"1\" nach=\"2\"/>
%<Winkel size=\"18\" color=\"blue\" id=\"blauerWinkel\" value=\"-90\"/>
%<Winkel size=\"18\" color=\"green\" id=\"gruenerWinkel\" value=\"-179.9999999999996\"/>
%<Winkel size=\"18\" color=\"orange\" id=\"orangerWinkel\" value=\"-90\"/>
%<Feinjustieren Anzahl=\"8,3\"/>
%<Rechenweg>
%P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(2,1); N(3,1,2); N(4,3,2); N(5,4,2); M(38,5,4,blauerWinkel); N(36,5,38); N(8,4,36); N(37,8,36); N(40,37,38); N(43,37,40); N(44,40,38); N(46,43,44); N(72,46,44); N(74,8,43); N(75,8,74); N(7,3,8); N(71,46,72); N(73,7,8); N(76,73,75); N(77,73,76); N(6,1,7); N(9,1,6); N(10,9,6); N(11,9,10); N(69,71,72); M(84,74,8,-180); N(70,84,71); N(83,75,84); N(85,84,70); N(68,70,69); N(67,68,69); N(66,68,67); N(64,66,67); N(65,85,66); N(63,65,64); N(62,63,64); N(61,63,62); N(59,61,62); N(60,65,61); N(58,60,59); N(57,58,59); N(56,58,57); N(54,56,57); N(55,60,56); N(87,85,55); N(53,55,54); N(86,83,87); N(88,86,87); N(52,53,54); N(82,83,86); N(51,53,52); N(79,76,82); N(81,82,86); N(42,81,88); N(49,51,52); N(50,51,42); N(78,77,79); N(80,79,42); N(48,50,49); N(45,42,48); N(47,45,48); N(41,45,47); N(39,42,41); N(34,39,41); N(35,42,39); N(32,80,35); N(33,32,34); N(27,78,32); N(31,33,34); N(30,32,31); N(28,27,30); N(29,28,30); N(26,28,29); N(25,27,26); N(24,25,26); N(23,25,24); N(21,23,24); M(22,23,25,blauerWinkel); N(20,22,21); N(19,20,21); N(18,20,19); N(16,18,19); N(17,22,18); N(12,17,10); N(13,11,12); N(14,11,13); N(15,14,13);
%A(50,88); R(50,88,\"green\");
%A(80,81); R(80,81,\"green\");
%A(47,49); R(47,49,\"green\");
%A(33,35); R(33,35,\"green\");
%A(29,31); R(29,31,\"green\");
%A(14,16); R(14,16,\"green\");
%A(15,16); R(15,16,\"green\");
%A(15,17); R(15,17,\"green\");
%</Rechenweg>
%
%<Knopf id=\"Stopp_alleWinkel\" color=\"LightGrey\"/>
%
%<Knopf id=\"Start_blauerWinkel\" color=\"blue\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#blauerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_blauerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_gruenerWinkel\" color=\"green\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#gruenerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_gruenerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_orangerWinkel\" color=\"orange\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#orangerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_orangerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/2.73/0.00,
2/3.73/0.00,
3/3.23/0.87,
4/4.23/0.87,
5/4.73/0.00,
6/2.73/1.00,
7/3.23/1.87,
8/4.23/1.87,
9/1.87/0.50,
10/1.87/1.50,
11/1.00/1.00,
12/2.37/2.37,
13/1.50/1.87,
14/0.50/1.87,
15/1.00/2.73,
16/0.00/2.73,
17/1.87/3.23,
18/0.87/3.23,
19/0.00/3.73,
20/0.87/4.23,
21/0.00/4.73,
22/1.87/4.23,
23/1.00/4.73,
24/0.50/5.60,
25/1.50/5.60,
26/1.00/6.46,
27/2.37/5.10,
28/1.87/5.96,
29/1.87/6.96,
30/2.73/6.46,
31/2.73/7.46,
32/3.23/5.60,
33/3.23/6.60,
34/3.73/7.46,
35/4.10/6.10,
36/4.73/1.00,
37/5.23/1.87,
38/5.60/0.50,
39/4.60/6.96,
40/6.10/1.37,
41/4.60/7.96,
42/5.10/6.10,
43/6.10/2.37,
44/6.60/0.50,
45/5.10/7.10,
46/6.60/1.50,
47/5.60/7.96,
48/6.10/7.10,
49/6.60/7.96,
50/6.10/6.10,
51/6.60/6.96,
52/7.46/7.46,
53/7.46/6.46,
54/8.33/6.96,
55/6.96/5.60,
56/7.83/6.10,
57/8.83/6.10,
58/8.33/5.23,
59/9.33/5.23,
60/7.46/4.73,
61/8.46/4.73,
62/9.33/4.23,
63/8.46/3.73,
64/9.33/3.23,
65/7.46/3.73,
66/8.33/3.23,
67/8.83/2.37,
68/7.83/2.37,
69/8.33/1.50,
70/6.96/2.87,
71/7.46/2.00,
72/7.46/1.00,
73/3.73/2.73,
74/5.10/2.37,
75/4.23/2.87,
76/3.73/3.73,
77/2.87/3.23,
78/2.87/4.23,
79/3.73/4.73,
80/4.23/5.60,
81/5.10/5.10,
82/4.60/4.23,
83/5.10/3.37,
84/5.96/2.87,
85/6.46/3.73,
86/5.60/4.23,
87/6.46/4.73,
88/5.60/5.23}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
5/120.00/390.00/0.4/Blue,
23/60.00/330.00/0.4/Blue}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
2/1,
3/1, 3/2,
4/3, 4/2,
5/4, 5/2,
6/1, 6/7,
7/3, 7/8,
8/4, 8/36,
9/1, 9/6,
10/9, 10/6,
11/9, 11/10,
12/17, 12/10,
13/11, 13/12,
14/11, 14/13, 14/16,
15/14, 15/13, 15/16, 15/17,
16/18, 16/19,
17/22, 17/18,
18/20, 18/19,
19/20, 19/21,
20/22, 20/21,
21/23, 21/24,
22/23,
23/25, 23/24,
24/25, 24/26,
25/27, 25/26,
26/28, 26/29,
27/78, 27/32,
28/27, 28/30,
29/28, 29/30, 29/31,
30/32, 30/31,
31/33, 31/34,
32/80, 32/35,
33/32, 33/34, 33/35,
34/39, 34/41,
35/42, 35/39,
36/5, 36/38,
37/8, 37/36,
38/5,
39/42, 39/41,
40/37, 40/38,
41/45, 41/47,
42/81, 42/88,
43/37, 43/40,
44/40, 44/38,
45/42, 45/48,
46/43, 46/44,
47/45, 47/48, 47/49,
48/50, 48/49,
49/51, 49/52,
50/51, 50/42, 50/88,
51/53, 51/52,
52/53, 52/54,
53/55, 53/54,
54/56, 54/57,
55/60, 55/56,
56/58, 56/57,
57/58, 57/59,
58/60, 58/59,
59/61, 59/62,
60/65, 60/61,
61/63, 61/62,
62/63, 62/64,
63/65, 63/64,
64/66, 64/67,
65/85, 65/66,
66/68, 66/67,
67/68, 67/69,
68/70, 68/69,
69/71, 69/72,
70/84, 70/71,
71/46, 71/72,
72/46, 72/44,
73/7, 73/8,
74/8, 74/43,
75/8, 75/74,
76/73, 76/75,
77/73, 77/76,
78/77, 78/79,
79/76, 79/82,
80/79, 80/42, 80/81,
81/82, 81/86,
82/83, 82/86,
83/75, 83/84,
84/74,
85/84, 85/70,
86/83, 86/87,
87/85, 87/55,
88/86, 88/87}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,88}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[Green,very thick] (p-50) -- (p-88);
\draw[Green,very thick] (p-80) -- (p-81);
\draw[Green,very thick] (p-47) -- (p-49);
\draw[Green,very thick] (p-33) -- (p-35);
\draw[Green,very thick] (p-29) -- (p-31);
\draw[Green,very thick] (p-14) -- (p-16);
\draw[Green,very thick] (p-15) -- (p-16);
\draw[Green,very thick] (p-15) -- (p-17);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
5/120.00/390.00/0.4/Blue,
23/60.00/330.00/0.4/Blue}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/210,
2/330,
3/150,
4/30,
5/330,
6/360,
7/210,
8/330,
9/180,
10/60,
11/180,
12/347,
13/30,
14/270,
15/30,
16/240,
17/77,
18/360,
19/120,
20/360,
21/120,
22/48,
23/330,
24/90,
25/330,
26/90,
27/167,
28/300,
29/180,
30/360,
31/60,
32/240,
33/270,
34/30,
35/210,
36/120,
37/30,
38/360,
39/300,
40/90,
41/150,
42/60,
43/60,
44/240,
45/210,
46/180,
47/30,
48/270,
49/120,
50/30,
51/180,
52/60,
53/300,
54/90,
55/93,
56/210,
57/30,
58/210,
59/60,
60/257,
61/120,
62/300,
63/180,
64/30,
65/227,
66/90,
67/30,
68/150,
69/360,
70/330,
71/60,
72/360,
73/300,
74/360,
75/120,
76/60,
77/180,
78/257,
79/62,
80/180,
81/90,
82/150,
83/270,
84/210,
85/90,
86/330,
87/360,
88/270}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
und das passt. Allein die Änderung des blauen Winkels [Animation "Start_blauerWinkel"] macht den Graph beweglich. So einen Tipp auf Knopfdruck ohne extra GAP-Programm erhalten wäre nicht schlecht.
|
Profil
Quote
Link |
StefanVogel
Senior
Dabei seit: 26.11.2005
Mitteilungen: 3446
Aus: Raun
| Beitrag No.1900, eingetragen 2020-02-01 06:22
|
Hierzu neu Streichholzgraph-1898.htm mit Button "beweglich?". Ich beginne eine neue Version neben der bisherigen Streichholzgraph-1554.htm wegen möglicher Änderungen anderer Programmfunktionen. Zum Beispiel die Buttons für neue Eingabe geben jetzt stets Anzahl="s,ws" als Attribut im xml-Element "Feinjustieren" zurück für s Einsetzkanten und ws Winkel. Anschließendes Feinjustieren(s,ws) wirkt bei s>ws wie bisher als Feinjustieren(ws,ws), das kann sich aber auch noch ändern.
Für den #467-2 ohne die beiden Kanten P22-P78 und P12-P77 erhalte ich nach Button neue Eingabe "wenig Winkel" jetzt
88 Knoten, 4×Grad 3, 80×Grad 4, 2×Grad 5, 2×Grad 7, 0 Überschneidungen
178 Kanten, minimal 0.99999999999998412381, maximal 1.00000000000001443290
einzustellende Kanten, Abstände und Winkel:
|P42-P80|=1.00000000000000577316
|P75-P83|=1.00000000000000044409
|P86-P87|=1.00000000000000310862
|P85-P87|=1.00000000000000910383
|P55-P87|=1.00000000000000799361
|P60-P61|=1.00000000000000288658
|P65-P66|=1.00000000000001443290
|P65-P85|=0.99999999999998412381
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78);</Bildtext>
%<Ausrichten von="1" nach="2"/>
%<Winkel size="18" color="blue" id="blauerWinkel" value="90"/>
%<Winkel size="18" color="green" id="gruenerWinkel" value="90"/>
%<Winkel size="18" color="orange" id="orangerWinkel" value="89.99999999999994"/>
%<Feinjustieren Anzahl="8,3"/>
%<Rechenweg>
%P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(1,2); L(3,1,2); L(4,3,2); L(5,4,2); M(6,1,2,blauerWinkel); L(9,1,6); L(10,9,6); L(11,9,10); N(7,6,3); M(109,7,3,95.00000000000001); L(73,7,109); Q(8,7,4,ab(109,7,73,"gedreht"),D); M(110,8,4,35.000000000000014); L(37,8,110); M(111,5,2,-85.00000000000001); L(38,111,5); Q(36,8,5,ab(110,8,37,"gedreht"),ab(111,5,38,"gedreht")); M(112,37,8,154.99999999999997); L(43,37,112); M(113,38,5,-144.99999999999994); L(44,113,38); Q(40,37,38,ab(112,37,43,"gedreht"),ab(113,38,44,"gedreht")); M(114,44,38,-85.00000000000017); M(71,114,44,125.00000000000043); M(69,71,114,125.00000000000016); L(116,69,71); Q(115,71,114,ab(116,71,69,"gedreht"),D); Q(72,114,44,ab(115,114,69,71,"gedreht"),D); Q(46,43,44,D,ab(114,44,69,71,72,"gedreht")); M(117,8,4,125.00000000000001); L(75,8,117); Q(74,8,43,ab(117,8,75,"gedreht"),D); M(118,73,7,-144.99999999999994); L(77,73,118); Q(76,73,75,ab(118,73,77,"gedreht"),D); M(12,10,6,gruenerWinkel); M(119,11,9,95.00000000000006); L(14,11,119); L(15,14,119); L(16,14,15); Q(13,11,12,ab(119,11,14,15,16,"gedreht"),D); N(17,15,12); M(120,16,14,94.99999999999991); L(19,16,120); L(20,19,120); L(21,19,20); Q(18,16,17,ab(120,16,19,20,21,"gedreht"),D); N(22,20,17); M(121,21,19,95.00000000000006); L(24,21,121); L(25,24,121); L(26,24,25); Q(23,21,22,ab(121,21,24,25,26,"gedreht"),D); M(27,25,23,orangerWinkel); M(122,26,24,95.00000000000001); L(29,26,122); L(30,29,122); L(31,29,30); Q(28,26,27,ab(122,26,29,30,31,"gedreht"),D); N(32,30,27); M(123,31,29,95.00000000000009); L(34,31,123); M(124,32,27,-114.99999999999997); L(35,124,32); Q(33,31,32,ab(123,31,34,"gedreht"),ab(124,32,35,"gedreht")); M(125,34,31,154.99999999999991); L(41,34,125); M(126,35,32,-144.99999999999986); L(42,126,35); Q(39,34,35,ab(125,34,41,"gedreht"),ab(126,35,42,"gedreht")); M(127,41,34,95.00000000000006); L(47,41,127); L(48,47,127); L(49,47,48); Q(45,41,42,ab(127,41,47,48,49,"gedreht"),D); M(128,42,35,-174.99999999999991); L(88,128,42); Q(50,48,42,D,ab(128,42,88,"gedreht")); M(129,49,47,95.00000000000014); L(52,49,129); L(53,52,129); L(54,52,53); Q(51,49,50,ab(129,49,52,53,54,"gedreht"),D); N(78,27,77); N(79,78,76); N(80,32,79); M(130,42,35,34.999999999999915); L(81,42,130); A(80,42,ab(130,42,81,"gedreht")); M(131,81,42,155.0000000000003); M(83,131,81,-115.0000000000004); L(132,131,83); Q(86,81,131,D,ab(132,131,83,"gedreht")); Q(82,81,79,ab(131,81,83,86,"gedreht"),D); A(75,83); M(87,86,81,-84.99999999999967); L(133,86,87); A(88,86,ab(133,86,87,"gedreht")); N(84,83,74); M(134,84,74,155.00000000000026); L(85,84,134); Q(70,84,71,ab(134,84,85,"gedreht"),D); A(85,87); M(67,69,71,-85.00000000000058); M(64,67,69,185); L(66,67,64); L(136,67,66); Q(135,69,67,D,ab(136,67,64,66,"gedreht")); Q(68,70,69,D,ab(135,69,64,66,67,"gedreht")); M(56,54,52,94.99999999999955); L(57,54,56); L(58,57,56); L(137,57,58); M(62,64,66,-84.99999999999945); M(138,62,64,185); L(61,62,138); L(139,62,61); Q(63,64,62,D,ab(139,62,138,61,"gedreht")); Q(59,54,64,ab(137,54,56,57,58,"gedreht"),ab(138,64,61,62,63,"gedreht")); N(55,56,53); A(55,87); N(60,58,55); A(60,61); N(65,63,60); A(65,66); A(65,85);
%R(42,80); // oder R(42,81);
%R(75,83);
%R(86,87); // oder R(86,88);
%R(85,87);
%R(55,87);
%R(60,61);
%R(65,66);
%R(65,85);
%</Rechenweg>
%
%<Knopf id="Stopp_alleWinkel" color="LightGrey"/>
%
%<Knopf id="Start_blauerWinkel" color="blue"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#blauerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_blauerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_gruenerWinkel" color="green"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#gruenerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_gruenerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_orangerWinkel" color="orange"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#orangerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_orangerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LimeGreen}{rgb}{0.20,0.80,0.20}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/2.73/0.00,
2/3.73/0.00,
3/3.23/0.87,
4/4.23/0.87,
5/4.73/0.00,
6/2.73/1.00,
7/3.23/1.87,
8/4.23/1.87,
9/1.87/0.50,
10/1.87/1.50,
11/1.00/1.00,
12/2.37/2.37,
13/1.50/1.87,
14/0.50/1.87,
15/1.00/2.73,
16/0.00/2.73,
17/1.87/3.23,
18/0.87/3.23,
19/0.00/3.73,
20/0.87/4.23,
21/0.00/4.73,
22/1.87/4.23,
23/1.00/4.73,
24/0.50/5.60,
25/1.50/5.60,
26/1.00/6.46,
27/2.37/5.10,
28/1.87/5.96,
29/1.87/6.96,
30/2.73/6.46,
31/2.73/7.46,
32/3.23/5.60,
33/3.23/6.60,
34/3.73/7.46,
35/4.10/6.10,
36/4.73/1.00,
37/5.23/1.87,
38/5.60/0.50,
39/4.60/6.96,
40/6.10/1.37,
41/4.60/7.96,
42/5.10/6.10,
43/6.10/2.37,
44/6.60/0.50,
45/5.10/7.10,
46/6.60/1.50,
47/5.60/7.96,
48/6.10/7.10,
49/6.60/7.96,
50/6.10/6.10,
51/6.60/6.96,
52/7.46/7.46,
53/7.46/6.46,
54/8.33/6.96,
55/6.96/5.60,
56/7.83/6.10,
57/8.83/6.10,
58/8.33/5.23,
59/9.33/5.23,
60/7.46/4.73,
61/8.46/4.73,
62/9.33/4.23,
63/8.46/3.73,
64/9.33/3.23,
65/7.46/3.73,
66/8.33/3.23,
67/8.83/2.37,
68/7.83/2.37,
69/8.33/1.50,
70/6.96/2.87,
71/7.46/2.00,
72/7.46/1.00,
73/3.73/2.73,
74/5.10/2.37,
75/4.23/2.87,
76/3.73/3.73,
77/2.87/3.23,
78/2.87/4.23,
79/3.73/4.73,
80/4.23/5.60,
81/5.10/5.10,
82/4.60/4.23,
83/5.10/3.37,
84/5.96/2.87,
85/6.46/3.73,
86/5.60/4.23,
87/6.46/4.73,
88/5.60/5.23}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
1/0.00/90.00/0.4/Blue,
10/330.00/420.00/0.4/Green,
25/240.00/330.00/0.4/Orange}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
1/2,
3/1, 3/2,
4/3, 4/2,
5/4, 5/2,
6/1,
7/6, 7/3,
8/7, 8/4,
9/1, 9/6,
10/9, 10/6,
11/9, 11/10,
12/10,
13/11, 13/12,
14/11, 14/13,
15/14, 15/13,
16/14, 16/15,
17/15, 17/12,
18/16, 18/17,
19/16, 19/18,
20/19, 20/18,
21/19, 21/20,
22/20, 22/17,
23/21, 23/22,
24/21, 24/23,
25/24, 25/23,
26/24, 26/25,
27/25,
28/26, 28/27,
29/26, 29/28,
30/29, 30/28,
31/29, 31/30,
32/30, 32/27,
33/31, 33/32,
34/31, 34/33,
35/33, 35/32,
36/8, 36/5,
37/8, 37/36,
38/36, 38/5,
39/34, 39/35,
40/37, 40/38,
41/34, 41/39,
42/39, 42/35,
43/37, 43/40,
44/40, 44/38,
45/41, 45/42,
46/43, 46/44,
47/41, 47/45,
48/47, 48/45,
49/47, 49/48,
50/48, 50/42,
51/49, 51/50,
52/49, 52/51,
53/52, 53/51,
54/52, 54/53,
55/56, 55/53, 55/87,
56/54,
57/54, 57/56,
58/57, 58/56,
59/57, 59/58, 59/62,
60/58, 60/55, 60/61,
61/62, 61/59,
62/64,
63/64, 63/61, 63/62,
64/67,
65/63, 65/60, 65/66, 65/85,
66/67, 66/64,
67/69,
68/70, 68/66, 68/67, 68/69,
69/71,
70/84, 70/71,
71/46,
72/69, 72/71, 72/46, 72/44,
73/7, 73/8,
74/8, 74/43,
75/8, 75/74, 75/83,
76/73, 76/75,
77/73, 77/76,
78/27, 78/77,
79/78, 79/76,
80/32, 80/79, 80/42,
81/42, 81/80,
82/81, 82/79,
83/82,
84/83, 84/74,
85/84, 85/70, 85/87,
86/81, 86/83, 86/82,
87/86,
88/50, 88/42, 88/86, 88/87}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,88}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[LimeGreen,very thick] (p-42) -- (p-80);
\draw[LimeGreen,very thick] (p-75) -- (p-83);
\draw[LimeGreen,very thick] (p-86) -- (p-87);
\draw[LimeGreen,very thick] (p-85) -- (p-87);
\draw[LimeGreen,very thick] (p-55) -- (p-87);
\draw[LimeGreen,very thick] (p-60) -- (p-61);
\draw[LimeGreen,very thick] (p-65) -- (p-66);
\draw[LimeGreen,very thick] (p-65) -- (p-85);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
1/0.00/90.00/0.4/Blue,
10/330.00/420.00/0.4/Green,
25/240.00/330.00/0.4/Orange}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/210,
2/330,
3/150,
4/30,
5/330,
6/60,
7/210,
8/240,
9/180,
10/60,
11/270,
12/348,
13/30,
14/270,
15/30,
16/240,
17/318,
18/300,
19/240,
20/60,
21/120,
22/48,
23/330,
24/150,
25/330,
26/180,
27/258,
28/240,
29/180,
30/360,
31/60,
32/240,
33/270,
34/180,
35/360,
36/270,
37/180,
38/360,
39/90,
40/90,
41/60,
42/60,
43/60,
44/330,
45/270,
46/120,
47/150,
48/330,
49/120,
50/30,
51/240,
52/120,
53/300,
54/360,
55/93,
56/210,
57/90,
58/210,
59/330,
60/137,
61/180,
62/300,
63/180,
64/30,
65/318,
66/90,
67/330,
68/150,
69/360,
70/330,
71/120,
72/360,
73/90,
74/360,
75/120,
76/60,
77/180,
78/257,
79/123,
80/180,
81/90,
82/150,
83/270,
84/210,
85/90,
86/240,
87/360,
88/270}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/1c21a65c2ef01578b09f25b2d14636bc.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78);</Bildtext>
%<Ausrichten von=\"1\" nach=\"2\"/>
%<Winkel size=\"18\" color=\"blue\" id=\"blauerWinkel\" value=\"90\"/>
%<Winkel size=\"18\" color=\"green\" id=\"gruenerWinkel\" value=\"90\"/>
%<Winkel size=\"18\" color=\"orange\" id=\"orangerWinkel\" value=\"89.99999999999994\"/>
%<Feinjustieren Anzahl=\"8,3\"/>
%<Rechenweg>
%P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(1,2); L(3,1,2); L(4,3,2); L(5,4,2); M(6,1,2,blauerWinkel); L(9,1,6); L(10,9,6); L(11,9,10); N(7,6,3); M(109,7,3,95.00000000000001); L(73,7,109); Q(8,7,4,ab(109,7,73,\"gedreht\"),D); M(110,8,4,35.000000000000014); L(37,8,110); M(111,5,2,-85.00000000000001); L(38,111,5); Q(36,8,5,ab(110,8,37,\"gedreht\"),ab(111,5,38,\"gedreht\")); M(112,37,8,154.99999999999997); L(43,37,112); M(113,38,5,-144.99999999999994); L(44,113,38); Q(40,37,38,ab(112,37,43,\"gedreht\"),ab(113,38,44,\"gedreht\")); M(114,44,38,-85.00000000000017); M(71,114,44,125.00000000000043); M(69,71,114,125.00000000000016); L(116,69,71); Q(115,71,114,ab(116,71,69,\"gedreht\"),D); Q(72,114,44,ab(115,114,69,71,\"gedreht\"),D); Q(46,43,44,D,ab(114,44,69,71,72,\"gedreht\")); M(117,8,4,125.00000000000001); L(75,8,117); Q(74,8,43,ab(117,8,75,\"gedreht\"),D); M(118,73,7,-144.99999999999994); L(77,73,118); Q(76,73,75,ab(118,73,77,\"gedreht\"),D); M(12,10,6,gruenerWinkel); M(119,11,9,95.00000000000006); L(14,11,119); L(15,14,119); L(16,14,15); Q(13,11,12,ab(119,11,14,15,16,\"gedreht\"),D); N(17,15,12); M(120,16,14,94.99999999999991); L(19,16,120); L(20,19,120); L(21,19,20); Q(18,16,17,ab(120,16,19,20,21,\"gedreht\"),D); N(22,20,17); M(121,21,19,95.00000000000006); L(24,21,121); L(25,24,121); L(26,24,25); Q(23,21,22,ab(121,21,24,25,26,\"gedreht\"),D); M(27,25,23,orangerWinkel); M(122,26,24,95.00000000000001); L(29,26,122); L(30,29,122); L(31,29,30); Q(28,26,27,ab(122,26,29,30,31,\"gedreht\"),D); N(32,30,27); M(123,31,29,95.00000000000009); L(34,31,123); M(124,32,27,-114.99999999999997); L(35,124,32); Q(33,31,32,ab(123,31,34,\"gedreht\"),ab(124,32,35,\"gedreht\")); M(125,34,31,154.99999999999991); L(41,34,125); M(126,35,32,-144.99999999999986); L(42,126,35); Q(39,34,35,ab(125,34,41,\"gedreht\"),ab(126,35,42,\"gedreht\")); M(127,41,34,95.00000000000006); L(47,41,127); L(48,47,127); L(49,47,48); Q(45,41,42,ab(127,41,47,48,49,\"gedreht\"),D); M(128,42,35,-174.99999999999991); L(88,128,42); Q(50,48,42,D,ab(128,42,88,\"gedreht\")); M(129,49,47,95.00000000000014); L(52,49,129); L(53,52,129); L(54,52,53); Q(51,49,50,ab(129,49,52,53,54,\"gedreht\"),D); N(78,27,77); N(79,78,76); N(80,32,79); M(130,42,35,34.999999999999915); L(81,42,130); A(80,42,ab(130,42,81,\"gedreht\")); M(131,81,42,155.0000000000003); M(83,131,81,-115.0000000000004); L(132,131,83); Q(86,81,131,D,ab(132,131,83,\"gedreht\")); Q(82,81,79,ab(131,81,83,86,\"gedreht\"),D); A(75,83); M(87,86,81,-84.99999999999967); L(133,86,87); A(88,86,ab(133,86,87,\"gedreht\")); N(84,83,74); M(134,84,74,155.00000000000026); L(85,84,134); Q(70,84,71,ab(134,84,85,\"gedreht\"),D); A(85,87); M(67,69,71,-85.00000000000058); M(64,67,69,185); L(66,67,64); L(136,67,66); Q(135,69,67,D,ab(136,67,64,66,\"gedreht\")); Q(68,70,69,D,ab(135,69,64,66,67,\"gedreht\")); M(56,54,52,94.99999999999955); L(57,54,56); L(58,57,56); L(137,57,58); M(62,64,66,-84.99999999999945); M(138,62,64,185); L(61,62,138); L(139,62,61); Q(63,64,62,D,ab(139,62,138,61,\"gedreht\")); Q(59,54,64,ab(137,54,56,57,58,\"gedreht\"),ab(138,64,61,62,63,\"gedreht\")); N(55,56,53); A(55,87); N(60,58,55); A(60,61); N(65,63,60); A(65,66); A(65,85);
%R(42,80); // oder R(42,81);
%R(75,83);
%R(86,87); // oder R(86,88);
%R(85,87);
%R(55,87);
%R(60,61);
%R(65,66);
%R(65,85);
%</Rechenweg>
%
%<Knopf id=\"Stopp_alleWinkel\" color=\"LightGrey\"/>
%
%<Knopf id=\"Start_blauerWinkel\" color=\"blue\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#blauerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_blauerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_gruenerWinkel\" color=\"green\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#gruenerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_gruenerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_orangerWinkel\" color=\"orange\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#orangerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_orangerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LimeGreen}{rgb}{0.20,0.80,0.20}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/2.73/0.00,
2/3.73/0.00,
3/3.23/0.87,
4/4.23/0.87,
5/4.73/0.00,
6/2.73/1.00,
7/3.23/1.87,
8/4.23/1.87,
9/1.87/0.50,
10/1.87/1.50,
11/1.00/1.00,
12/2.37/2.37,
13/1.50/1.87,
14/0.50/1.87,
15/1.00/2.73,
16/0.00/2.73,
17/1.87/3.23,
18/0.87/3.23,
19/0.00/3.73,
20/0.87/4.23,
21/0.00/4.73,
22/1.87/4.23,
23/1.00/4.73,
24/0.50/5.60,
25/1.50/5.60,
26/1.00/6.46,
27/2.37/5.10,
28/1.87/5.96,
29/1.87/6.96,
30/2.73/6.46,
31/2.73/7.46,
32/3.23/5.60,
33/3.23/6.60,
34/3.73/7.46,
35/4.10/6.10,
36/4.73/1.00,
37/5.23/1.87,
38/5.60/0.50,
39/4.60/6.96,
40/6.10/1.37,
41/4.60/7.96,
42/5.10/6.10,
43/6.10/2.37,
44/6.60/0.50,
45/5.10/7.10,
46/6.60/1.50,
47/5.60/7.96,
48/6.10/7.10,
49/6.60/7.96,
50/6.10/6.10,
51/6.60/6.96,
52/7.46/7.46,
53/7.46/6.46,
54/8.33/6.96,
55/6.96/5.60,
56/7.83/6.10,
57/8.83/6.10,
58/8.33/5.23,
59/9.33/5.23,
60/7.46/4.73,
61/8.46/4.73,
62/9.33/4.23,
63/8.46/3.73,
64/9.33/3.23,
65/7.46/3.73,
66/8.33/3.23,
67/8.83/2.37,
68/7.83/2.37,
69/8.33/1.50,
70/6.96/2.87,
71/7.46/2.00,
72/7.46/1.00,
73/3.73/2.73,
74/5.10/2.37,
75/4.23/2.87,
76/3.73/3.73,
77/2.87/3.23,
78/2.87/4.23,
79/3.73/4.73,
80/4.23/5.60,
81/5.10/5.10,
82/4.60/4.23,
83/5.10/3.37,
84/5.96/2.87,
85/6.46/3.73,
86/5.60/4.23,
87/6.46/4.73,
88/5.60/5.23}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
1/0.00/90.00/0.4/Blue,
10/330.00/420.00/0.4/Green,
25/240.00/330.00/0.4/Orange}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
1/2,
3/1, 3/2,
4/3, 4/2,
5/4, 5/2,
6/1,
7/6, 7/3,
8/7, 8/4,
9/1, 9/6,
10/9, 10/6,
11/9, 11/10,
12/10,
13/11, 13/12,
14/11, 14/13,
15/14, 15/13,
16/14, 16/15,
17/15, 17/12,
18/16, 18/17,
19/16, 19/18,
20/19, 20/18,
21/19, 21/20,
22/20, 22/17,
23/21, 23/22,
24/21, 24/23,
25/24, 25/23,
26/24, 26/25,
27/25,
28/26, 28/27,
29/26, 29/28,
30/29, 30/28,
31/29, 31/30,
32/30, 32/27,
33/31, 33/32,
34/31, 34/33,
35/33, 35/32,
36/8, 36/5,
37/8, 37/36,
38/36, 38/5,
39/34, 39/35,
40/37, 40/38,
41/34, 41/39,
42/39, 42/35,
43/37, 43/40,
44/40, 44/38,
45/41, 45/42,
46/43, 46/44,
47/41, 47/45,
48/47, 48/45,
49/47, 49/48,
50/48, 50/42,
51/49, 51/50,
52/49, 52/51,
53/52, 53/51,
54/52, 54/53,
55/56, 55/53, 55/87,
56/54,
57/54, 57/56,
58/57, 58/56,
59/57, 59/58, 59/62,
60/58, 60/55, 60/61,
61/62, 61/59,
62/64,
63/64, 63/61, 63/62,
64/67,
65/63, 65/60, 65/66, 65/85,
66/67, 66/64,
67/69,
68/70, 68/66, 68/67, 68/69,
69/71,
70/84, 70/71,
71/46,
72/69, 72/71, 72/46, 72/44,
73/7, 73/8,
74/8, 74/43,
75/8, 75/74, 75/83,
76/73, 76/75,
77/73, 77/76,
78/27, 78/77,
79/78, 79/76,
80/32, 80/79, 80/42,
81/42, 81/80,
82/81, 82/79,
83/82,
84/83, 84/74,
85/84, 85/70, 85/87,
86/81, 86/83, 86/82,
87/86,
88/50, 88/42, 88/86, 88/87}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,88}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[LimeGreen,very thick] (p-42) -- (p-80);
\draw[LimeGreen,very thick] (p-75) -- (p-83);
\draw[LimeGreen,very thick] (p-86) -- (p-87);
\draw[LimeGreen,very thick] (p-85) -- (p-87);
\draw[LimeGreen,very thick] (p-55) -- (p-87);
\draw[LimeGreen,very thick] (p-60) -- (p-61);
\draw[LimeGreen,very thick] (p-65) -- (p-66);
\draw[LimeGreen,very thick] (p-65) -- (p-85);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
1/0.00/90.00/0.4/Blue,
10/330.00/420.00/0.4/Green,
25/240.00/330.00/0.4/Orange}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/210,
2/330,
3/150,
4/30,
5/330,
6/60,
7/210,
8/240,
9/180,
10/60,
11/270,
12/348,
13/30,
14/270,
15/30,
16/240,
17/318,
18/300,
19/240,
20/60,
21/120,
22/48,
23/330,
24/150,
25/330,
26/180,
27/258,
28/240,
29/180,
30/360,
31/60,
32/240,
33/270,
34/180,
35/360,
36/270,
37/180,
38/360,
39/90,
40/90,
41/60,
42/60,
43/60,
44/330,
45/270,
46/120,
47/150,
48/330,
49/120,
50/30,
51/240,
52/120,
53/300,
54/360,
55/93,
56/210,
57/90,
58/210,
59/330,
60/137,
61/180,
62/300,
63/180,
64/30,
65/318,
66/90,
67/330,
68/150,
69/360,
70/330,
71/120,
72/360,
73/90,
74/360,
75/120,
76/60,
77/180,
78/257,
79/123,
80/180,
81/90,
82/150,
83/270,
84/210,
85/90,
86/240,
87/360,
88/270}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
Anschließender Button "beweglich?" sucht die lineare Abhängigkeit und packt sie gleich mit in die Eingabe zum Graph
88 Knoten, 4×Grad 3, 80×Grad 4, 2×Grad 5, 2×Grad 7, 0 Überschneidungen
178 Kanten, minimal 0.99999999999998412381, maximal 1.00000000000001443290
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78);</Bildtext>
%<Ausrichten von="1" nach="2"/>
%<Winkel size="18" color="orange" id="orangerWinkel" value="89.99999999999994"/>
%<Feinjustieren Anzahl="8,3"/>
%<Rechenweg>
%blauerWinkel=90+(0.9999981653287288)*(orangerWinkel-(89.99999999999994));
%gruenerWinkel=90+(-0.9999997980150385)*(orangerWinkel-(89.99999999999994));
%P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(1,2); L(3,1,2); L(4,3,2); L(5,4,2); M(6,1,2,blauerWinkel); L(9,1,6); L(10,9,6); L(11,9,10); N(7,6,3); M(109,7,3,95.00000000000001); L(73,7,109); Q(8,7,4,ab(109,7,73,"gedreht"),D); M(110,8,4,35.000000000000014); L(37,8,110); M(111,5,2,-85.00000000000001); L(38,111,5); Q(36,8,5,ab(110,8,37,"gedreht"),ab(111,5,38,"gedreht")); M(112,37,8,154.99999999999997); L(43,37,112); M(113,38,5,-144.99999999999994); L(44,113,38); Q(40,37,38,ab(112,37,43,"gedreht"),ab(113,38,44,"gedreht")); M(114,44,38,-85.00000000000017); M(71,114,44,125.00000000000043); M(69,71,114,125.00000000000016); L(116,69,71); Q(115,71,114,ab(116,71,69,"gedreht"),D); Q(72,114,44,ab(115,114,69,71,"gedreht"),D); Q(46,43,44,D,ab(114,44,69,71,72,"gedreht")); M(117,8,4,125.00000000000001); L(75,8,117); Q(74,8,43,ab(117,8,75,"gedreht"),D); M(118,73,7,-144.99999999999994); L(77,73,118); Q(76,73,75,ab(118,73,77,"gedreht"),D); M(12,10,6,gruenerWinkel); M(119,11,9,95.00000000000006); L(14,11,119); L(15,14,119); L(16,14,15); Q(13,11,12,ab(119,11,14,15,16,"gedreht"),D); N(17,15,12); M(120,16,14,94.99999999999991); L(19,16,120); L(20,19,120); L(21,19,20); Q(18,16,17,ab(120,16,19,20,21,"gedreht"),D); N(22,20,17); M(121,21,19,95.00000000000006); L(24,21,121); L(25,24,121); L(26,24,25); Q(23,21,22,ab(121,21,24,25,26,"gedreht"),D); M(27,25,23,orangerWinkel); M(122,26,24,95.00000000000001); L(29,26,122); L(30,29,122); L(31,29,30); Q(28,26,27,ab(122,26,29,30,31,"gedreht"),D); N(32,30,27); M(123,31,29,95.00000000000009); L(34,31,123); M(124,32,27,-114.99999999999997); L(35,124,32); Q(33,31,32,ab(123,31,34,"gedreht"),ab(124,32,35,"gedreht")); M(125,34,31,154.99999999999991); L(41,34,125); M(126,35,32,-144.99999999999986); L(42,126,35); Q(39,34,35,ab(125,34,41,"gedreht"),ab(126,35,42,"gedreht")); M(127,41,34,95.00000000000006); L(47,41,127); L(48,47,127); L(49,47,48); Q(45,41,42,ab(127,41,47,48,49,"gedreht"),D); M(128,42,35,-174.99999999999991); L(88,128,42); Q(50,48,42,D,ab(128,42,88,"gedreht")); M(129,49,47,95.00000000000014); L(52,49,129); L(53,52,129); L(54,52,53); Q(51,49,50,ab(129,49,52,53,54,"gedreht"),D); N(78,27,77); N(79,78,76); N(80,32,79); M(130,42,35,34.999999999999915); L(81,42,130); A(80,42,ab(130,42,81,"gedreht")); M(131,81,42,155.0000000000003); M(83,131,81,-115.0000000000004); L(132,131,83); Q(86,81,131,D,ab(132,131,83,"gedreht")); Q(82,81,79,ab(131,81,83,86,"gedreht"),D); A(75,83); M(87,86,81,-84.99999999999967); L(133,86,87); A(88,86,ab(133,86,87,"gedreht")); N(84,83,74); M(134,84,74,155.00000000000026); L(85,84,134); Q(70,84,71,ab(134,84,85,"gedreht"),D); A(85,87); M(67,69,71,-85.00000000000058); M(64,67,69,185); L(66,67,64); L(136,67,66); Q(135,69,67,D,ab(136,67,64,66,"gedreht")); Q(68,70,69,D,ab(135,69,64,66,67,"gedreht")); M(56,54,52,94.99999999999955); L(57,54,56); L(58,57,56); L(137,57,58); M(62,64,66,-84.99999999999945); M(138,62,64,185); L(61,62,138); L(139,62,61); Q(63,64,62,D,ab(139,62,138,61,"gedreht")); Q(59,54,64,ab(137,54,56,57,58,"gedreht"),ab(138,64,61,62,63,"gedreht")); N(55,56,53); A(55,87); N(60,58,55); A(60,61); N(65,63,60); A(65,66); A(65,85);
%R(42,80); // oder R(42,81);
%R(75,83);
%R(86,87); // oder R(86,88);
%R(85,87);
%R(55,87);
%R(60,61);
%R(65,66);
%R(65,85);
%</Rechenweg>
%
%<Knopf id="Stopp_alleWinkel" color="LightGrey"/>
%
%<Knopf id="Start_orangerWinkel" color="orange"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#orangerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_orangerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{LimeGreen}{rgb}{0.20,0.80,0.20}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/2.73/0.00,
2/3.73/0.00,
3/3.23/0.87,
4/4.23/0.87,
5/4.73/0.00,
6/2.73/1.00,
7/3.23/1.87,
8/4.23/1.87,
9/1.87/0.50,
10/1.87/1.50,
11/1.00/1.00,
12/2.37/2.37,
13/1.50/1.87,
14/0.50/1.87,
15/1.00/2.73,
16/0.00/2.73,
17/1.87/3.23,
18/0.87/3.23,
19/0.00/3.73,
20/0.87/4.23,
21/0.00/4.73,
22/1.87/4.23,
23/1.00/4.73,
24/0.50/5.60,
25/1.50/5.60,
26/1.00/6.46,
27/2.37/5.10,
28/1.87/5.96,
29/1.87/6.96,
30/2.73/6.46,
31/2.73/7.46,
32/3.23/5.60,
33/3.23/6.60,
34/3.73/7.46,
35/4.10/6.10,
36/4.73/1.00,
37/5.23/1.87,
38/5.60/0.50,
39/4.60/6.96,
40/6.10/1.37,
41/4.60/7.96,
42/5.10/6.10,
43/6.10/2.37,
44/6.60/0.50,
45/5.10/7.10,
46/6.60/1.50,
47/5.60/7.96,
48/6.10/7.10,
49/6.60/7.96,
50/6.10/6.10,
51/6.60/6.96,
52/7.46/7.46,
53/7.46/6.46,
54/8.33/6.96,
55/6.96/5.60,
56/7.83/6.10,
57/8.83/6.10,
58/8.33/5.23,
59/9.33/5.23,
60/7.46/4.73,
61/8.46/4.73,
62/9.33/4.23,
63/8.46/3.73,
64/9.33/3.23,
65/7.46/3.73,
66/8.33/3.23,
67/8.83/2.37,
68/7.83/2.37,
69/8.33/1.50,
70/6.96/2.87,
71/7.46/2.00,
72/7.46/1.00,
73/3.73/2.73,
74/5.10/2.37,
75/4.23/2.87,
76/3.73/3.73,
77/2.87/3.23,
78/2.87/4.23,
79/3.73/4.73,
80/4.23/5.60,
81/5.10/5.10,
82/4.60/4.23,
83/5.10/3.37,
84/5.96/2.87,
85/6.46/3.73,
86/5.60/4.23,
87/6.46/4.73,
88/5.60/5.23}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
25/240.00/330.00/0.4/Orange}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
1/2,
3/1, 3/2,
4/3, 4/2,
5/4, 5/2,
6/1,
7/6, 7/3,
8/7, 8/4,
9/1, 9/6,
10/9, 10/6,
11/9, 11/10,
12/10,
13/11, 13/12,
14/11, 14/13,
15/14, 15/13,
16/14, 16/15,
17/15, 17/12,
18/16, 18/17,
19/16, 19/18,
20/19, 20/18,
21/19, 21/20,
22/20, 22/17,
23/21, 23/22,
24/21, 24/23,
25/24, 25/23,
26/24, 26/25,
27/25,
28/26, 28/27,
29/26, 29/28,
30/29, 30/28,
31/29, 31/30,
32/30, 32/27,
33/31, 33/32,
34/31, 34/33,
35/33, 35/32,
36/8, 36/5,
37/8, 37/36,
38/36, 38/5,
39/34, 39/35,
40/37, 40/38,
41/34, 41/39,
42/39, 42/35,
43/37, 43/40,
44/40, 44/38,
45/41, 45/42,
46/43, 46/44,
47/41, 47/45,
48/47, 48/45,
49/47, 49/48,
50/48, 50/42,
51/49, 51/50,
52/49, 52/51,
53/52, 53/51,
54/52, 54/53,
55/56, 55/53, 55/87,
56/54,
57/54, 57/56,
58/57, 58/56,
59/57, 59/58, 59/62,
60/58, 60/55, 60/61,
61/62, 61/59,
62/64,
63/64, 63/61, 63/62,
64/67,
65/63, 65/60, 65/66, 65/85,
66/67, 66/64,
67/69,
68/70, 68/66, 68/67, 68/69,
69/71,
70/84, 70/71,
71/46,
72/69, 72/71, 72/46, 72/44,
73/7, 73/8,
74/8, 74/43,
75/8, 75/74, 75/83,
76/73, 76/75,
77/73, 77/76,
78/27, 78/77,
79/78, 79/76,
80/32, 80/79, 80/42,
81/42, 81/80,
82/81, 82/79,
83/82,
84/83, 84/74,
85/84, 85/70, 85/87,
86/81, 86/83, 86/82,
87/86,
88/50, 88/42, 88/86, 88/87}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,88}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[LimeGreen,very thick] (p-42) -- (p-80);
\draw[LimeGreen,very thick] (p-75) -- (p-83);
\draw[LimeGreen,very thick] (p-86) -- (p-87);
\draw[LimeGreen,very thick] (p-85) -- (p-87);
\draw[LimeGreen,very thick] (p-55) -- (p-87);
\draw[LimeGreen,very thick] (p-60) -- (p-61);
\draw[LimeGreen,very thick] (p-65) -- (p-66);
\draw[LimeGreen,very thick] (p-65) -- (p-85);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
25/240.00/330.00/0.4/Orange}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/210,
2/330,
3/150,
4/30,
5/330,
6/60,
7/210,
8/240,
9/180,
10/60,
11/270,
12/348,
13/30,
14/270,
15/30,
16/240,
17/318,
18/300,
19/240,
20/60,
21/120,
22/48,
23/330,
24/150,
25/330,
26/180,
27/258,
28/240,
29/180,
30/360,
31/60,
32/240,
33/270,
34/180,
35/360,
36/270,
37/180,
38/360,
39/90,
40/90,
41/60,
42/60,
43/60,
44/330,
45/270,
46/120,
47/150,
48/330,
49/120,
50/30,
51/240,
52/120,
53/300,
54/360,
55/93,
56/210,
57/90,
58/210,
59/330,
60/137,
61/180,
62/300,
63/180,
64/30,
65/318,
66/90,
67/330,
68/150,
69/360,
70/330,
71/120,
72/360,
73/90,
74/360,
75/120,
76/60,
77/180,
78/257,
79/123,
80/180,
81/90,
82/150,
83/270,
84/210,
85/90,
86/240,
87/360,
88/270}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/9ef55fd4890bf89126a8018632773d2a.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78);</Bildtext>
%<Ausrichten von=\"1\" nach=\"2\"/>
%<Winkel size=\"18\" color=\"orange\" id=\"orangerWinkel\" value=\"89.99999999999994\"/>
%<Feinjustieren Anzahl=\"8,3\"/>
%<Rechenweg>
%blauerWinkel=90+(0.9999981653287288)*(orangerWinkel-(89.99999999999994));
%gruenerWinkel=90+(-0.9999997980150385)*(orangerWinkel-(89.99999999999994));
%P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(1,2); L(3,1,2); L(4,3,2); L(5,4,2); M(6,1,2,blauerWinkel); L(9,1,6); L(10,9,6); L(11,9,10); N(7,6,3); M(109,7,3,95.00000000000001); L(73,7,109); Q(8,7,4,ab(109,7,73,\"gedreht\"),D); M(110,8,4,35.000000000000014); L(37,8,110); M(111,5,2,-85.00000000000001); L(38,111,5); Q(36,8,5,ab(110,8,37,\"gedreht\"),ab(111,5,38,\"gedreht\")); M(112,37,8,154.99999999999997); L(43,37,112); M(113,38,5,-144.99999999999994); L(44,113,38); Q(40,37,38,ab(112,37,43,\"gedreht\"),ab(113,38,44,\"gedreht\")); M(114,44,38,-85.00000000000017); M(71,114,44,125.00000000000043); M(69,71,114,125.00000000000016); L(116,69,71); Q(115,71,114,ab(116,71,69,\"gedreht\"),D); Q(72,114,44,ab(115,114,69,71,\"gedreht\"),D); Q(46,43,44,D,ab(114,44,69,71,72,\"gedreht\")); M(117,8,4,125.00000000000001); L(75,8,117); Q(74,8,43,ab(117,8,75,\"gedreht\"),D); M(118,73,7,-144.99999999999994); L(77,73,118); Q(76,73,75,ab(118,73,77,\"gedreht\"),D); M(12,10,6,gruenerWinkel); M(119,11,9,95.00000000000006); L(14,11,119); L(15,14,119); L(16,14,15); Q(13,11,12,ab(119,11,14,15,16,\"gedreht\"),D); N(17,15,12); M(120,16,14,94.99999999999991); L(19,16,120); L(20,19,120); L(21,19,20); Q(18,16,17,ab(120,16,19,20,21,\"gedreht\"),D); N(22,20,17); M(121,21,19,95.00000000000006); L(24,21,121); L(25,24,121); L(26,24,25); Q(23,21,22,ab(121,21,24,25,26,\"gedreht\"),D); M(27,25,23,orangerWinkel); M(122,26,24,95.00000000000001); L(29,26,122); L(30,29,122); L(31,29,30); Q(28,26,27,ab(122,26,29,30,31,\"gedreht\"),D); N(32,30,27); M(123,31,29,95.00000000000009); L(34,31,123); M(124,32,27,-114.99999999999997); L(35,124,32); Q(33,31,32,ab(123,31,34,\"gedreht\"),ab(124,32,35,\"gedreht\")); M(125,34,31,154.99999999999991); L(41,34,125); M(126,35,32,-144.99999999999986); L(42,126,35); Q(39,34,35,ab(125,34,41,\"gedreht\"),ab(126,35,42,\"gedreht\")); M(127,41,34,95.00000000000006); L(47,41,127); L(48,47,127); L(49,47,48); Q(45,41,42,ab(127,41,47,48,49,\"gedreht\"),D); M(128,42,35,-174.99999999999991); L(88,128,42); Q(50,48,42,D,ab(128,42,88,\"gedreht\")); M(129,49,47,95.00000000000014); L(52,49,129); L(53,52,129); L(54,52,53); Q(51,49,50,ab(129,49,52,53,54,\"gedreht\"),D); N(78,27,77); N(79,78,76); N(80,32,79); M(130,42,35,34.999999999999915); L(81,42,130); A(80,42,ab(130,42,81,\"gedreht\")); M(131,81,42,155.0000000000003); M(83,131,81,-115.0000000000004); L(132,131,83); Q(86,81,131,D,ab(132,131,83,\"gedreht\")); Q(82,81,79,ab(131,81,83,86,\"gedreht\"),D); A(75,83); M(87,86,81,-84.99999999999967); L(133,86,87); A(88,86,ab(133,86,87,\"gedreht\")); N(84,83,74); M(134,84,74,155.00000000000026); L(85,84,134); Q(70,84,71,ab(134,84,85,\"gedreht\"),D); A(85,87); M(67,69,71,-85.00000000000058); M(64,67,69,185); L(66,67,64); L(136,67,66); Q(135,69,67,D,ab(136,67,64,66,\"gedreht\")); Q(68,70,69,D,ab(135,69,64,66,67,\"gedreht\")); M(56,54,52,94.99999999999955); L(57,54,56); L(58,57,56); L(137,57,58); M(62,64,66,-84.99999999999945); M(138,62,64,185); L(61,62,138); L(139,62,61); Q(63,64,62,D,ab(139,62,138,61,\"gedreht\")); Q(59,54,64,ab(137,54,56,57,58,\"gedreht\"),ab(138,64,61,62,63,\"gedreht\")); N(55,56,53); A(55,87); N(60,58,55); A(60,61); N(65,63,60); A(65,66); A(65,85);
%R(42,80); // oder R(42,81);
%R(75,83);
%R(86,87); // oder R(86,88);
%R(85,87);
%R(55,87);
%R(60,61);
%R(65,66);
%R(65,85);
%</Rechenweg>
%
%<Knopf id=\"Stopp_alleWinkel\" color=\"LightGrey\"/>
%
%<Knopf id=\"Start_orangerWinkel\" color=\"orange\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#orangerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_orangerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{LimeGreen}{rgb}{0.20,0.80,0.20}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/2.73/0.00,
2/3.73/0.00,
3/3.23/0.87,
4/4.23/0.87,
5/4.73/0.00,
6/2.73/1.00,
7/3.23/1.87,
8/4.23/1.87,
9/1.87/0.50,
10/1.87/1.50,
11/1.00/1.00,
12/2.37/2.37,
13/1.50/1.87,
14/0.50/1.87,
15/1.00/2.73,
16/0.00/2.73,
17/1.87/3.23,
18/0.87/3.23,
19/0.00/3.73,
20/0.87/4.23,
21/0.00/4.73,
22/1.87/4.23,
23/1.00/4.73,
24/0.50/5.60,
25/1.50/5.60,
26/1.00/6.46,
27/2.37/5.10,
28/1.87/5.96,
29/1.87/6.96,
30/2.73/6.46,
31/2.73/7.46,
32/3.23/5.60,
33/3.23/6.60,
34/3.73/7.46,
35/4.10/6.10,
36/4.73/1.00,
37/5.23/1.87,
38/5.60/0.50,
39/4.60/6.96,
40/6.10/1.37,
41/4.60/7.96,
42/5.10/6.10,
43/6.10/2.37,
44/6.60/0.50,
45/5.10/7.10,
46/6.60/1.50,
47/5.60/7.96,
48/6.10/7.10,
49/6.60/7.96,
50/6.10/6.10,
51/6.60/6.96,
52/7.46/7.46,
53/7.46/6.46,
54/8.33/6.96,
55/6.96/5.60,
56/7.83/6.10,
57/8.83/6.10,
58/8.33/5.23,
59/9.33/5.23,
60/7.46/4.73,
61/8.46/4.73,
62/9.33/4.23,
63/8.46/3.73,
64/9.33/3.23,
65/7.46/3.73,
66/8.33/3.23,
67/8.83/2.37,
68/7.83/2.37,
69/8.33/1.50,
70/6.96/2.87,
71/7.46/2.00,
72/7.46/1.00,
73/3.73/2.73,
74/5.10/2.37,
75/4.23/2.87,
76/3.73/3.73,
77/2.87/3.23,
78/2.87/4.23,
79/3.73/4.73,
80/4.23/5.60,
81/5.10/5.10,
82/4.60/4.23,
83/5.10/3.37,
84/5.96/2.87,
85/6.46/3.73,
86/5.60/4.23,
87/6.46/4.73,
88/5.60/5.23}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
25/240.00/330.00/0.4/Orange}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
1/2,
3/1, 3/2,
4/3, 4/2,
5/4, 5/2,
6/1,
7/6, 7/3,
8/7, 8/4,
9/1, 9/6,
10/9, 10/6,
11/9, 11/10,
12/10,
13/11, 13/12,
14/11, 14/13,
15/14, 15/13,
16/14, 16/15,
17/15, 17/12,
18/16, 18/17,
19/16, 19/18,
20/19, 20/18,
21/19, 21/20,
22/20, 22/17,
23/21, 23/22,
24/21, 24/23,
25/24, 25/23,
26/24, 26/25,
27/25,
28/26, 28/27,
29/26, 29/28,
30/29, 30/28,
31/29, 31/30,
32/30, 32/27,
33/31, 33/32,
34/31, 34/33,
35/33, 35/32,
36/8, 36/5,
37/8, 37/36,
38/36, 38/5,
39/34, 39/35,
40/37, 40/38,
41/34, 41/39,
42/39, 42/35,
43/37, 43/40,
44/40, 44/38,
45/41, 45/42,
46/43, 46/44,
47/41, 47/45,
48/47, 48/45,
49/47, 49/48,
50/48, 50/42,
51/49, 51/50,
52/49, 52/51,
53/52, 53/51,
54/52, 54/53,
55/56, 55/53, 55/87,
56/54,
57/54, 57/56,
58/57, 58/56,
59/57, 59/58, 59/62,
60/58, 60/55, 60/61,
61/62, 61/59,
62/64,
63/64, 63/61, 63/62,
64/67,
65/63, 65/60, 65/66, 65/85,
66/67, 66/64,
67/69,
68/70, 68/66, 68/67, 68/69,
69/71,
70/84, 70/71,
71/46,
72/69, 72/71, 72/46, 72/44,
73/7, 73/8,
74/8, 74/43,
75/8, 75/74, 75/83,
76/73, 76/75,
77/73, 77/76,
78/27, 78/77,
79/78, 79/76,
80/32, 80/79, 80/42,
81/42, 81/80,
82/81, 82/79,
83/82,
84/83, 84/74,
85/84, 85/70, 85/87,
86/81, 86/83, 86/82,
87/86,
88/50, 88/42, 88/86, 88/87}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,88}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[LimeGreen,very thick] (p-42) -- (p-80);
\draw[LimeGreen,very thick] (p-75) -- (p-83);
\draw[LimeGreen,very thick] (p-86) -- (p-87);
\draw[LimeGreen,very thick] (p-85) -- (p-87);
\draw[LimeGreen,very thick] (p-55) -- (p-87);
\draw[LimeGreen,very thick] (p-60) -- (p-61);
\draw[LimeGreen,very thick] (p-65) -- (p-66);
\draw[LimeGreen,very thick] (p-65) -- (p-85);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
25/240.00/330.00/0.4/Orange}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/210,
2/330,
3/150,
4/30,
5/330,
6/60,
7/210,
8/240,
9/180,
10/60,
11/270,
12/348,
13/30,
14/270,
15/30,
16/240,
17/318,
18/300,
19/240,
20/60,
21/120,
22/48,
23/330,
24/150,
25/330,
26/180,
27/258,
28/240,
29/180,
30/360,
31/60,
32/240,
33/270,
34/180,
35/360,
36/270,
37/180,
38/360,
39/90,
40/90,
41/60,
42/60,
43/60,
44/330,
45/270,
46/120,
47/150,
48/330,
49/120,
50/30,
51/240,
52/120,
53/300,
54/360,
55/93,
56/210,
57/90,
58/210,
59/330,
60/137,
61/180,
62/300,
63/180,
64/30,
65/318,
66/90,
67/330,
68/150,
69/360,
70/330,
71/120,
72/360,
73/90,
74/360,
75/120,
76/60,
77/180,
78/257,
79/123,
80/180,
81/90,
82/150,
83/270,
84/210,
85/90,
86/240,
87/360,
88/270}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
so dass man allein mit Button "+1" oder "+10"... oder Animationsknopf "Start_orangerWinkel" links neben dem Graph die Bewegung starten kann. Button "zurück" macht das alles wieder rückgängig.
Nach Button neue Eingabe "egal wie"
88 Knoten, 4×Grad 3, 80×Grad 4, 2×Grad 5, 2×Grad 7, 0 Überschneidungen
178 Kanten, minimal 0.99999999999960431651, maximal 1.00000000000029243274
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>Automatisch generierte Eingabe zu: #1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78); nach Button neue Eingabe "egal wie"</Bildtext>
%<Ausrichten von="1" nach="2"/>
%<Winkel size="18" color="blue" id="blauerWinkel" value="-90"/>
%<Winkel size="18" color="green" id="gruenerWinkel" value="-179.9999999999996"/>
%<Winkel size="18" color="orange" id="orangerWinkel" value="-90.00000000000018"/>
%<Feinjustieren Anzahl="8,3"/>
%<Rechenweg>
%P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(2,1); N(3,1,2); N(4,3,2); N(5,4,2); M(38,5,4,blauerWinkel); N(36,5,38); N(8,4,36); N(37,8,36); N(40,37,38); N(43,37,40); N(44,40,38); N(46,43,44); N(72,46,44); N(74,8,43); N(75,8,74); N(7,3,8); N(71,46,72); N(73,7,8); N(76,73,75); N(77,73,76); N(6,1,7); N(9,1,6); N(10,9,6); N(11,9,10); N(69,71,72); M(84,74,8,gruenerWinkel); N(70,84,71); N(83,75,84); N(85,84,70); N(68,70,69); N(67,68,69); N(66,68,67); N(64,66,67); N(65,85,66); N(63,65,64); N(62,63,64); N(61,63,62); N(59,61,62); N(60,65,61); N(58,60,59); N(57,58,59); N(56,58,57); N(54,56,57); N(55,60,56); N(87,85,55); N(53,55,54); N(86,83,87); N(88,86,87); N(52,53,54); N(82,83,86); N(51,53,52); N(79,76,82); N(81,82,86); N(42,81,88); N(49,51,52); N(50,51,42); N(78,77,79); N(80,79,42); N(48,50,49); N(45,42,48); N(47,45,48); N(41,45,47); N(39,42,41); N(34,39,41); N(35,42,39); N(32,80,35); N(33,32,34); N(27,78,32); N(31,33,34); N(30,32,31); N(28,27,30); N(29,28,30); N(26,28,29); N(25,27,26); N(24,25,26); N(23,25,24); N(21,23,24); M(22,23,25,orangerWinkel); N(20,22,21); N(19,20,21); N(18,20,19); N(16,18,19); N(17,22,18); N(12,17,10); N(13,11,12); N(14,11,13); N(15,14,13);
%A(50,88); R(50,88,"green");
%A(80,81); R(80,81,"green");
%A(47,49); R(47,49,"green");
%A(33,35); R(33,35,"green");
%A(29,31); R(29,31,"green");
%A(14,16); R(14,16,"green");
%A(15,16); R(15,16,"green");
%A(15,17); R(15,17,"green");
%</Rechenweg>
%
%<Knopf id="Stopp_alleWinkel" color="LightGrey"/>
%
%<Knopf id="Start_blauerWinkel" color="blue"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#blauerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_blauerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_gruenerWinkel" color="green"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#gruenerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_gruenerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_orangerWinkel" color="orange"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#orangerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_orangerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/2.73/0.00,
2/3.73/0.00,
3/3.23/0.87,
4/4.23/0.87,
5/4.73/0.00,
6/2.73/1.00,
7/3.23/1.87,
8/4.23/1.87,
9/1.87/0.50,
10/1.87/1.50,
11/1.00/1.00,
12/2.37/2.37,
13/1.50/1.87,
14/0.50/1.87,
15/1.00/2.73,
16/0.00/2.73,
17/1.87/3.23,
18/0.87/3.23,
19/0.00/3.73,
20/0.87/4.23,
21/0.00/4.73,
22/1.87/4.23,
23/1.00/4.73,
24/0.50/5.60,
25/1.50/5.60,
26/1.00/6.46,
27/2.37/5.10,
28/1.87/5.96,
29/1.87/6.96,
30/2.73/6.46,
31/2.73/7.46,
32/3.23/5.60,
33/3.23/6.60,
34/3.73/7.46,
35/4.10/6.10,
36/4.73/1.00,
37/5.23/1.87,
38/5.60/0.50,
39/4.60/6.96,
40/6.10/1.37,
41/4.60/7.96,
42/5.10/6.10,
43/6.10/2.37,
44/6.60/0.50,
45/5.10/7.10,
46/6.60/1.50,
47/5.60/7.96,
48/6.10/7.10,
49/6.60/7.96,
50/6.10/6.10,
51/6.60/6.96,
52/7.46/7.46,
53/7.46/6.46,
54/8.33/6.96,
55/6.96/5.60,
56/7.83/6.10,
57/8.83/6.10,
58/8.33/5.23,
59/9.33/5.23,
60/7.46/4.73,
61/8.46/4.73,
62/9.33/4.23,
63/8.46/3.73,
64/9.33/3.23,
65/7.46/3.73,
66/8.33/3.23,
67/8.83/2.37,
68/7.83/2.37,
69/8.33/1.50,
70/6.96/2.87,
71/7.46/2.00,
72/7.46/1.00,
73/3.73/2.73,
74/5.10/2.37,
75/4.23/2.87,
76/3.73/3.73,
77/2.87/3.23,
78/2.87/4.23,
79/3.73/4.73,
80/4.23/5.60,
81/5.10/5.10,
82/4.60/4.23,
83/5.10/3.37,
84/5.96/2.87,
85/6.46/3.73,
86/5.60/4.23,
87/6.46/4.73,
88/5.60/5.23}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
5/120.00/390.00/0.4/Blue,
74/210.00/390.00/0.4/Green,
23/60.00/330.00/0.4/Orange}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
2/1,
3/1, 3/2,
4/3, 4/2,
5/4, 5/2,
6/1, 6/7,
7/3, 7/8,
8/4, 8/36,
9/1, 9/6,
10/9, 10/6,
11/9, 11/10,
12/17, 12/10,
13/11, 13/12,
14/11, 14/13, 14/16,
15/14, 15/13, 15/16, 15/17,
16/18, 16/19,
17/22, 17/18,
18/20, 18/19,
19/20, 19/21,
20/22, 20/21,
21/23, 21/24,
22/23,
23/25, 23/24,
24/25, 24/26,
25/27, 25/26,
26/28, 26/29,
27/78, 27/32,
28/27, 28/30,
29/28, 29/30, 29/31,
30/32, 30/31,
31/33, 31/34,
32/80, 32/35,
33/32, 33/34, 33/35,
34/39, 34/41,
35/42, 35/39,
36/5, 36/38,
37/8, 37/36,
38/5,
39/42, 39/41,
40/37, 40/38,
41/45, 41/47,
42/81, 42/88,
43/37, 43/40,
44/40, 44/38,
45/42, 45/48,
46/43, 46/44,
47/45, 47/48, 47/49,
48/50, 48/49,
49/51, 49/52,
50/51, 50/42, 50/88,
51/53, 51/52,
52/53, 52/54,
53/55, 53/54,
54/56, 54/57,
55/60, 55/56,
56/58, 56/57,
57/58, 57/59,
58/60, 58/59,
59/61, 59/62,
60/65, 60/61,
61/63, 61/62,
62/63, 62/64,
63/65, 63/64,
64/66, 64/67,
65/85, 65/66,
66/68, 66/67,
67/68, 67/69,
68/70, 68/69,
69/71, 69/72,
70/84, 70/71,
71/46, 71/72,
72/46, 72/44,
73/7, 73/8,
74/8, 74/43,
75/8, 75/74,
76/73, 76/75,
77/73, 77/76,
78/77, 78/79,
79/76, 79/82,
80/79, 80/42, 80/81,
81/82, 81/86,
82/83, 82/86,
83/75, 83/84,
84/74,
85/84, 85/70,
86/83, 86/87,
87/85, 87/55,
88/86, 88/87}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,88}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[Green,very thick] (p-50) -- (p-88);
\draw[Green,very thick] (p-80) -- (p-81);
\draw[Green,very thick] (p-47) -- (p-49);
\draw[Green,very thick] (p-33) -- (p-35);
\draw[Green,very thick] (p-29) -- (p-31);
\draw[Green,very thick] (p-14) -- (p-16);
\draw[Green,very thick] (p-15) -- (p-16);
\draw[Green,very thick] (p-15) -- (p-17);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
5/120.00/390.00/0.4/Blue,
74/210.00/390.00/0.4/Green,
23/60.00/330.00/0.4/Orange}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/210,
2/330,
3/150,
4/30,
5/330,
6/360,
7/210,
8/330,
9/180,
10/60,
11/180,
12/347,
13/30,
14/270,
15/30,
16/240,
17/77,
18/300,
19/120,
20/60,
21/120,
22/48,
23/330,
24/210,
25/30,
26/90,
27/167,
28/240,
29/180,
30/360,
31/60,
32/240,
33/270,
34/30,
35/210,
36/120,
37/30,
38/360,
39/300,
40/90,
41/60,
42/60,
43/60,
44/240,
45/270,
46/180,
47/30,
48/270,
49/120,
50/30,
51/240,
52/60,
53/240,
54/360,
55/93,
56/210,
57/330,
58/210,
59/60,
60/137,
61/120,
62/360,
63/180,
64/300,
65/227,
66/90,
67/270,
68/150,
69/360,
70/330,
71/60,
72/360,
73/300,
74/360,
75/120,
76/60,
77/180,
78/257,
79/62,
80/180,
81/90,
82/150,
83/270,
84/210,
85/90,
86/240,
87/360,
88/270}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/b362e457d0a86f5709ea91c92f4a0d9a.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>Automatisch generierte Eingabe zu: #1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78); nach Button neue Eingabe \"egal wie\"</Bildtext>
%<Ausrichten von=\"1\" nach=\"2\"/>
%<Winkel size=\"18\" color=\"blue\" id=\"blauerWinkel\" value=\"-90\"/>
%<Winkel size=\"18\" color=\"green\" id=\"gruenerWinkel\" value=\"-179.9999999999996\"/>
%<Winkel size=\"18\" color=\"orange\" id=\"orangerWinkel\" value=\"-90.00000000000018\"/>
%<Feinjustieren Anzahl=\"8,3\"/>
%<Rechenweg>
%P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(2,1); N(3,1,2); N(4,3,2); N(5,4,2); M(38,5,4,blauerWinkel); N(36,5,38); N(8,4,36); N(37,8,36); N(40,37,38); N(43,37,40); N(44,40,38); N(46,43,44); N(72,46,44); N(74,8,43); N(75,8,74); N(7,3,8); N(71,46,72); N(73,7,8); N(76,73,75); N(77,73,76); N(6,1,7); N(9,1,6); N(10,9,6); N(11,9,10); N(69,71,72); M(84,74,8,gruenerWinkel); N(70,84,71); N(83,75,84); N(85,84,70); N(68,70,69); N(67,68,69); N(66,68,67); N(64,66,67); N(65,85,66); N(63,65,64); N(62,63,64); N(61,63,62); N(59,61,62); N(60,65,61); N(58,60,59); N(57,58,59); N(56,58,57); N(54,56,57); N(55,60,56); N(87,85,55); N(53,55,54); N(86,83,87); N(88,86,87); N(52,53,54); N(82,83,86); N(51,53,52); N(79,76,82); N(81,82,86); N(42,81,88); N(49,51,52); N(50,51,42); N(78,77,79); N(80,79,42); N(48,50,49); N(45,42,48); N(47,45,48); N(41,45,47); N(39,42,41); N(34,39,41); N(35,42,39); N(32,80,35); N(33,32,34); N(27,78,32); N(31,33,34); N(30,32,31); N(28,27,30); N(29,28,30); N(26,28,29); N(25,27,26); N(24,25,26); N(23,25,24); N(21,23,24); M(22,23,25,orangerWinkel); N(20,22,21); N(19,20,21); N(18,20,19); N(16,18,19); N(17,22,18); N(12,17,10); N(13,11,12); N(14,11,13); N(15,14,13);
%A(50,88); R(50,88,\"green\");
%A(80,81); R(80,81,\"green\");
%A(47,49); R(47,49,\"green\");
%A(33,35); R(33,35,\"green\");
%A(29,31); R(29,31,\"green\");
%A(14,16); R(14,16,\"green\");
%A(15,16); R(15,16,\"green\");
%A(15,17); R(15,17,\"green\");
%</Rechenweg>
%
%<Knopf id=\"Stopp_alleWinkel\" color=\"LightGrey\"/>
%
%<Knopf id=\"Start_blauerWinkel\" color=\"blue\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#blauerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_blauerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_gruenerWinkel\" color=\"green\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#gruenerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_gruenerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_orangerWinkel\" color=\"orange\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#orangerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_orangerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/2.73/0.00,
2/3.73/0.00,
3/3.23/0.87,
4/4.23/0.87,
5/4.73/0.00,
6/2.73/1.00,
7/3.23/1.87,
8/4.23/1.87,
9/1.87/0.50,
10/1.87/1.50,
11/1.00/1.00,
12/2.37/2.37,
13/1.50/1.87,
14/0.50/1.87,
15/1.00/2.73,
16/0.00/2.73,
17/1.87/3.23,
18/0.87/3.23,
19/0.00/3.73,
20/0.87/4.23,
21/0.00/4.73,
22/1.87/4.23,
23/1.00/4.73,
24/0.50/5.60,
25/1.50/5.60,
26/1.00/6.46,
27/2.37/5.10,
28/1.87/5.96,
29/1.87/6.96,
30/2.73/6.46,
31/2.73/7.46,
32/3.23/5.60,
33/3.23/6.60,
34/3.73/7.46,
35/4.10/6.10,
36/4.73/1.00,
37/5.23/1.87,
38/5.60/0.50,
39/4.60/6.96,
40/6.10/1.37,
41/4.60/7.96,
42/5.10/6.10,
43/6.10/2.37,
44/6.60/0.50,
45/5.10/7.10,
46/6.60/1.50,
47/5.60/7.96,
48/6.10/7.10,
49/6.60/7.96,
50/6.10/6.10,
51/6.60/6.96,
52/7.46/7.46,
53/7.46/6.46,
54/8.33/6.96,
55/6.96/5.60,
56/7.83/6.10,
57/8.83/6.10,
58/8.33/5.23,
59/9.33/5.23,
60/7.46/4.73,
61/8.46/4.73,
62/9.33/4.23,
63/8.46/3.73,
64/9.33/3.23,
65/7.46/3.73,
66/8.33/3.23,
67/8.83/2.37,
68/7.83/2.37,
69/8.33/1.50,
70/6.96/2.87,
71/7.46/2.00,
72/7.46/1.00,
73/3.73/2.73,
74/5.10/2.37,
75/4.23/2.87,
76/3.73/3.73,
77/2.87/3.23,
78/2.87/4.23,
79/3.73/4.73,
80/4.23/5.60,
81/5.10/5.10,
82/4.60/4.23,
83/5.10/3.37,
84/5.96/2.87,
85/6.46/3.73,
86/5.60/4.23,
87/6.46/4.73,
88/5.60/5.23}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
5/120.00/390.00/0.4/Blue,
74/210.00/390.00/0.4/Green,
23/60.00/330.00/0.4/Orange}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
2/1,
3/1, 3/2,
4/3, 4/2,
5/4, 5/2,
6/1, 6/7,
7/3, 7/8,
8/4, 8/36,
9/1, 9/6,
10/9, 10/6,
11/9, 11/10,
12/17, 12/10,
13/11, 13/12,
14/11, 14/13, 14/16,
15/14, 15/13, 15/16, 15/17,
16/18, 16/19,
17/22, 17/18,
18/20, 18/19,
19/20, 19/21,
20/22, 20/21,
21/23, 21/24,
22/23,
23/25, 23/24,
24/25, 24/26,
25/27, 25/26,
26/28, 26/29,
27/78, 27/32,
28/27, 28/30,
29/28, 29/30, 29/31,
30/32, 30/31,
31/33, 31/34,
32/80, 32/35,
33/32, 33/34, 33/35,
34/39, 34/41,
35/42, 35/39,
36/5, 36/38,
37/8, 37/36,
38/5,
39/42, 39/41,
40/37, 40/38,
41/45, 41/47,
42/81, 42/88,
43/37, 43/40,
44/40, 44/38,
45/42, 45/48,
46/43, 46/44,
47/45, 47/48, 47/49,
48/50, 48/49,
49/51, 49/52,
50/51, 50/42, 50/88,
51/53, 51/52,
52/53, 52/54,
53/55, 53/54,
54/56, 54/57,
55/60, 55/56,
56/58, 56/57,
57/58, 57/59,
58/60, 58/59,
59/61, 59/62,
60/65, 60/61,
61/63, 61/62,
62/63, 62/64,
63/65, 63/64,
64/66, 64/67,
65/85, 65/66,
66/68, 66/67,
67/68, 67/69,
68/70, 68/69,
69/71, 69/72,
70/84, 70/71,
71/46, 71/72,
72/46, 72/44,
73/7, 73/8,
74/8, 74/43,
75/8, 75/74,
76/73, 76/75,
77/73, 77/76,
78/77, 78/79,
79/76, 79/82,
80/79, 80/42, 80/81,
81/82, 81/86,
82/83, 82/86,
83/75, 83/84,
84/74,
85/84, 85/70,
86/83, 86/87,
87/85, 87/55,
88/86, 88/87}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,88}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[Green,very thick] (p-50) -- (p-88);
\draw[Green,very thick] (p-80) -- (p-81);
\draw[Green,very thick] (p-47) -- (p-49);
\draw[Green,very thick] (p-33) -- (p-35);
\draw[Green,very thick] (p-29) -- (p-31);
\draw[Green,very thick] (p-14) -- (p-16);
\draw[Green,very thick] (p-15) -- (p-16);
\draw[Green,very thick] (p-15) -- (p-17);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
5/120.00/390.00/0.4/Blue,
74/210.00/390.00/0.4/Green,
23/60.00/330.00/0.4/Orange}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/210,
2/330,
3/150,
4/30,
5/330,
6/360,
7/210,
8/330,
9/180,
10/60,
11/180,
12/347,
13/30,
14/270,
15/30,
16/240,
17/77,
18/300,
19/120,
20/60,
21/120,
22/48,
23/330,
24/210,
25/30,
26/90,
27/167,
28/240,
29/180,
30/360,
31/60,
32/240,
33/270,
34/30,
35/210,
36/120,
37/30,
38/360,
39/300,
40/90,
41/60,
42/60,
43/60,
44/240,
45/270,
46/180,
47/30,
48/270,
49/120,
50/30,
51/240,
52/60,
53/240,
54/360,
55/93,
56/210,
57/330,
58/210,
59/60,
60/137,
61/120,
62/360,
63/180,
64/300,
65/227,
66/90,
67/270,
68/150,
69/360,
70/330,
71/60,
72/360,
73/300,
74/360,
75/120,
76/60,
77/180,
78/257,
79/62,
80/180,
81/90,
82/150,
83/270,
84/210,
85/90,
86/240,
87/360,
88/270}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
liefert Button "beweglich?" ebenfalls einen beweglichen Graph
88 Knoten, 4×Grad 3, 80×Grad 4, 2×Grad 5, 2×Grad 7, 0 Überschneidungen
178 Kanten, minimal 0.99999999999960431651, maximal 1.00000000000029243274
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>Automatisch generierte Eingabe zu: #1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78); nach Button neue Eingabe "egal wie"</Bildtext>
%<Ausrichten von="1" nach="2"/>
%<Winkel size="18" color="orange" id="orangerWinkel" value="-90.00000000000018"/>
%<Feinjustieren Anzahl="8,3"/>
%<Rechenweg>
%blauerWinkel=-90+(0.9999576819615411)*(orangerWinkel-(-90.00000000000018));
%gruenerWinkel=-179.9999999999996+(3.305192664070729e-7)*(orangerWinkel-(-90.00000000000018));
%P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(2,1); N(3,1,2); N(4,3,2); N(5,4,2); M(38,5,4,blauerWinkel); N(36,5,38); N(8,4,36); N(37,8,36); N(40,37,38); N(43,37,40); N(44,40,38); N(46,43,44); N(72,46,44); N(74,8,43); N(75,8,74); N(7,3,8); N(71,46,72); N(73,7,8); N(76,73,75); N(77,73,76); N(6,1,7); N(9,1,6); N(10,9,6); N(11,9,10); N(69,71,72); M(84,74,8,gruenerWinkel); N(70,84,71); N(83,75,84); N(85,84,70); N(68,70,69); N(67,68,69); N(66,68,67); N(64,66,67); N(65,85,66); N(63,65,64); N(62,63,64); N(61,63,62); N(59,61,62); N(60,65,61); N(58,60,59); N(57,58,59); N(56,58,57); N(54,56,57); N(55,60,56); N(87,85,55); N(53,55,54); N(86,83,87); N(88,86,87); N(52,53,54); N(82,83,86); N(51,53,52); N(79,76,82); N(81,82,86); N(42,81,88); N(49,51,52); N(50,51,42); N(78,77,79); N(80,79,42); N(48,50,49); N(45,42,48); N(47,45,48); N(41,45,47); N(39,42,41); N(34,39,41); N(35,42,39); N(32,80,35); N(33,32,34); N(27,78,32); N(31,33,34); N(30,32,31); N(28,27,30); N(29,28,30); N(26,28,29); N(25,27,26); N(24,25,26); N(23,25,24); N(21,23,24); M(22,23,25,orangerWinkel); N(20,22,21); N(19,20,21); N(18,20,19); N(16,18,19); N(17,22,18); N(12,17,10); N(13,11,12); N(14,11,13); N(15,14,13);
%A(50,88); R(50,88,"green");
%A(80,81); R(80,81,"green");
%A(47,49); R(47,49,"green");
%A(33,35); R(33,35,"green");
%A(29,31); R(29,31,"green");
%A(14,16); R(14,16,"green");
%A(15,16); R(15,16,"green");
%A(15,17); R(15,17,"green");
%</Rechenweg>
%
%<Knopf id="Stopp_alleWinkel" color="LightGrey"/>
%
%<Knopf id="Start_orangerWinkel" color="orange"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#orangerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_orangerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/2.73/0.00,
2/3.73/0.00,
3/3.23/0.87,
4/4.23/0.87,
5/4.73/0.00,
6/2.73/1.00,
7/3.23/1.87,
8/4.23/1.87,
9/1.87/0.50,
10/1.87/1.50,
11/1.00/1.00,
12/2.37/2.37,
13/1.50/1.87,
14/0.50/1.87,
15/1.00/2.73,
16/0.00/2.73,
17/1.87/3.23,
18/0.87/3.23,
19/0.00/3.73,
20/0.87/4.23,
21/0.00/4.73,
22/1.87/4.23,
23/1.00/4.73,
24/0.50/5.60,
25/1.50/5.60,
26/1.00/6.46,
27/2.37/5.10,
28/1.87/5.96,
29/1.87/6.96,
30/2.73/6.46,
31/2.73/7.46,
32/3.23/5.60,
33/3.23/6.60,
34/3.73/7.46,
35/4.10/6.10,
36/4.73/1.00,
37/5.23/1.87,
38/5.60/0.50,
39/4.60/6.96,
40/6.10/1.37,
41/4.60/7.96,
42/5.10/6.10,
43/6.10/2.37,
44/6.60/0.50,
45/5.10/7.10,
46/6.60/1.50,
47/5.60/7.96,
48/6.10/7.10,
49/6.60/7.96,
50/6.10/6.10,
51/6.60/6.96,
52/7.46/7.46,
53/7.46/6.46,
54/8.33/6.96,
55/6.96/5.60,
56/7.83/6.10,
57/8.83/6.10,
58/8.33/5.23,
59/9.33/5.23,
60/7.46/4.73,
61/8.46/4.73,
62/9.33/4.23,
63/8.46/3.73,
64/9.33/3.23,
65/7.46/3.73,
66/8.33/3.23,
67/8.83/2.37,
68/7.83/2.37,
69/8.33/1.50,
70/6.96/2.87,
71/7.46/2.00,
72/7.46/1.00,
73/3.73/2.73,
74/5.10/2.37,
75/4.23/2.87,
76/3.73/3.73,
77/2.87/3.23,
78/2.87/4.23,
79/3.73/4.73,
80/4.23/5.60,
81/5.10/5.10,
82/4.60/4.23,
83/5.10/3.37,
84/5.96/2.87,
85/6.46/3.73,
86/5.60/4.23,
87/6.46/4.73,
88/5.60/5.23}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
23/60.00/330.00/0.4/Orange}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
2/1,
3/1, 3/2,
4/3, 4/2,
5/4, 5/2,
6/1, 6/7,
7/3, 7/8,
8/4, 8/36,
9/1, 9/6,
10/9, 10/6,
11/9, 11/10,
12/17, 12/10,
13/11, 13/12,
14/11, 14/13, 14/16,
15/14, 15/13, 15/16, 15/17,
16/18, 16/19,
17/22, 17/18,
18/20, 18/19,
19/20, 19/21,
20/22, 20/21,
21/23, 21/24,
22/23,
23/25, 23/24,
24/25, 24/26,
25/27, 25/26,
26/28, 26/29,
27/78, 27/32,
28/27, 28/30,
29/28, 29/30, 29/31,
30/32, 30/31,
31/33, 31/34,
32/80, 32/35,
33/32, 33/34, 33/35,
34/39, 34/41,
35/42, 35/39,
36/5, 36/38,
37/8, 37/36,
38/5,
39/42, 39/41,
40/37, 40/38,
41/45, 41/47,
42/81, 42/88,
43/37, 43/40,
44/40, 44/38,
45/42, 45/48,
46/43, 46/44,
47/45, 47/48, 47/49,
48/50, 48/49,
49/51, 49/52,
50/51, 50/42, 50/88,
51/53, 51/52,
52/53, 52/54,
53/55, 53/54,
54/56, 54/57,
55/60, 55/56,
56/58, 56/57,
57/58, 57/59,
58/60, 58/59,
59/61, 59/62,
60/65, 60/61,
61/63, 61/62,
62/63, 62/64,
63/65, 63/64,
64/66, 64/67,
65/85, 65/66,
66/68, 66/67,
67/68, 67/69,
68/70, 68/69,
69/71, 69/72,
70/84, 70/71,
71/46, 71/72,
72/46, 72/44,
73/7, 73/8,
74/8, 74/43,
75/8, 75/74,
76/73, 76/75,
77/73, 77/76,
78/77, 78/79,
79/76, 79/82,
80/79, 80/42, 80/81,
81/82, 81/86,
82/83, 82/86,
83/75, 83/84,
84/74,
85/84, 85/70,
86/83, 86/87,
87/85, 87/55,
88/86, 88/87}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,88}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[Green,very thick] (p-50) -- (p-88);
\draw[Green,very thick] (p-80) -- (p-81);
\draw[Green,very thick] (p-47) -- (p-49);
\draw[Green,very thick] (p-33) -- (p-35);
\draw[Green,very thick] (p-29) -- (p-31);
\draw[Green,very thick] (p-14) -- (p-16);
\draw[Green,very thick] (p-15) -- (p-16);
\draw[Green,very thick] (p-15) -- (p-17);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
23/60.00/330.00/0.4/Orange}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/210,
2/330,
3/150,
4/30,
5/330,
6/360,
7/210,
8/330,
9/180,
10/60,
11/180,
12/347,
13/30,
14/270,
15/30,
16/240,
17/77,
18/300,
19/120,
20/60,
21/120,
22/48,
23/330,
24/210,
25/30,
26/90,
27/167,
28/240,
29/180,
30/360,
31/60,
32/240,
33/270,
34/30,
35/210,
36/120,
37/30,
38/360,
39/300,
40/90,
41/60,
42/60,
43/60,
44/240,
45/270,
46/180,
47/30,
48/270,
49/120,
50/30,
51/240,
52/60,
53/240,
54/360,
55/93,
56/210,
57/330,
58/210,
59/60,
60/137,
61/120,
62/360,
63/180,
64/300,
65/227,
66/90,
67/270,
68/150,
69/360,
70/330,
71/60,
72/360,
73/300,
74/360,
75/120,
76/60,
77/180,
78/257,
79/62,
80/180,
81/90,
82/150,
83/270,
84/210,
85/90,
86/240,
87/360,
88/270}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/6463252f17f4db6e9ae2dcc25d0197a5.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>Automatisch generierte Eingabe zu: #1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78); nach Button neue Eingabe \"egal wie\"</Bildtext>
%<Ausrichten von=\"1\" nach=\"2\"/>
%<Winkel size=\"18\" color=\"orange\" id=\"orangerWinkel\" value=\"-90.00000000000018\"/>
%<Feinjustieren Anzahl=\"8,3\"/>
%<Rechenweg>
%blauerWinkel=-90+(0.9999576819615411)*(orangerWinkel-(-90.00000000000018));
%gruenerWinkel=-179.9999999999996+(3.305192664070729e-7)*(orangerWinkel-(-90.00000000000018));
%P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(2,1); N(3,1,2); N(4,3,2); N(5,4,2); M(38,5,4,blauerWinkel); N(36,5,38); N(8,4,36); N(37,8,36); N(40,37,38); N(43,37,40); N(44,40,38); N(46,43,44); N(72,46,44); N(74,8,43); N(75,8,74); N(7,3,8); N(71,46,72); N(73,7,8); N(76,73,75); N(77,73,76); N(6,1,7); N(9,1,6); N(10,9,6); N(11,9,10); N(69,71,72); M(84,74,8,gruenerWinkel); N(70,84,71); N(83,75,84); N(85,84,70); N(68,70,69); N(67,68,69); N(66,68,67); N(64,66,67); N(65,85,66); N(63,65,64); N(62,63,64); N(61,63,62); N(59,61,62); N(60,65,61); N(58,60,59); N(57,58,59); N(56,58,57); N(54,56,57); N(55,60,56); N(87,85,55); N(53,55,54); N(86,83,87); N(88,86,87); N(52,53,54); N(82,83,86); N(51,53,52); N(79,76,82); N(81,82,86); N(42,81,88); N(49,51,52); N(50,51,42); N(78,77,79); N(80,79,42); N(48,50,49); N(45,42,48); N(47,45,48); N(41,45,47); N(39,42,41); N(34,39,41); N(35,42,39); N(32,80,35); N(33,32,34); N(27,78,32); N(31,33,34); N(30,32,31); N(28,27,30); N(29,28,30); N(26,28,29); N(25,27,26); N(24,25,26); N(23,25,24); N(21,23,24); M(22,23,25,orangerWinkel); N(20,22,21); N(19,20,21); N(18,20,19); N(16,18,19); N(17,22,18); N(12,17,10); N(13,11,12); N(14,11,13); N(15,14,13);
%A(50,88); R(50,88,\"green\");
%A(80,81); R(80,81,\"green\");
%A(47,49); R(47,49,\"green\");
%A(33,35); R(33,35,\"green\");
%A(29,31); R(29,31,\"green\");
%A(14,16); R(14,16,\"green\");
%A(15,16); R(15,16,\"green\");
%A(15,17); R(15,17,\"green\");
%</Rechenweg>
%
%<Knopf id=\"Stopp_alleWinkel\" color=\"LightGrey\"/>
%
%<Knopf id=\"Start_orangerWinkel\" color=\"orange\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#orangerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_orangerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/2.73/0.00,
2/3.73/0.00,
3/3.23/0.87,
4/4.23/0.87,
5/4.73/0.00,
6/2.73/1.00,
7/3.23/1.87,
8/4.23/1.87,
9/1.87/0.50,
10/1.87/1.50,
11/1.00/1.00,
12/2.37/2.37,
13/1.50/1.87,
14/0.50/1.87,
15/1.00/2.73,
16/0.00/2.73,
17/1.87/3.23,
18/0.87/3.23,
19/0.00/3.73,
20/0.87/4.23,
21/0.00/4.73,
22/1.87/4.23,
23/1.00/4.73,
24/0.50/5.60,
25/1.50/5.60,
26/1.00/6.46,
27/2.37/5.10,
28/1.87/5.96,
29/1.87/6.96,
30/2.73/6.46,
31/2.73/7.46,
32/3.23/5.60,
33/3.23/6.60,
34/3.73/7.46,
35/4.10/6.10,
36/4.73/1.00,
37/5.23/1.87,
38/5.60/0.50,
39/4.60/6.96,
40/6.10/1.37,
41/4.60/7.96,
42/5.10/6.10,
43/6.10/2.37,
44/6.60/0.50,
45/5.10/7.10,
46/6.60/1.50,
47/5.60/7.96,
48/6.10/7.10,
49/6.60/7.96,
50/6.10/6.10,
51/6.60/6.96,
52/7.46/7.46,
53/7.46/6.46,
54/8.33/6.96,
55/6.96/5.60,
56/7.83/6.10,
57/8.83/6.10,
58/8.33/5.23,
59/9.33/5.23,
60/7.46/4.73,
61/8.46/4.73,
62/9.33/4.23,
63/8.46/3.73,
64/9.33/3.23,
65/7.46/3.73,
66/8.33/3.23,
67/8.83/2.37,
68/7.83/2.37,
69/8.33/1.50,
70/6.96/2.87,
71/7.46/2.00,
72/7.46/1.00,
73/3.73/2.73,
74/5.10/2.37,
75/4.23/2.87,
76/3.73/3.73,
77/2.87/3.23,
78/2.87/4.23,
79/3.73/4.73,
80/4.23/5.60,
81/5.10/5.10,
82/4.60/4.23,
83/5.10/3.37,
84/5.96/2.87,
85/6.46/3.73,
86/5.60/4.23,
87/6.46/4.73,
88/5.60/5.23}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
23/60.00/330.00/0.4/Orange}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
2/1,
3/1, 3/2,
4/3, 4/2,
5/4, 5/2,
6/1, 6/7,
7/3, 7/8,
8/4, 8/36,
9/1, 9/6,
10/9, 10/6,
11/9, 11/10,
12/17, 12/10,
13/11, 13/12,
14/11, 14/13, 14/16,
15/14, 15/13, 15/16, 15/17,
16/18, 16/19,
17/22, 17/18,
18/20, 18/19,
19/20, 19/21,
20/22, 20/21,
21/23, 21/24,
22/23,
23/25, 23/24,
24/25, 24/26,
25/27, 25/26,
26/28, 26/29,
27/78, 27/32,
28/27, 28/30,
29/28, 29/30, 29/31,
30/32, 30/31,
31/33, 31/34,
32/80, 32/35,
33/32, 33/34, 33/35,
34/39, 34/41,
35/42, 35/39,
36/5, 36/38,
37/8, 37/36,
38/5,
39/42, 39/41,
40/37, 40/38,
41/45, 41/47,
42/81, 42/88,
43/37, 43/40,
44/40, 44/38,
45/42, 45/48,
46/43, 46/44,
47/45, 47/48, 47/49,
48/50, 48/49,
49/51, 49/52,
50/51, 50/42, 50/88,
51/53, 51/52,
52/53, 52/54,
53/55, 53/54,
54/56, 54/57,
55/60, 55/56,
56/58, 56/57,
57/58, 57/59,
58/60, 58/59,
59/61, 59/62,
60/65, 60/61,
61/63, 61/62,
62/63, 62/64,
63/65, 63/64,
64/66, 64/67,
65/85, 65/66,
66/68, 66/67,
67/68, 67/69,
68/70, 68/69,
69/71, 69/72,
70/84, 70/71,
71/46, 71/72,
72/46, 72/44,
73/7, 73/8,
74/8, 74/43,
75/8, 75/74,
76/73, 76/75,
77/73, 77/76,
78/77, 78/79,
79/76, 79/82,
80/79, 80/42, 80/81,
81/82, 81/86,
82/83, 82/86,
83/75, 83/84,
84/74,
85/84, 85/70,
86/83, 86/87,
87/85, 87/55,
88/86, 88/87}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,88}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[Green,very thick] (p-50) -- (p-88);
\draw[Green,very thick] (p-80) -- (p-81);
\draw[Green,very thick] (p-47) -- (p-49);
\draw[Green,very thick] (p-33) -- (p-35);
\draw[Green,very thick] (p-29) -- (p-31);
\draw[Green,very thick] (p-14) -- (p-16);
\draw[Green,very thick] (p-15) -- (p-16);
\draw[Green,very thick] (p-15) -- (p-17);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
23/60.00/330.00/0.4/Orange}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/210,
2/330,
3/150,
4/30,
5/330,
6/360,
7/210,
8/330,
9/180,
10/60,
11/180,
12/347,
13/30,
14/270,
15/30,
16/240,
17/77,
18/300,
19/120,
20/60,
21/120,
22/48,
23/330,
24/210,
25/30,
26/90,
27/167,
28/240,
29/180,
30/360,
31/60,
32/240,
33/270,
34/30,
35/210,
36/120,
37/30,
38/360,
39/300,
40/90,
41/60,
42/60,
43/60,
44/240,
45/270,
46/180,
47/30,
48/270,
49/120,
50/30,
51/240,
52/60,
53/240,
54/360,
55/93,
56/210,
57/330,
58/210,
59/60,
60/137,
61/120,
62/360,
63/180,
64/300,
65/227,
66/90,
67/270,
68/150,
69/360,
70/330,
71/60,
72/360,
73/300,
74/360,
75/120,
76/60,
77/180,
78/257,
79/62,
80/180,
81/90,
82/150,
83/270,
84/210,
85/90,
86/240,
87/360,
88/270}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
und sogar nach Button neue Eingabe "Rahmen zuerst" mit den vielen einzustellenden Winkeln
88 Knoten, 4×Grad 3, 80×Grad 4, 2×Grad 5, 2×Grad 7, 0 Überschneidungen
178 Kanten, minimal 0.99999999999980404564, maximal 1.00000000000011546319
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78);</Bildtext>
%<Ausrichten von="1" nach="2"/>
%<Winkel size="18" color="blue" id="blauerWinkel" value="150.00000000000009"/>
%<Winkel size="18" color="green" id="gruenerWinkel" value="150"/>
%<Winkel size="18" color="orange" id="orangerWinkel" value="150.0000000000002"/>
%<Winkel size="18" color="violet" id="vierterWinkel" value="149.99999999999974"/>
%<Winkel size="18" color="teal" id="fuenfterWinkel" value="150.00000000000063"/>
%<Winkel size="18" color="lime" id="sechsterWinkel" value="-150.00000000000074"/>
%<Winkel size="18" color="LightBlue" id="siebenterWinkel" value="150.00000000000063"/>
%<Winkel size="18" color="LightCoral" id="achterWinkel" value="149.99999999999918"/>
%<Winkel size="18" color="LightCyan" id="neunterWinkel" value="150"/>
%<Winkel size="18" color="LightGoldenrodYellow" id="zehnterWinkel" value="150.0000000000002"/>
%<Winkel size="18" color="LightGreen" id="elfterWinkel" value="150.00000000000006"/>
%<Winkel size="18" color="LightGray" id="zwölfterWinkel" value="149.99999999999966"/>
%<Winkel size="18" color="LightPink" id="dreizehnterWinkel" value="90"/>
%<Winkel size="18" color="LightSalmon" id="vierzehnterWinkel" value="179.99999999999943"/>
%<Feinjustieren Anzahl="19,14"/>
%<Rechenweg>
%P[1]=[0,0]; P[9]=[-43.30127018922193,25.000000000000004]; D=ab(1,9); A(9,1); N(6,9,1); N(10,9,6); N(11,9,10); M(14,11,9,blauerWinkel); N(13,14,11); N(15,14,13); N(16,14,15); M(19,16,14,gruenerWinkel); N(18,19,16); N(20,19,18); N(21,19,20); M(24,21,19,orangerWinkel); N(23,24,21); N(25,24,23); N(26,24,25); M(29,26,24,vierterWinkel); N(28,29,26); N(30,29,28); N(31,29,30); M(34,31,29,fuenfterWinkel); N(33,34,31); M(41,34,31,sechsterWinkel); N(39,41,34); M(47,41,34,siebenterWinkel); N(45,47,41); N(48,47,45); N(49,47,48); M(52,49,47,achterWinkel); N(51,52,49); N(53,52,51); N(54,52,53); M(57,54,52,neunterWinkel); N(56,57,54); N(58,57,56); N(59,57,58); M(62,59,57,zehnterWinkel); N(61,62,59); N(63,62,61); N(64,62,63); M(67,64,62,elfterWinkel); N(66,67,64); N(68,67,66); N(69,67,68); M(72,69,67,zwölfterWinkel); N(71,72,69); N(46,72,71); N(44,72,46); M(40,44,72,dreizehnterWinkel); N(38,44,40); Q(5,38,1,1*D,2*D); A(5,38); A(5,1); H(2,1,5,2); A(2,1); L(3,1,2); H(5,38,5,1); A(5,38); L(36,5,38); A(2,5); L(4,2,5); A(3,4); N(7,6,3); N(8,4,36); N(12,13,10); N(17,18,12); N(22,23,17); N(27,28,25); N(32,33,27); N(35,39,32); N(37,36,40); N(42,45,35); N(43,40,46); N(50,51,42); N(55,56,53); N(60,61,55); N(65,66,60); N(70,71,68); N(73,7,8); N(74,8,43); N(75,8,74); N(80,42,32); N(81,42,80); N(84,74,70); N(85,84,70); N(87,85,55); N(88,87,42); M(78,27,28,vierzehnterWinkel); N(76,73,75); N(77,76,78); N(79,76,80); N(82,81,79); N(83,84,82); N(86,87,88);
%A(8,7); R(8,7,"green");
%A(17,15); R(17,15,"green");
%A(22,20); R(22,20,"green");
%A(32,30); R(32,30,"green");
%A(35,33); R(35,33,"green");
%A(37,8); R(37,8,"green");
%A(42,39); R(42,39,"green");
%A(43,37); R(43,37,"green");
%A(50,48); R(50,48,"green");
%A(60,58); R(60,58,"green");
%A(65,63); R(65,63,"green");
%A(85,65); R(85,65,"green");
%A(88,50); R(88,50,"green");
%A(77,73); R(77,73,"green");
%A(79,78); R(79,78,"green");
%A(83,75); R(83,75,"green");
%A(86,81); R(86,81,"green");
%A(86,83); R(86,83,"green");
%A(86,82); R(86,82,"green");
%</Rechenweg>
%
%<Knopf id="Stopp_alleWinkel" color="LightGrey"/>
%
%<Knopf id="Start_blauerWinkel" color="blue"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#blauerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_blauerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_gruenerWinkel" color="green"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#gruenerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_gruenerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_orangerWinkel" color="orange"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#orangerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_orangerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_vierterWinkel" color="violet"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#vierterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_vierterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_fuenfterWinkel" color="teal"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#fuenfterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_fuenfterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_sechsterWinkel" color="lime"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#sechsterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_sechsterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_siebenterWinkel" color="LightBlue"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#siebenterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_siebenterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_achterWinkel" color="LightCoral"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#achterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_achterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_neunterWinkel" color="LightCyan"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#neunterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_neunterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_zehnterWinkel" color="LightGoldenrodYellow"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#zehnterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_zehnterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_elfterWinkel" color="LightGreen"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#elfterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_elfterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_zwölfterWinkel" color="LightGray"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#zwölfterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_zwölfterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_dreizehnterWinkel" color="LightPink"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#dreizehnterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_dreizehnterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_vierzehnterWinkel" color="LightSalmon"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#vierzehnterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_vierzehnterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LightBlue}{rgb}{0.68,0.84,0.90}
\definecolor{LightCoral}{rgb}{0.94,0.50,0.50}
\definecolor{LightCyan}{rgb}{0.88,1.00,1.00}
\definecolor{LightGoldenrodYellow}{rgb}{0.98,0.98,0.82}
\definecolor{LightGreen}{rgb}{0.56,0.93,0.56}
\definecolor{LightGray}{rgb}{0.82,0.82,0.82}
\definecolor{LightPink}{rgb}{1.00,0.71,0.75}
\definecolor{LightSalmon}{rgb}{1.00,0.63,0.48}
\definecolor{Lime}{rgb}{0.00,1.00,0.00}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
\definecolor{Teal}{rgb}{0.00,0.50,0.50}
\definecolor{Violet}{rgb}{0.93,0.51,0.93}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/2.73/0.00,
2/3.73/0.00,
3/3.23/0.87,
4/4.23/0.87,
5/4.73/0.00,
6/2.73/1.00,
7/3.23/1.87,
8/4.23/1.87,
9/1.87/0.50,
10/1.87/1.50,
11/1.00/1.00,
12/2.37/2.37,
13/1.50/1.87,
14/0.50/1.87,
15/1.00/2.73,
16/0.00/2.73,
17/1.87/3.23,
18/0.87/3.23,
19/0.00/3.73,
20/0.87/4.23,
21/0.00/4.73,
22/1.87/4.23,
23/1.00/4.73,
24/0.50/5.60,
25/1.50/5.60,
26/1.00/6.46,
27/2.37/5.10,
28/1.87/5.96,
29/1.87/6.96,
30/2.73/6.46,
31/2.73/7.46,
32/3.23/5.60,
33/3.23/6.60,
34/3.73/7.46,
35/4.10/6.10,
36/4.73/1.00,
37/5.23/1.87,
38/5.60/0.50,
39/4.60/6.96,
40/6.10/1.37,
41/4.60/7.96,
42/5.10/6.10,
43/6.10/2.37,
44/6.60/0.50,
45/5.10/7.10,
46/6.60/1.50,
47/5.60/7.96,
48/6.10/7.10,
49/6.60/7.96,
50/6.10/6.10,
51/6.60/6.96,
52/7.46/7.46,
53/7.46/6.46,
54/8.33/6.96,
55/6.96/5.60,
56/7.83/6.10,
57/8.83/6.10,
58/8.33/5.23,
59/9.33/5.23,
60/7.46/4.73,
61/8.46/4.73,
62/9.33/4.23,
63/8.46/3.73,
64/9.33/3.23,
65/7.46/3.73,
66/8.33/3.23,
67/8.83/2.37,
68/7.83/2.37,
69/8.33/1.50,
70/6.96/2.87,
71/7.46/2.00,
72/7.46/1.00,
73/3.73/2.73,
74/5.10/2.37,
75/4.23/2.87,
76/3.73/3.73,
77/2.87/3.23,
78/2.87/4.23,
79/3.73/4.73,
80/4.23/5.60,
81/5.10/5.10,
82/4.60/4.23,
83/5.10/3.37,
84/5.96/2.87,
85/6.46/3.73,
86/5.60/4.23,
87/6.46/4.73,
88/5.60/5.23}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
11/330.00/480.00/0.4/Blue,
16/300.00/450.00/0.4/Green,
21/270.00/420.00/0.4/Orange,
26/240.00/390.00/0.4/Violet,
31/210.00/360.00/0.4/Teal,
34/180.00/390.00/0.4/Lime,
41/210.00/360.00/0.4/LightBlue,
49/180.00/330.00/0.4/LightCoral,
54/150.00/300.00/0.4/LightCyan,
59/120.00/270.00/0.4/LightGoldenrodYellow,
64/90.00/240.00/0.4/LightGreen,
69/60.00/210.00/0.4/LightGray,
44/30.00/120.00/0.4/LightPink,
27/120.00/300.00/0.4/LightSalmon}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
2/1, 2/5,
3/1, 3/2, 3/4,
4/2, 4/5,
5/38,
6/9, 6/1,
7/6, 7/3,
8/4, 8/36, 8/7,
9/1,
10/9, 10/6,
11/9, 11/10,
12/13, 12/10,
13/14, 13/11,
14/11,
15/14, 15/13,
16/14, 16/15,
17/18, 17/12, 17/15,
18/19, 18/16,
19/16,
20/19, 20/18,
21/19, 21/20,
22/23, 22/17, 22/20,
23/24, 23/21,
24/21,
25/24, 25/23,
26/24, 26/25,
27/28, 27/25,
28/29, 28/26,
29/26,
30/29, 30/28,
31/29, 31/30,
32/33, 32/27, 32/30,
33/34, 33/31,
34/31,
35/39, 35/32, 35/33,
36/5, 36/38,
37/36, 37/40, 37/8,
38/44, 38/40,
39/41, 39/34,
40/44,
41/34,
42/45, 42/35, 42/39,
43/40, 43/46, 43/37,
44/72, 44/46,
45/47, 45/41,
46/72, 46/71,
47/41,
48/47, 48/45,
49/47, 49/48,
50/51, 50/42, 50/48,
51/52, 51/49,
52/49,
53/52, 53/51,
54/52, 54/53,
55/56, 55/53,
56/57, 56/54,
57/54,
58/57, 58/56,
59/57, 59/58,
60/61, 60/55, 60/58,
61/62, 61/59,
62/59,
63/62, 63/61,
64/62, 64/63,
65/66, 65/60, 65/63,
66/67, 66/64,
67/64,
68/67, 68/66,
69/67, 69/68,
70/71, 70/68,
71/72, 71/69,
72/69,
73/7, 73/8,
74/8, 74/43,
75/8, 75/74,
76/73, 76/75,
77/76, 77/78, 77/73,
78/27,
79/76, 79/80, 79/78,
80/42, 80/32,
81/42, 81/80,
82/81, 82/79,
83/84, 83/82, 83/75,
84/74, 84/70,
85/84, 85/70, 85/65,
86/87, 86/88, 86/81, 86/83, 86/82,
87/85, 87/55,
88/87, 88/42, 88/50}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,88}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[Green,very thick] (p-8) -- (p-7);
\draw[Green,very thick] (p-17) -- (p-15);
\draw[Green,very thick] (p-22) -- (p-20);
\draw[Green,very thick] (p-32) -- (p-30);
\draw[Green,very thick] (p-35) -- (p-33);
\draw[Green,very thick] (p-37) -- (p-8);
\draw[Green,very thick] (p-42) -- (p-39);
\draw[Green,very thick] (p-43) -- (p-37);
\draw[Green,very thick] (p-50) -- (p-48);
\draw[Green,very thick] (p-60) -- (p-58);
\draw[Green,very thick] (p-65) -- (p-63);
\draw[Green,very thick] (p-85) -- (p-65);
\draw[Green,very thick] (p-88) -- (p-50);
\draw[Green,very thick] (p-77) -- (p-73);
\draw[Green,very thick] (p-79) -- (p-78);
\draw[Green,very thick] (p-83) -- (p-75);
\draw[Green,very thick] (p-86) -- (p-81);
\draw[Green,very thick] (p-86) -- (p-83);
\draw[Green,very thick] (p-86) -- (p-82);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
11/330.00/480.00/0.4/Blue,
16/300.00/450.00/0.4/Green,
21/270.00/420.00/0.4/Orange,
26/240.00/390.00/0.4/Violet,
31/210.00/360.00/0.4/Teal,
34/180.00/390.00/0.4/Lime,
41/210.00/360.00/0.4/LightBlue,
49/180.00/330.00/0.4/LightCoral,
54/150.00/300.00/0.4/LightCyan,
59/120.00/270.00/0.4/LightGoldenrodYellow,
64/90.00/240.00/0.4/LightGreen,
69/60.00/210.00/0.4/LightGray,
44/30.00/120.00/0.4/LightPink,
27/120.00/300.00/0.4/LightSalmon}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/210,
2/330,
3/150,
4/30,
5/330,
6/60,
7/210,
8/240,
9/180,
10/60,
11/180,
12/348,
13/30,
14/210,
15/30,
16/150,
17/318,
18/300,
19/180,
20/60,
21/210,
22/48,
23/270,
24/90,
25/30,
26/90,
27/258,
28/300,
29/180,
30/300,
31/150,
32/240,
33/270,
34/180,
35/210,
36/270,
37/180,
38/360,
39/300,
40/90,
41/60,
42/150,
43/60,
44/330,
45/270,
46/180,
47/150,
48/330,
49/120,
50/30,
51/180,
52/360,
53/240,
54/360,
55/93,
56/150,
57/30,
58/210,
59/330,
60/137,
61/180,
62/360,
63/180,
64/30,
65/227,
66/90,
67/30,
68/210,
69/270,
70/330,
71/60,
72/360,
73/90,
74/360,
75/120,
76/60,
77/180,
78/257,
79/123,
80/180,
81/300,
82/210,
83/270,
84/210,
85/90,
86/30,
87/360,
88/120}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/bfd80f3c328ef3a3c46350ab5ed30895.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78);</Bildtext>
%<Ausrichten von=\"1\" nach=\"2\"/>
%<Winkel size=\"18\" color=\"blue\" id=\"blauerWinkel\" value=\"150.00000000000009\"/>
%<Winkel size=\"18\" color=\"green\" id=\"gruenerWinkel\" value=\"150\"/>
%<Winkel size=\"18\" color=\"orange\" id=\"orangerWinkel\" value=\"150.0000000000002\"/>
%<Winkel size=\"18\" color=\"violet\" id=\"vierterWinkel\" value=\"149.99999999999974\"/>
%<Winkel size=\"18\" color=\"teal\" id=\"fuenfterWinkel\" value=\"150.00000000000063\"/>
%<Winkel size=\"18\" color=\"lime\" id=\"sechsterWinkel\" value=\"-150.00000000000074\"/>
%<Winkel size=\"18\" color=\"LightBlue\" id=\"siebenterWinkel\" value=\"150.00000000000063\"/>
%<Winkel size=\"18\" color=\"LightCoral\" id=\"achterWinkel\" value=\"149.99999999999918\"/>
%<Winkel size=\"18\" color=\"LightCyan\" id=\"neunterWinkel\" value=\"150\"/>
%<Winkel size=\"18\" color=\"LightGoldenrodYellow\" id=\"zehnterWinkel\" value=\"150.0000000000002\"/>
%<Winkel size=\"18\" color=\"LightGreen\" id=\"elfterWinkel\" value=\"150.00000000000006\"/>
%<Winkel size=\"18\" color=\"LightGray\" id=\"zwölfterWinkel\" value=\"149.99999999999966\"/>
%<Winkel size=\"18\" color=\"LightPink\" id=\"dreizehnterWinkel\" value=\"90\"/>
%<Winkel size=\"18\" color=\"LightSalmon\" id=\"vierzehnterWinkel\" value=\"179.99999999999943\"/>
%<Feinjustieren Anzahl=\"19,14\"/>
%<Rechenweg>
%P[1]=[0,0]; P[9]=[-43.30127018922193,25.000000000000004]; D=ab(1,9); A(9,1); N(6,9,1); N(10,9,6); N(11,9,10); M(14,11,9,blauerWinkel); N(13,14,11); N(15,14,13); N(16,14,15); M(19,16,14,gruenerWinkel); N(18,19,16); N(20,19,18); N(21,19,20); M(24,21,19,orangerWinkel); N(23,24,21); N(25,24,23); N(26,24,25); M(29,26,24,vierterWinkel); N(28,29,26); N(30,29,28); N(31,29,30); M(34,31,29,fuenfterWinkel); N(33,34,31); M(41,34,31,sechsterWinkel); N(39,41,34); M(47,41,34,siebenterWinkel); N(45,47,41); N(48,47,45); N(49,47,48); M(52,49,47,achterWinkel); N(51,52,49); N(53,52,51); N(54,52,53); M(57,54,52,neunterWinkel); N(56,57,54); N(58,57,56); N(59,57,58); M(62,59,57,zehnterWinkel); N(61,62,59); N(63,62,61); N(64,62,63); M(67,64,62,elfterWinkel); N(66,67,64); N(68,67,66); N(69,67,68); M(72,69,67,zwölfterWinkel); N(71,72,69); N(46,72,71); N(44,72,46); M(40,44,72,dreizehnterWinkel); N(38,44,40); Q(5,38,1,1*D,2*D); A(5,38); A(5,1); H(2,1,5,2); A(2,1); L(3,1,2); H(5,38,5,1); A(5,38); L(36,5,38); A(2,5); L(4,2,5); A(3,4); N(7,6,3); N(8,4,36); N(12,13,10); N(17,18,12); N(22,23,17); N(27,28,25); N(32,33,27); N(35,39,32); N(37,36,40); N(42,45,35); N(43,40,46); N(50,51,42); N(55,56,53); N(60,61,55); N(65,66,60); N(70,71,68); N(73,7,8); N(74,8,43); N(75,8,74); N(80,42,32); N(81,42,80); N(84,74,70); N(85,84,70); N(87,85,55); N(88,87,42); M(78,27,28,vierzehnterWinkel); N(76,73,75); N(77,76,78); N(79,76,80); N(82,81,79); N(83,84,82); N(86,87,88);
%A(8,7); R(8,7,\"green\");
%A(17,15); R(17,15,\"green\");
%A(22,20); R(22,20,\"green\");
%A(32,30); R(32,30,\"green\");
%A(35,33); R(35,33,\"green\");
%A(37,8); R(37,8,\"green\");
%A(42,39); R(42,39,\"green\");
%A(43,37); R(43,37,\"green\");
%A(50,48); R(50,48,\"green\");
%A(60,58); R(60,58,\"green\");
%A(65,63); R(65,63,\"green\");
%A(85,65); R(85,65,\"green\");
%A(88,50); R(88,50,\"green\");
%A(77,73); R(77,73,\"green\");
%A(79,78); R(79,78,\"green\");
%A(83,75); R(83,75,\"green\");
%A(86,81); R(86,81,\"green\");
%A(86,83); R(86,83,\"green\");
%A(86,82); R(86,82,\"green\");
%</Rechenweg>
%
%<Knopf id=\"Stopp_alleWinkel\" color=\"LightGrey\"/>
%
%<Knopf id=\"Start_blauerWinkel\" color=\"blue\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#blauerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_blauerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_gruenerWinkel\" color=\"green\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#gruenerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_gruenerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_orangerWinkel\" color=\"orange\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#orangerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_orangerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_vierterWinkel\" color=\"violet\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#vierterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_vierterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_fuenfterWinkel\" color=\"teal\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#fuenfterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_fuenfterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_sechsterWinkel\" color=\"lime\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#sechsterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_sechsterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_siebenterWinkel\" color=\"LightBlue\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#siebenterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_siebenterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_achterWinkel\" color=\"LightCoral\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#achterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_achterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_neunterWinkel\" color=\"LightCyan\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#neunterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_neunterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_zehnterWinkel\" color=\"LightGoldenrodYellow\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#zehnterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_zehnterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_elfterWinkel\" color=\"LightGreen\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#elfterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_elfterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_zwölfterWinkel\" color=\"LightGray\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#zwölfterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_zwölfterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_dreizehnterWinkel\" color=\"LightPink\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#dreizehnterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_dreizehnterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_vierzehnterWinkel\" color=\"LightSalmon\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#vierzehnterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_vierzehnterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LightBlue}{rgb}{0.68,0.84,0.90}
\definecolor{LightCoral}{rgb}{0.94,0.50,0.50}
\definecolor{LightCyan}{rgb}{0.88,1.00,1.00}
\definecolor{LightGoldenrodYellow}{rgb}{0.98,0.98,0.82}
\definecolor{LightGreen}{rgb}{0.56,0.93,0.56}
\definecolor{LightGray}{rgb}{0.82,0.82,0.82}
\definecolor{LightPink}{rgb}{1.00,0.71,0.75}
\definecolor{LightSalmon}{rgb}{1.00,0.63,0.48}
\definecolor{Lime}{rgb}{0.00,1.00,0.00}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
\definecolor{Teal}{rgb}{0.00,0.50,0.50}
\definecolor{Violet}{rgb}{0.93,0.51,0.93}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/2.73/0.00,
2/3.73/0.00,
3/3.23/0.87,
4/4.23/0.87,
5/4.73/0.00,
6/2.73/1.00,
7/3.23/1.87,
8/4.23/1.87,
9/1.87/0.50,
10/1.87/1.50,
11/1.00/1.00,
12/2.37/2.37,
13/1.50/1.87,
14/0.50/1.87,
15/1.00/2.73,
16/0.00/2.73,
17/1.87/3.23,
18/0.87/3.23,
19/0.00/3.73,
20/0.87/4.23,
21/0.00/4.73,
22/1.87/4.23,
23/1.00/4.73,
24/0.50/5.60,
25/1.50/5.60,
26/1.00/6.46,
27/2.37/5.10,
28/1.87/5.96,
29/1.87/6.96,
30/2.73/6.46,
31/2.73/7.46,
32/3.23/5.60,
33/3.23/6.60,
34/3.73/7.46,
35/4.10/6.10,
36/4.73/1.00,
37/5.23/1.87,
38/5.60/0.50,
39/4.60/6.96,
40/6.10/1.37,
41/4.60/7.96,
42/5.10/6.10,
43/6.10/2.37,
44/6.60/0.50,
45/5.10/7.10,
46/6.60/1.50,
47/5.60/7.96,
48/6.10/7.10,
49/6.60/7.96,
50/6.10/6.10,
51/6.60/6.96,
52/7.46/7.46,
53/7.46/6.46,
54/8.33/6.96,
55/6.96/5.60,
56/7.83/6.10,
57/8.83/6.10,
58/8.33/5.23,
59/9.33/5.23,
60/7.46/4.73,
61/8.46/4.73,
62/9.33/4.23,
63/8.46/3.73,
64/9.33/3.23,
65/7.46/3.73,
66/8.33/3.23,
67/8.83/2.37,
68/7.83/2.37,
69/8.33/1.50,
70/6.96/2.87,
71/7.46/2.00,
72/7.46/1.00,
73/3.73/2.73,
74/5.10/2.37,
75/4.23/2.87,
76/3.73/3.73,
77/2.87/3.23,
78/2.87/4.23,
79/3.73/4.73,
80/4.23/5.60,
81/5.10/5.10,
82/4.60/4.23,
83/5.10/3.37,
84/5.96/2.87,
85/6.46/3.73,
86/5.60/4.23,
87/6.46/4.73,
88/5.60/5.23}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
11/330.00/480.00/0.4/Blue,
16/300.00/450.00/0.4/Green,
21/270.00/420.00/0.4/Orange,
26/240.00/390.00/0.4/Violet,
31/210.00/360.00/0.4/Teal,
34/180.00/390.00/0.4/Lime,
41/210.00/360.00/0.4/LightBlue,
49/180.00/330.00/0.4/LightCoral,
54/150.00/300.00/0.4/LightCyan,
59/120.00/270.00/0.4/LightGoldenrodYellow,
64/90.00/240.00/0.4/LightGreen,
69/60.00/210.00/0.4/LightGray,
44/30.00/120.00/0.4/LightPink,
27/120.00/300.00/0.4/LightSalmon}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
2/1, 2/5,
3/1, 3/2, 3/4,
4/2, 4/5,
5/38,
6/9, 6/1,
7/6, 7/3,
8/4, 8/36, 8/7,
9/1,
10/9, 10/6,
11/9, 11/10,
12/13, 12/10,
13/14, 13/11,
14/11,
15/14, 15/13,
16/14, 16/15,
17/18, 17/12, 17/15,
18/19, 18/16,
19/16,
20/19, 20/18,
21/19, 21/20,
22/23, 22/17, 22/20,
23/24, 23/21,
24/21,
25/24, 25/23,
26/24, 26/25,
27/28, 27/25,
28/29, 28/26,
29/26,
30/29, 30/28,
31/29, 31/30,
32/33, 32/27, 32/30,
33/34, 33/31,
34/31,
35/39, 35/32, 35/33,
36/5, 36/38,
37/36, 37/40, 37/8,
38/44, 38/40,
39/41, 39/34,
40/44,
41/34,
42/45, 42/35, 42/39,
43/40, 43/46, 43/37,
44/72, 44/46,
45/47, 45/41,
46/72, 46/71,
47/41,
48/47, 48/45,
49/47, 49/48,
50/51, 50/42, 50/48,
51/52, 51/49,
52/49,
53/52, 53/51,
54/52, 54/53,
55/56, 55/53,
56/57, 56/54,
57/54,
58/57, 58/56,
59/57, 59/58,
60/61, 60/55, 60/58,
61/62, 61/59,
62/59,
63/62, 63/61,
64/62, 64/63,
65/66, 65/60, 65/63,
66/67, 66/64,
67/64,
68/67, 68/66,
69/67, 69/68,
70/71, 70/68,
71/72, 71/69,
72/69,
73/7, 73/8,
74/8, 74/43,
75/8, 75/74,
76/73, 76/75,
77/76, 77/78, 77/73,
78/27,
79/76, 79/80, 79/78,
80/42, 80/32,
81/42, 81/80,
82/81, 82/79,
83/84, 83/82, 83/75,
84/74, 84/70,
85/84, 85/70, 85/65,
86/87, 86/88, 86/81, 86/83, 86/82,
87/85, 87/55,
88/87, 88/42, 88/50}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,88}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[Green,very thick] (p-8) -- (p-7);
\draw[Green,very thick] (p-17) -- (p-15);
\draw[Green,very thick] (p-22) -- (p-20);
\draw[Green,very thick] (p-32) -- (p-30);
\draw[Green,very thick] (p-35) -- (p-33);
\draw[Green,very thick] (p-37) -- (p-8);
\draw[Green,very thick] (p-42) -- (p-39);
\draw[Green,very thick] (p-43) -- (p-37);
\draw[Green,very thick] (p-50) -- (p-48);
\draw[Green,very thick] (p-60) -- (p-58);
\draw[Green,very thick] (p-65) -- (p-63);
\draw[Green,very thick] (p-85) -- (p-65);
\draw[Green,very thick] (p-88) -- (p-50);
\draw[Green,very thick] (p-77) -- (p-73);
\draw[Green,very thick] (p-79) -- (p-78);
\draw[Green,very thick] (p-83) -- (p-75);
\draw[Green,very thick] (p-86) -- (p-81);
\draw[Green,very thick] (p-86) -- (p-83);
\draw[Green,very thick] (p-86) -- (p-82);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
11/330.00/480.00/0.4/Blue,
16/300.00/450.00/0.4/Green,
21/270.00/420.00/0.4/Orange,
26/240.00/390.00/0.4/Violet,
31/210.00/360.00/0.4/Teal,
34/180.00/390.00/0.4/Lime,
41/210.00/360.00/0.4/LightBlue,
49/180.00/330.00/0.4/LightCoral,
54/150.00/300.00/0.4/LightCyan,
59/120.00/270.00/0.4/LightGoldenrodYellow,
64/90.00/240.00/0.4/LightGreen,
69/60.00/210.00/0.4/LightGray,
44/30.00/120.00/0.4/LightPink,
27/120.00/300.00/0.4/LightSalmon}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/210,
2/330,
3/150,
4/30,
5/330,
6/60,
7/210,
8/240,
9/180,
10/60,
11/180,
12/348,
13/30,
14/210,
15/30,
16/150,
17/318,
18/300,
19/180,
20/60,
21/210,
22/48,
23/270,
24/90,
25/30,
26/90,
27/258,
28/300,
29/180,
30/300,
31/150,
32/240,
33/270,
34/180,
35/210,
36/270,
37/180,
38/360,
39/300,
40/90,
41/60,
42/150,
43/60,
44/330,
45/270,
46/180,
47/150,
48/330,
49/120,
50/30,
51/180,
52/360,
53/240,
54/360,
55/93,
56/150,
57/30,
58/210,
59/330,
60/137,
61/180,
62/360,
63/180,
64/30,
65/227,
66/90,
67/30,
68/210,
69/270,
70/330,
71/60,
72/360,
73/90,
74/360,
75/120,
76/60,
77/180,
78/257,
79/123,
80/180,
81/300,
82/210,
83/270,
84/210,
85/90,
86/30,
87/360,
88/120}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
findet Button "beweglich?" eine Beweglichkeit.
88 Knoten, 4×Grad 3, 80×Grad 4, 2×Grad 5, 2×Grad 7, 0 Überschneidungen
178 Kanten, minimal 0.99999999999980404564, maximal 1.00000000000011546319
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78);</Bildtext>
%<Ausrichten von="1" nach="2"/>
%<Winkel size="18" color="LightPink" id="dreizehnterWinkel" value="90"/>
%<Feinjustieren Anzahl="19,14"/>
%<Rechenweg>
%blauerWinkel=150.00000000000009+(0.9999983168393314)*(dreizehnterWinkel-(90));
%gruenerWinkel=150+(-0.9999983168393296)*(dreizehnterWinkel-(90));
%orangerWinkel=150.0000000000002+(0.9999987575491853)*(dreizehnterWinkel-(90));
%vierterWinkel=149.99999999999974+(-1.0000001604326674)*(dreizehnterWinkel-(90));
%fuenfterWinkel=150.00000000000063+(1.0000024741707787)*(dreizehnterWinkel-(90));
%sechsterWinkel=-150.00000000000074+(-1.000004852037189)*(dreizehnterWinkel-(90));
%siebenterWinkel=150.00000000000063+(1.000004049339543)*(dreizehnterWinkel-(90));
%achterWinkel=149.99999999999918+(-1.0000014811475222)*(dreizehnterWinkel-(90));
%neunterWinkel=150+(1.0000023821281057)*(dreizehnterWinkel-(90));
%zehnterWinkel=150.0000000000002+(-1.0000010600001117)*(dreizehnterWinkel-(90));
%elfterWinkel=150.00000000000006+(1.0000010758308997)*(dreizehnterWinkel-(90));
%zwölfterWinkel=149.99999999999966+(-1.000000418101856)*(dreizehnterWinkel-(90));
%vierzehnterWinkel=179.99999999999943+(6.8801574023397e-7)*(dreizehnterWinkel-(90));
%P[1]=[0,0]; P[9]=[-43.30127018922193,25.000000000000004]; D=ab(1,9); A(9,1); N(6,9,1); N(10,9,6); N(11,9,10); M(14,11,9,blauerWinkel); N(13,14,11); N(15,14,13); N(16,14,15); M(19,16,14,gruenerWinkel); N(18,19,16); N(20,19,18); N(21,19,20); M(24,21,19,orangerWinkel); N(23,24,21); N(25,24,23); N(26,24,25); M(29,26,24,vierterWinkel); N(28,29,26); N(30,29,28); N(31,29,30); M(34,31,29,fuenfterWinkel); N(33,34,31); M(41,34,31,sechsterWinkel); N(39,41,34); M(47,41,34,siebenterWinkel); N(45,47,41); N(48,47,45); N(49,47,48); M(52,49,47,achterWinkel); N(51,52,49); N(53,52,51); N(54,52,53); M(57,54,52,neunterWinkel); N(56,57,54); N(58,57,56); N(59,57,58); M(62,59,57,zehnterWinkel); N(61,62,59); N(63,62,61); N(64,62,63); M(67,64,62,elfterWinkel); N(66,67,64); N(68,67,66); N(69,67,68); M(72,69,67,zwölfterWinkel); N(71,72,69); N(46,72,71); N(44,72,46); M(40,44,72,dreizehnterWinkel); N(38,44,40); Q(5,38,1,1*D,2*D); A(5,38); A(5,1); H(2,1,5,2); A(2,1); L(3,1,2); H(5,38,5,1); A(5,38); L(36,5,38); A(2,5); L(4,2,5); A(3,4); N(7,6,3); N(8,4,36); N(12,13,10); N(17,18,12); N(22,23,17); N(27,28,25); N(32,33,27); N(35,39,32); N(37,36,40); N(42,45,35); N(43,40,46); N(50,51,42); N(55,56,53); N(60,61,55); N(65,66,60); N(70,71,68); N(73,7,8); N(74,8,43); N(75,8,74); N(80,42,32); N(81,42,80); N(84,74,70); N(85,84,70); N(87,85,55); N(88,87,42); M(78,27,28,vierzehnterWinkel); N(76,73,75); N(77,76,78); N(79,76,80); N(82,81,79); N(83,84,82); N(86,87,88);
%A(8,7); R(8,7,"green");
%A(17,15); R(17,15,"green");
%A(22,20); R(22,20,"green");
%A(32,30); R(32,30,"green");
%A(35,33); R(35,33,"green");
%A(37,8); R(37,8,"green");
%A(42,39); R(42,39,"green");
%A(43,37); R(43,37,"green");
%A(50,48); R(50,48,"green");
%A(60,58); R(60,58,"green");
%A(65,63); R(65,63,"green");
%A(85,65); R(85,65,"green");
%A(88,50); R(88,50,"green");
%A(77,73); R(77,73,"green");
%A(79,78); R(79,78,"green");
%A(83,75); R(83,75,"green");
%A(86,81); R(86,81,"green");
%A(86,83); R(86,83,"green");
%A(86,82); R(86,82,"green");
%</Rechenweg>
%
%<Knopf id="Stopp_alleWinkel" color="LightGrey"/>
%
%<Knopf id="Start_dreizehnterWinkel" color="LightPink"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#dreizehnterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_dreizehnterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LightPink}{rgb}{1.00,0.71,0.75}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/2.73/0.00,
2/3.73/0.00,
3/3.23/0.87,
4/4.23/0.87,
5/4.73/0.00,
6/2.73/1.00,
7/3.23/1.87,
8/4.23/1.87,
9/1.87/0.50,
10/1.87/1.50,
11/1.00/1.00,
12/2.37/2.37,
13/1.50/1.87,
14/0.50/1.87,
15/1.00/2.73,
16/0.00/2.73,
17/1.87/3.23,
18/0.87/3.23,
19/0.00/3.73,
20/0.87/4.23,
21/0.00/4.73,
22/1.87/4.23,
23/1.00/4.73,
24/0.50/5.60,
25/1.50/5.60,
26/1.00/6.46,
27/2.37/5.10,
28/1.87/5.96,
29/1.87/6.96,
30/2.73/6.46,
31/2.73/7.46,
32/3.23/5.60,
33/3.23/6.60,
34/3.73/7.46,
35/4.10/6.10,
36/4.73/1.00,
37/5.23/1.87,
38/5.60/0.50,
39/4.60/6.96,
40/6.10/1.37,
41/4.60/7.96,
42/5.10/6.10,
43/6.10/2.37,
44/6.60/0.50,
45/5.10/7.10,
46/6.60/1.50,
47/5.60/7.96,
48/6.10/7.10,
49/6.60/7.96,
50/6.10/6.10,
51/6.60/6.96,
52/7.46/7.46,
53/7.46/6.46,
54/8.33/6.96,
55/6.96/5.60,
56/7.83/6.10,
57/8.83/6.10,
58/8.33/5.23,
59/9.33/5.23,
60/7.46/4.73,
61/8.46/4.73,
62/9.33/4.23,
63/8.46/3.73,
64/9.33/3.23,
65/7.46/3.73,
66/8.33/3.23,
67/8.83/2.37,
68/7.83/2.37,
69/8.33/1.50,
70/6.96/2.87,
71/7.46/2.00,
72/7.46/1.00,
73/3.73/2.73,
74/5.10/2.37,
75/4.23/2.87,
76/3.73/3.73,
77/2.87/3.23,
78/2.87/4.23,
79/3.73/4.73,
80/4.23/5.60,
81/5.10/5.10,
82/4.60/4.23,
83/5.10/3.37,
84/5.96/2.87,
85/6.46/3.73,
86/5.60/4.23,
87/6.46/4.73,
88/5.60/5.23}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
44/30.00/120.00/0.4/LightPink}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
2/1, 2/5,
3/1, 3/2, 3/4,
4/2, 4/5,
5/38,
6/9, 6/1,
7/6, 7/3,
8/4, 8/36, 8/7,
9/1,
10/9, 10/6,
11/9, 11/10,
12/13, 12/10,
13/14, 13/11,
14/11,
15/14, 15/13,
16/14, 16/15,
17/18, 17/12, 17/15,
18/19, 18/16,
19/16,
20/19, 20/18,
21/19, 21/20,
22/23, 22/17, 22/20,
23/24, 23/21,
24/21,
25/24, 25/23,
26/24, 26/25,
27/28, 27/25,
28/29, 28/26,
29/26,
30/29, 30/28,
31/29, 31/30,
32/33, 32/27, 32/30,
33/34, 33/31,
34/31,
35/39, 35/32, 35/33,
36/5, 36/38,
37/36, 37/40, 37/8,
38/44, 38/40,
39/41, 39/34,
40/44,
41/34,
42/45, 42/35, 42/39,
43/40, 43/46, 43/37,
44/72, 44/46,
45/47, 45/41,
46/72, 46/71,
47/41,
48/47, 48/45,
49/47, 49/48,
50/51, 50/42, 50/48,
51/52, 51/49,
52/49,
53/52, 53/51,
54/52, 54/53,
55/56, 55/53,
56/57, 56/54,
57/54,
58/57, 58/56,
59/57, 59/58,
60/61, 60/55, 60/58,
61/62, 61/59,
62/59,
63/62, 63/61,
64/62, 64/63,
65/66, 65/60, 65/63,
66/67, 66/64,
67/64,
68/67, 68/66,
69/67, 69/68,
70/71, 70/68,
71/72, 71/69,
72/69,
73/7, 73/8,
74/8, 74/43,
75/8, 75/74,
76/73, 76/75,
77/76, 77/78, 77/73,
78/27,
79/76, 79/80, 79/78,
80/42, 80/32,
81/42, 81/80,
82/81, 82/79,
83/84, 83/82, 83/75,
84/74, 84/70,
85/84, 85/70, 85/65,
86/87, 86/88, 86/81, 86/83, 86/82,
87/85, 87/55,
88/87, 88/42, 88/50}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,88}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[Green,very thick] (p-8) -- (p-7);
\draw[Green,very thick] (p-17) -- (p-15);
\draw[Green,very thick] (p-22) -- (p-20);
\draw[Green,very thick] (p-32) -- (p-30);
\draw[Green,very thick] (p-35) -- (p-33);
\draw[Green,very thick] (p-37) -- (p-8);
\draw[Green,very thick] (p-42) -- (p-39);
\draw[Green,very thick] (p-43) -- (p-37);
\draw[Green,very thick] (p-50) -- (p-48);
\draw[Green,very thick] (p-60) -- (p-58);
\draw[Green,very thick] (p-65) -- (p-63);
\draw[Green,very thick] (p-85) -- (p-65);
\draw[Green,very thick] (p-88) -- (p-50);
\draw[Green,very thick] (p-77) -- (p-73);
\draw[Green,very thick] (p-79) -- (p-78);
\draw[Green,very thick] (p-83) -- (p-75);
\draw[Green,very thick] (p-86) -- (p-81);
\draw[Green,very thick] (p-86) -- (p-83);
\draw[Green,very thick] (p-86) -- (p-82);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
44/30.00/120.00/0.4/LightPink}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/210,
2/330,
3/150,
4/30,
5/330,
6/60,
7/210,
8/240,
9/180,
10/60,
11/180,
12/348,
13/30,
14/210,
15/30,
16/150,
17/318,
18/300,
19/180,
20/60,
21/210,
22/48,
23/270,
24/90,
25/30,
26/90,
27/258,
28/300,
29/180,
30/300,
31/150,
32/240,
33/270,
34/180,
35/210,
36/270,
37/180,
38/360,
39/300,
40/90,
41/60,
42/150,
43/60,
44/330,
45/270,
46/180,
47/150,
48/330,
49/120,
50/30,
51/180,
52/360,
53/240,
54/360,
55/93,
56/150,
57/30,
58/210,
59/330,
60/137,
61/180,
62/360,
63/180,
64/30,
65/227,
66/90,
67/30,
68/210,
69/270,
70/330,
71/60,
72/360,
73/90,
74/360,
75/120,
76/60,
77/180,
78/257,
79/123,
80/180,
81/300,
82/210,
83/270,
84/210,
85/90,
86/30,
87/360,
88/120}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/b4ebbcf2467ec12accc09d1c02ac9fed.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78);</Bildtext>
%<Ausrichten von=\"1\" nach=\"2\"/>
%<Winkel size=\"18\" color=\"LightPink\" id=\"dreizehnterWinkel\" value=\"90\"/>
%<Feinjustieren Anzahl=\"19,14\"/>
%<Rechenweg>
%blauerWinkel=150.00000000000009+(0.9999983168393314)*(dreizehnterWinkel-(90));
%gruenerWinkel=150+(-0.9999983168393296)*(dreizehnterWinkel-(90));
%orangerWinkel=150.0000000000002+(0.9999987575491853)*(dreizehnterWinkel-(90));
%vierterWinkel=149.99999999999974+(-1.0000001604326674)*(dreizehnterWinkel-(90));
%fuenfterWinkel=150.00000000000063+(1.0000024741707787)*(dreizehnterWinkel-(90));
%sechsterWinkel=-150.00000000000074+(-1.000004852037189)*(dreizehnterWinkel-(90));
%siebenterWinkel=150.00000000000063+(1.000004049339543)*(dreizehnterWinkel-(90));
%achterWinkel=149.99999999999918+(-1.0000014811475222)*(dreizehnterWinkel-(90));
%neunterWinkel=150+(1.0000023821281057)*(dreizehnterWinkel-(90));
%zehnterWinkel=150.0000000000002+(-1.0000010600001117)*(dreizehnterWinkel-(90));
%elfterWinkel=150.00000000000006+(1.0000010758308997)*(dreizehnterWinkel-(90));
%zwölfterWinkel=149.99999999999966+(-1.000000418101856)*(dreizehnterWinkel-(90));
%vierzehnterWinkel=179.99999999999943+(6.8801574023397e-7)*(dreizehnterWinkel-(90));
%P[1]=[0,0]; P[9]=[-43.30127018922193,25.000000000000004]; D=ab(1,9); A(9,1); N(6,9,1); N(10,9,6); N(11,9,10); M(14,11,9,blauerWinkel); N(13,14,11); N(15,14,13); N(16,14,15); M(19,16,14,gruenerWinkel); N(18,19,16); N(20,19,18); N(21,19,20); M(24,21,19,orangerWinkel); N(23,24,21); N(25,24,23); N(26,24,25); M(29,26,24,vierterWinkel); N(28,29,26); N(30,29,28); N(31,29,30); M(34,31,29,fuenfterWinkel); N(33,34,31); M(41,34,31,sechsterWinkel); N(39,41,34); M(47,41,34,siebenterWinkel); N(45,47,41); N(48,47,45); N(49,47,48); M(52,49,47,achterWinkel); N(51,52,49); N(53,52,51); N(54,52,53); M(57,54,52,neunterWinkel); N(56,57,54); N(58,57,56); N(59,57,58); M(62,59,57,zehnterWinkel); N(61,62,59); N(63,62,61); N(64,62,63); M(67,64,62,elfterWinkel); N(66,67,64); N(68,67,66); N(69,67,68); M(72,69,67,zwölfterWinkel); N(71,72,69); N(46,72,71); N(44,72,46); M(40,44,72,dreizehnterWinkel); N(38,44,40); Q(5,38,1,1*D,2*D); A(5,38); A(5,1); H(2,1,5,2); A(2,1); L(3,1,2); H(5,38,5,1); A(5,38); L(36,5,38); A(2,5); L(4,2,5); A(3,4); N(7,6,3); N(8,4,36); N(12,13,10); N(17,18,12); N(22,23,17); N(27,28,25); N(32,33,27); N(35,39,32); N(37,36,40); N(42,45,35); N(43,40,46); N(50,51,42); N(55,56,53); N(60,61,55); N(65,66,60); N(70,71,68); N(73,7,8); N(74,8,43); N(75,8,74); N(80,42,32); N(81,42,80); N(84,74,70); N(85,84,70); N(87,85,55); N(88,87,42); M(78,27,28,vierzehnterWinkel); N(76,73,75); N(77,76,78); N(79,76,80); N(82,81,79); N(83,84,82); N(86,87,88);
%A(8,7); R(8,7,\"green\");
%A(17,15); R(17,15,\"green\");
%A(22,20); R(22,20,\"green\");
%A(32,30); R(32,30,\"green\");
%A(35,33); R(35,33,\"green\");
%A(37,8); R(37,8,\"green\");
%A(42,39); R(42,39,\"green\");
%A(43,37); R(43,37,\"green\");
%A(50,48); R(50,48,\"green\");
%A(60,58); R(60,58,\"green\");
%A(65,63); R(65,63,\"green\");
%A(85,65); R(85,65,\"green\");
%A(88,50); R(88,50,\"green\");
%A(77,73); R(77,73,\"green\");
%A(79,78); R(79,78,\"green\");
%A(83,75); R(83,75,\"green\");
%A(86,81); R(86,81,\"green\");
%A(86,83); R(86,83,\"green\");
%A(86,82); R(86,82,\"green\");
%</Rechenweg>
%
%<Knopf id=\"Stopp_alleWinkel\" color=\"LightGrey\"/>
%
%<Knopf id=\"Start_dreizehnterWinkel\" color=\"LightPink\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#dreizehnterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_dreizehnterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LightPink}{rgb}{1.00,0.71,0.75}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/2.73/0.00,
2/3.73/0.00,
3/3.23/0.87,
4/4.23/0.87,
5/4.73/0.00,
6/2.73/1.00,
7/3.23/1.87,
8/4.23/1.87,
9/1.87/0.50,
10/1.87/1.50,
11/1.00/1.00,
12/2.37/2.37,
13/1.50/1.87,
14/0.50/1.87,
15/1.00/2.73,
16/0.00/2.73,
17/1.87/3.23,
18/0.87/3.23,
19/0.00/3.73,
20/0.87/4.23,
21/0.00/4.73,
22/1.87/4.23,
23/1.00/4.73,
24/0.50/5.60,
25/1.50/5.60,
26/1.00/6.46,
27/2.37/5.10,
28/1.87/5.96,
29/1.87/6.96,
30/2.73/6.46,
31/2.73/7.46,
32/3.23/5.60,
33/3.23/6.60,
34/3.73/7.46,
35/4.10/6.10,
36/4.73/1.00,
37/5.23/1.87,
38/5.60/0.50,
39/4.60/6.96,
40/6.10/1.37,
41/4.60/7.96,
42/5.10/6.10,
43/6.10/2.37,
44/6.60/0.50,
45/5.10/7.10,
46/6.60/1.50,
47/5.60/7.96,
48/6.10/7.10,
49/6.60/7.96,
50/6.10/6.10,
51/6.60/6.96,
52/7.46/7.46,
53/7.46/6.46,
54/8.33/6.96,
55/6.96/5.60,
56/7.83/6.10,
57/8.83/6.10,
58/8.33/5.23,
59/9.33/5.23,
60/7.46/4.73,
61/8.46/4.73,
62/9.33/4.23,
63/8.46/3.73,
64/9.33/3.23,
65/7.46/3.73,
66/8.33/3.23,
67/8.83/2.37,
68/7.83/2.37,
69/8.33/1.50,
70/6.96/2.87,
71/7.46/2.00,
72/7.46/1.00,
73/3.73/2.73,
74/5.10/2.37,
75/4.23/2.87,
76/3.73/3.73,
77/2.87/3.23,
78/2.87/4.23,
79/3.73/4.73,
80/4.23/5.60,
81/5.10/5.10,
82/4.60/4.23,
83/5.10/3.37,
84/5.96/2.87,
85/6.46/3.73,
86/5.60/4.23,
87/6.46/4.73,
88/5.60/5.23}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
44/30.00/120.00/0.4/LightPink}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
2/1, 2/5,
3/1, 3/2, 3/4,
4/2, 4/5,
5/38,
6/9, 6/1,
7/6, 7/3,
8/4, 8/36, 8/7,
9/1,
10/9, 10/6,
11/9, 11/10,
12/13, 12/10,
13/14, 13/11,
14/11,
15/14, 15/13,
16/14, 16/15,
17/18, 17/12, 17/15,
18/19, 18/16,
19/16,
20/19, 20/18,
21/19, 21/20,
22/23, 22/17, 22/20,
23/24, 23/21,
24/21,
25/24, 25/23,
26/24, 26/25,
27/28, 27/25,
28/29, 28/26,
29/26,
30/29, 30/28,
31/29, 31/30,
32/33, 32/27, 32/30,
33/34, 33/31,
34/31,
35/39, 35/32, 35/33,
36/5, 36/38,
37/36, 37/40, 37/8,
38/44, 38/40,
39/41, 39/34,
40/44,
41/34,
42/45, 42/35, 42/39,
43/40, 43/46, 43/37,
44/72, 44/46,
45/47, 45/41,
46/72, 46/71,
47/41,
48/47, 48/45,
49/47, 49/48,
50/51, 50/42, 50/48,
51/52, 51/49,
52/49,
53/52, 53/51,
54/52, 54/53,
55/56, 55/53,
56/57, 56/54,
57/54,
58/57, 58/56,
59/57, 59/58,
60/61, 60/55, 60/58,
61/62, 61/59,
62/59,
63/62, 63/61,
64/62, 64/63,
65/66, 65/60, 65/63,
66/67, 66/64,
67/64,
68/67, 68/66,
69/67, 69/68,
70/71, 70/68,
71/72, 71/69,
72/69,
73/7, 73/8,
74/8, 74/43,
75/8, 75/74,
76/73, 76/75,
77/76, 77/78, 77/73,
78/27,
79/76, 79/80, 79/78,
80/42, 80/32,
81/42, 81/80,
82/81, 82/79,
83/84, 83/82, 83/75,
84/74, 84/70,
85/84, 85/70, 85/65,
86/87, 86/88, 86/81, 86/83, 86/82,
87/85, 87/55,
88/87, 88/42, 88/50}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,88}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[Green,very thick] (p-8) -- (p-7);
\draw[Green,very thick] (p-17) -- (p-15);
\draw[Green,very thick] (p-22) -- (p-20);
\draw[Green,very thick] (p-32) -- (p-30);
\draw[Green,very thick] (p-35) -- (p-33);
\draw[Green,very thick] (p-37) -- (p-8);
\draw[Green,very thick] (p-42) -- (p-39);
\draw[Green,very thick] (p-43) -- (p-37);
\draw[Green,very thick] (p-50) -- (p-48);
\draw[Green,very thick] (p-60) -- (p-58);
\draw[Green,very thick] (p-65) -- (p-63);
\draw[Green,very thick] (p-85) -- (p-65);
\draw[Green,very thick] (p-88) -- (p-50);
\draw[Green,very thick] (p-77) -- (p-73);
\draw[Green,very thick] (p-79) -- (p-78);
\draw[Green,very thick] (p-83) -- (p-75);
\draw[Green,very thick] (p-86) -- (p-81);
\draw[Green,very thick] (p-86) -- (p-83);
\draw[Green,very thick] (p-86) -- (p-82);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
44/30.00/120.00/0.4/LightPink}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/210,
2/330,
3/150,
4/30,
5/330,
6/60,
7/210,
8/240,
9/180,
10/60,
11/180,
12/348,
13/30,
14/210,
15/30,
16/150,
17/318,
18/300,
19/180,
20/60,
21/210,
22/48,
23/270,
24/90,
25/30,
26/90,
27/258,
28/300,
29/180,
30/300,
31/150,
32/240,
33/270,
34/180,
35/210,
36/270,
37/180,
38/360,
39/300,
40/90,
41/60,
42/150,
43/60,
44/330,
45/270,
46/180,
47/150,
48/330,
49/120,
50/30,
51/180,
52/360,
53/240,
54/360,
55/93,
56/150,
57/30,
58/210,
59/330,
60/137,
61/180,
62/360,
63/180,
64/30,
65/227,
66/90,
67/30,
68/210,
69/270,
70/330,
71/60,
72/360,
73/90,
74/360,
75/120,
76/60,
77/180,
78/257,
79/123,
80/180,
81/300,
82/210,
83/270,
84/210,
85/90,
86/30,
87/360,
88/120}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
Das hatte ich nicht erwartet. Weitere Beispielgraphen aber gar nicht erst versuchen, die gehen alle nicht. Bis hierher sind das nur ausgewählte Testbeispiele zum Ausprobieren als Demoversion. Es ist nicht immer so, daß die lineare Abhängigkeit zwischen den Winkeln über das gesamte Bewegungsintervall hinweg erhalten bleibt. Allgemein gilt das nur annähernd für kleinste Bewegungsschritte, danach muss man den Graph neu zurechtziehen und die nächste Bewegungsrichtung bestimmen. Oder höhere Ableitungen zur Bestimmung der Bewegung auswerten. Zuguterletzt macht dann die begrenzte Rechengenauigkeit noch einen Strich durch die Rechnung. Hierzu gleich als Beispiel obiger Graph nach zweimal Button neue Eingabe "wenig Winkel"
88 Knoten, 4×Grad 3, 80×Grad 4, 2×Grad 5, 2×Grad 7, 0 Überschneidungen
178 Kanten, minimal 0.99999999999999800160, maximal 1.00000000000001798561
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78);</Bildtext>
%<Ausrichten von="1" nach="2"/>
%<Winkel size="18" color="blue" id="blauerWinkel" value="90"/>
%<Winkel size="18" color="green" id="gruenerWinkel" value="90"/>
%<Winkel size="18" color="orange" id="orangerWinkel" value="89.99999999999994"/>
%<Feinjustieren Anzahl="8,3"/>
%<Rechenweg>
%P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(1,2); L(3,1,2); L(4,3,2); L(5,4,2); M(6,1,2,blauerWinkel); L(9,1,6); L(10,9,6); L(11,9,10); N(7,6,3); M(109,7,3,95.00000000000001); L(73,7,109); Q(8,7,4,ab(109,7,73,"gedreht"),D); M(110,8,4,34.99999999999997); L(37,8,110); M(111,5,2,275.00000000000006); L(38,111,5); Q(36,8,5,ab(110,8,37,"gedreht"),ab(111,5,38,"gedreht")); M(112,37,8,155.00000000000003); L(43,37,112); M(113,38,5,215); L(44,113,38); Q(40,37,38,ab(112,37,43,"gedreht"),ab(113,38,44,"gedreht")); M(114,44,38,275); M(71,114,44,125.00000000000001); M(69,71,114,125); L(116,69,71); Q(115,71,114,ab(116,71,69,"gedreht"),D); Q(72,114,44,ab(115,114,69,71,"gedreht"),D); Q(46,43,44,D,ab(114,44,69,71,72,"gedreht")); M(117,8,4,125.00000000000001); L(75,8,117); Q(74,8,43,ab(117,8,75,"gedreht"),D); M(118,73,7,215); L(77,73,118); Q(76,73,75,ab(118,73,77,"gedreht"),D); M(12,10,6,gruenerWinkel); M(119,11,9,95.00000000000006); L(14,11,119); L(15,14,119); L(16,14,15); Q(13,11,12,ab(119,11,14,15,16,"gedreht"),D); N(17,15,12); M(120,16,14,94.99999999999991); L(19,16,120); L(20,19,120); L(21,19,20); Q(18,16,17,ab(120,16,19,20,21,"gedreht"),D); N(22,20,17); M(121,21,19,95.00000000000014); L(24,21,121); L(25,24,121); L(26,24,25); Q(23,21,22,ab(121,21,24,25,26,"gedreht"),D); M(27,25,23,orangerWinkel); M(122,26,24,95); L(29,26,122); L(30,29,122); L(31,29,30); Q(28,26,27,ab(122,26,29,30,31,"gedreht"),D); N(32,30,27); M(123,31,29,95.00000000000011); L(34,31,123); M(124,32,27,244.99999999999986); L(35,124,32); Q(33,31,32,ab(123,31,34,"gedreht"),ab(124,32,35,"gedreht")); M(125,34,31,154.99999999999974); L(41,34,125); M(126,35,32,215.00000000000034); L(42,126,35); Q(39,34,35,ab(125,34,41,"gedreht"),ab(126,35,42,"gedreht")); M(127,41,34,95.00000000000016); L(47,41,127); L(48,47,127); L(49,47,48); Q(45,41,42,ab(127,41,47,48,49,"gedreht"),D); M(128,42,35,184.9999999999999); L(88,128,42); Q(50,48,42,D,ab(128,42,88,"gedreht")); M(129,49,47,95.0000000000004); L(52,49,129); L(53,52,129); L(54,52,53); Q(51,49,50,ab(129,49,52,53,54,"gedreht"),D); N(78,27,77); N(79,78,76); N(80,32,79); M(130,42,35,35.0000000000003); L(81,42,130); A(80,42,ab(130,42,81,"gedreht")); M(82,81,42,154.99999999999943); L(86,81,82); L(131,86,82); Q(83,81,75,ab(131,81,82,86,"gedreht"),D); A(79,82); M(87,86,81,275.00000000000057); L(132,86,87); A(88,86,ab(132,86,87,"gedreht")); N(55,87,53); M(133,54,52,94.9999999999983); L(57,54,133); L(58,57,133); L(59,57,58); Q(56,54,55,ab(133,54,57,58,59,"gedreht"),D); N(60,58,55); M(134,59,57,95.00000000000199); L(62,59,134); M(135,62,59,124.99999999999986); L(64,62,135); Q(63,62,134,ab(135,62,64,"gedreht"),D); Q(61,59,60,ab(134,59,62,63,64,"gedreht"),D); M(66,64,62,94.99999999999955); L(67,64,66); L(68,67,66); L(136,67,68); A(69,64,ab(136,64,66,67,68,"gedreht")); N(65,63,60); A(65,66); N(70,71,68); M(84,70,68,214.9999999999997); L(137,84,70); Q(85,70,65,ab(137,70,84,"gedreht"),D); A(83,84); A(74,84); A(85,87);
%R(42,80); // oder R(42,81);
%R(79,82);
%R(86,87); // oder R(86,88);
%R(64,66); // oder R(64,67);
%R(65,66);
%R(83,84);
%R(74,84);
%R(85,87);
%</Rechenweg>
%
%<Knopf id="Stopp_alleWinkel" color="LightGrey"/>
%
%<Knopf id="Start_blauerWinkel" color="blue"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#blauerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_blauerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_gruenerWinkel" color="green"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#gruenerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_gruenerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_orangerWinkel" color="orange"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#orangerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_orangerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LimeGreen}{rgb}{0.20,0.80,0.20}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/2.73/0.00,
2/3.73/0.00,
3/3.23/0.87,
4/4.23/0.87,
5/4.73/0.00,
6/2.73/1.00,
7/3.23/1.87,
8/4.23/1.87,
9/1.87/0.50,
10/1.87/1.50,
11/1.00/1.00,
12/2.37/2.37,
13/1.50/1.87,
14/0.50/1.87,
15/1.00/2.73,
16/0.00/2.73,
17/1.87/3.23,
18/0.87/3.23,
19/0.00/3.73,
20/0.87/4.23,
21/0.00/4.73,
22/1.87/4.23,
23/1.00/4.73,
24/0.50/5.60,
25/1.50/5.60,
26/1.00/6.46,
27/2.37/5.10,
28/1.87/5.96,
29/1.87/6.96,
30/2.73/6.46,
31/2.73/7.46,
32/3.23/5.60,
33/3.23/6.60,
34/3.73/7.46,
35/4.10/6.10,
36/4.73/1.00,
37/5.23/1.87,
38/5.60/0.50,
39/4.60/6.96,
40/6.10/1.37,
41/4.60/7.96,
42/5.10/6.10,
43/6.10/2.37,
44/6.60/0.50,
45/5.10/7.10,
46/6.60/1.50,
47/5.60/7.96,
48/6.10/7.10,
49/6.60/7.96,
50/6.10/6.10,
51/6.60/6.96,
52/7.46/7.46,
53/7.46/6.46,
54/8.33/6.96,
55/6.96/5.60,
56/7.83/6.10,
57/8.83/6.10,
58/8.33/5.23,
59/9.33/5.23,
60/7.46/4.73,
61/8.46/4.73,
62/9.33/4.23,
63/8.46/3.73,
64/9.33/3.23,
65/7.46/3.73,
66/8.33/3.23,
67/8.83/2.37,
68/7.83/2.37,
69/8.33/1.50,
70/6.96/2.87,
71/7.46/2.00,
72/7.46/1.00,
73/3.73/2.73,
74/5.10/2.37,
75/4.23/2.87,
76/3.73/3.73,
77/2.87/3.23,
78/2.87/4.23,
79/3.73/4.73,
80/4.23/5.60,
81/5.10/5.10,
82/4.60/4.23,
83/5.10/3.37,
84/5.96/2.87,
85/6.46/3.73,
86/5.60/4.23,
87/6.46/4.73,
88/5.60/5.23}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
1/0.00/90.00/0.4/Blue,
10/330.00/420.00/0.4/Green,
25/240.00/330.00/0.4/Orange}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
1/2,
3/1, 3/2,
4/3, 4/2,
5/4, 5/2,
6/1,
7/6, 7/3,
8/7, 8/4,
9/1, 9/6,
10/9, 10/6,
11/9, 11/10,
12/10,
13/11, 13/12,
14/11, 14/13,
15/14, 15/13,
16/14, 16/15,
17/15, 17/12,
18/16, 18/17,
19/16, 19/18,
20/19, 20/18,
21/19, 21/20,
22/20, 22/17,
23/21, 23/22,
24/21, 24/23,
25/24, 25/23,
26/24, 26/25,
27/25,
28/26, 28/27,
29/26, 29/28,
30/29, 30/28,
31/29, 31/30,
32/30, 32/27,
33/31, 33/32,
34/31, 34/33,
35/33, 35/32,
36/8, 36/5,
37/8, 37/36,
38/36, 38/5,
39/34, 39/35,
40/37, 40/38,
41/34, 41/39,
42/39, 42/35,
43/37, 43/40,
44/40, 44/38,
45/41, 45/42,
46/43, 46/44,
47/41, 47/45,
48/47, 48/45,
49/47, 49/48,
50/48, 50/42,
51/49, 51/50,
52/49, 52/51,
53/52, 53/51,
54/52, 54/53,
55/87, 55/53,
56/54, 56/55,
57/54, 57/56,
58/57, 58/56,
59/57, 59/58,
60/58, 60/55,
61/59, 61/60,
62/59, 62/61,
63/62, 63/61,
64/62, 64/63,
65/63, 65/60, 65/66,
66/64,
67/64, 67/66,
68/67, 68/66,
69/71, 69/67, 69/68,
70/71, 70/68,
71/46,
72/69, 72/71, 72/46, 72/44,
73/7, 73/8,
74/8, 74/43, 74/84,
75/8, 75/74,
76/73, 76/75,
77/73, 77/76,
78/27, 78/77,
79/78, 79/76, 79/82,
80/32, 80/79, 80/42,
81/42, 81/80,
82/81,
83/82, 83/86, 83/75, 83/84,
84/70,
85/70, 85/84, 85/65, 85/87,
86/81, 86/82,
87/86,
88/50, 88/42, 88/86, 88/87}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,88}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[LimeGreen,very thick] (p-42) -- (p-80);
\draw[LimeGreen,very thick] (p-79) -- (p-82);
\draw[LimeGreen,very thick] (p-86) -- (p-87);
\draw[LimeGreen,very thick] (p-64) -- (p-66);
\draw[LimeGreen,very thick] (p-65) -- (p-66);
\draw[LimeGreen,very thick] (p-83) -- (p-84);
\draw[LimeGreen,very thick] (p-74) -- (p-84);
\draw[LimeGreen,very thick] (p-85) -- (p-87);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
1/0.00/90.00/0.4/Blue,
10/330.00/420.00/0.4/Green,
25/240.00/330.00/0.4/Orange}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/210,
2/330,
3/150,
4/30,
5/330,
6/60,
7/210,
8/240,
9/180,
10/60,
11/270,
12/348,
13/30,
14/270,
15/30,
16/240,
17/318,
18/300,
19/240,
20/60,
21/120,
22/48,
23/330,
24/210,
25/30,
26/180,
27/258,
28/300,
29/120,
30/300,
31/60,
32/240,
33/270,
34/30,
35/210,
36/270,
37/30,
38/360,
39/90,
40/90,
41/60,
42/60,
43/60,
44/330,
45/210,
46/180,
47/150,
48/270,
49/120,
50/30,
51/180,
52/360,
53/240,
54/360,
55/92,
56/210,
57/30,
58/210,
59/60,
60/258,
61/120,
62/60,
63/240,
64/30,
65/318,
66/90,
67/270,
68/210,
69/360,
70/330,
71/120,
72/360,
73/90,
74/360,
75/120,
76/60,
77/180,
78/257,
79/123,
80/180,
81/300,
82/210,
83/270,
84/210,
85/90,
86/240,
87/360,
88/120}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/12af99b1405e7a0b819489dfd66e3d12.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78);</Bildtext>
%<Ausrichten von=\"1\" nach=\"2\"/>
%<Winkel size=\"18\" color=\"blue\" id=\"blauerWinkel\" value=\"90\"/>
%<Winkel size=\"18\" color=\"green\" id=\"gruenerWinkel\" value=\"90\"/>
%<Winkel size=\"18\" color=\"orange\" id=\"orangerWinkel\" value=\"89.99999999999994\"/>
%<Feinjustieren Anzahl=\"8,3\"/>
%<Rechenweg>
%P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(1,2); L(3,1,2); L(4,3,2); L(5,4,2); M(6,1,2,blauerWinkel); L(9,1,6); L(10,9,6); L(11,9,10); N(7,6,3); M(109,7,3,95.00000000000001); L(73,7,109); Q(8,7,4,ab(109,7,73,\"gedreht\"),D); M(110,8,4,34.99999999999997); L(37,8,110); M(111,5,2,275.00000000000006); L(38,111,5); Q(36,8,5,ab(110,8,37,\"gedreht\"),ab(111,5,38,\"gedreht\")); M(112,37,8,155.00000000000003); L(43,37,112); M(113,38,5,215); L(44,113,38); Q(40,37,38,ab(112,37,43,\"gedreht\"),ab(113,38,44,\"gedreht\")); M(114,44,38,275); M(71,114,44,125.00000000000001); M(69,71,114,125); L(116,69,71); Q(115,71,114,ab(116,71,69,\"gedreht\"),D); Q(72,114,44,ab(115,114,69,71,\"gedreht\"),D); Q(46,43,44,D,ab(114,44,69,71,72,\"gedreht\")); M(117,8,4,125.00000000000001); L(75,8,117); Q(74,8,43,ab(117,8,75,\"gedreht\"),D); M(118,73,7,215); L(77,73,118); Q(76,73,75,ab(118,73,77,\"gedreht\"),D); M(12,10,6,gruenerWinkel); M(119,11,9,95.00000000000006); L(14,11,119); L(15,14,119); L(16,14,15); Q(13,11,12,ab(119,11,14,15,16,\"gedreht\"),D); N(17,15,12); M(120,16,14,94.99999999999991); L(19,16,120); L(20,19,120); L(21,19,20); Q(18,16,17,ab(120,16,19,20,21,\"gedreht\"),D); N(22,20,17); M(121,21,19,95.00000000000014); L(24,21,121); L(25,24,121); L(26,24,25); Q(23,21,22,ab(121,21,24,25,26,\"gedreht\"),D); M(27,25,23,orangerWinkel); M(122,26,24,95); L(29,26,122); L(30,29,122); L(31,29,30); Q(28,26,27,ab(122,26,29,30,31,\"gedreht\"),D); N(32,30,27); M(123,31,29,95.00000000000011); L(34,31,123); M(124,32,27,244.99999999999986); L(35,124,32); Q(33,31,32,ab(123,31,34,\"gedreht\"),ab(124,32,35,\"gedreht\")); M(125,34,31,154.99999999999974); L(41,34,125); M(126,35,32,215.00000000000034); L(42,126,35); Q(39,34,35,ab(125,34,41,\"gedreht\"),ab(126,35,42,\"gedreht\")); M(127,41,34,95.00000000000016); L(47,41,127); L(48,47,127); L(49,47,48); Q(45,41,42,ab(127,41,47,48,49,\"gedreht\"),D); M(128,42,35,184.9999999999999); L(88,128,42); Q(50,48,42,D,ab(128,42,88,\"gedreht\")); M(129,49,47,95.0000000000004); L(52,49,129); L(53,52,129); L(54,52,53); Q(51,49,50,ab(129,49,52,53,54,\"gedreht\"),D); N(78,27,77); N(79,78,76); N(80,32,79); M(130,42,35,35.0000000000003); L(81,42,130); A(80,42,ab(130,42,81,\"gedreht\")); M(82,81,42,154.99999999999943); L(86,81,82); L(131,86,82); Q(83,81,75,ab(131,81,82,86,\"gedreht\"),D); A(79,82); M(87,86,81,275.00000000000057); L(132,86,87); A(88,86,ab(132,86,87,\"gedreht\")); N(55,87,53); M(133,54,52,94.9999999999983); L(57,54,133); L(58,57,133); L(59,57,58); Q(56,54,55,ab(133,54,57,58,59,\"gedreht\"),D); N(60,58,55); M(134,59,57,95.00000000000199); L(62,59,134); M(135,62,59,124.99999999999986); L(64,62,135); Q(63,62,134,ab(135,62,64,\"gedreht\"),D); Q(61,59,60,ab(134,59,62,63,64,\"gedreht\"),D); M(66,64,62,94.99999999999955); L(67,64,66); L(68,67,66); L(136,67,68); A(69,64,ab(136,64,66,67,68,\"gedreht\")); N(65,63,60); A(65,66); N(70,71,68); M(84,70,68,214.9999999999997); L(137,84,70); Q(85,70,65,ab(137,70,84,\"gedreht\"),D); A(83,84); A(74,84); A(85,87);
%R(42,80); // oder R(42,81);
%R(79,82);
%R(86,87); // oder R(86,88);
%R(64,66); // oder R(64,67);
%R(65,66);
%R(83,84);
%R(74,84);
%R(85,87);
%</Rechenweg>
%
%<Knopf id=\"Stopp_alleWinkel\" color=\"LightGrey\"/>
%
%<Knopf id=\"Start_blauerWinkel\" color=\"blue\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#blauerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_blauerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_gruenerWinkel\" color=\"green\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#gruenerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_gruenerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_orangerWinkel\" color=\"orange\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#orangerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_orangerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LimeGreen}{rgb}{0.20,0.80,0.20}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/2.73/0.00,
2/3.73/0.00,
3/3.23/0.87,
4/4.23/0.87,
5/4.73/0.00,
6/2.73/1.00,
7/3.23/1.87,
8/4.23/1.87,
9/1.87/0.50,
10/1.87/1.50,
11/1.00/1.00,
12/2.37/2.37,
13/1.50/1.87,
14/0.50/1.87,
15/1.00/2.73,
16/0.00/2.73,
17/1.87/3.23,
18/0.87/3.23,
19/0.00/3.73,
20/0.87/4.23,
21/0.00/4.73,
22/1.87/4.23,
23/1.00/4.73,
24/0.50/5.60,
25/1.50/5.60,
26/1.00/6.46,
27/2.37/5.10,
28/1.87/5.96,
29/1.87/6.96,
30/2.73/6.46,
31/2.73/7.46,
32/3.23/5.60,
33/3.23/6.60,
34/3.73/7.46,
35/4.10/6.10,
36/4.73/1.00,
37/5.23/1.87,
38/5.60/0.50,
39/4.60/6.96,
40/6.10/1.37,
41/4.60/7.96,
42/5.10/6.10,
43/6.10/2.37,
44/6.60/0.50,
45/5.10/7.10,
46/6.60/1.50,
47/5.60/7.96,
48/6.10/7.10,
49/6.60/7.96,
50/6.10/6.10,
51/6.60/6.96,
52/7.46/7.46,
53/7.46/6.46,
54/8.33/6.96,
55/6.96/5.60,
56/7.83/6.10,
57/8.83/6.10,
58/8.33/5.23,
59/9.33/5.23,
60/7.46/4.73,
61/8.46/4.73,
62/9.33/4.23,
63/8.46/3.73,
64/9.33/3.23,
65/7.46/3.73,
66/8.33/3.23,
67/8.83/2.37,
68/7.83/2.37,
69/8.33/1.50,
70/6.96/2.87,
71/7.46/2.00,
72/7.46/1.00,
73/3.73/2.73,
74/5.10/2.37,
75/4.23/2.87,
76/3.73/3.73,
77/2.87/3.23,
78/2.87/4.23,
79/3.73/4.73,
80/4.23/5.60,
81/5.10/5.10,
82/4.60/4.23,
83/5.10/3.37,
84/5.96/2.87,
85/6.46/3.73,
86/5.60/4.23,
87/6.46/4.73,
88/5.60/5.23}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
1/0.00/90.00/0.4/Blue,
10/330.00/420.00/0.4/Green,
25/240.00/330.00/0.4/Orange}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
1/2,
3/1, 3/2,
4/3, 4/2,
5/4, 5/2,
6/1,
7/6, 7/3,
8/7, 8/4,
9/1, 9/6,
10/9, 10/6,
11/9, 11/10,
12/10,
13/11, 13/12,
14/11, 14/13,
15/14, 15/13,
16/14, 16/15,
17/15, 17/12,
18/16, 18/17,
19/16, 19/18,
20/19, 20/18,
21/19, 21/20,
22/20, 22/17,
23/21, 23/22,
24/21, 24/23,
25/24, 25/23,
26/24, 26/25,
27/25,
28/26, 28/27,
29/26, 29/28,
30/29, 30/28,
31/29, 31/30,
32/30, 32/27,
33/31, 33/32,
34/31, 34/33,
35/33, 35/32,
36/8, 36/5,
37/8, 37/36,
38/36, 38/5,
39/34, 39/35,
40/37, 40/38,
41/34, 41/39,
42/39, 42/35,
43/37, 43/40,
44/40, 44/38,
45/41, 45/42,
46/43, 46/44,
47/41, 47/45,
48/47, 48/45,
49/47, 49/48,
50/48, 50/42,
51/49, 51/50,
52/49, 52/51,
53/52, 53/51,
54/52, 54/53,
55/87, 55/53,
56/54, 56/55,
57/54, 57/56,
58/57, 58/56,
59/57, 59/58,
60/58, 60/55,
61/59, 61/60,
62/59, 62/61,
63/62, 63/61,
64/62, 64/63,
65/63, 65/60, 65/66,
66/64,
67/64, 67/66,
68/67, 68/66,
69/71, 69/67, 69/68,
70/71, 70/68,
71/46,
72/69, 72/71, 72/46, 72/44,
73/7, 73/8,
74/8, 74/43, 74/84,
75/8, 75/74,
76/73, 76/75,
77/73, 77/76,
78/27, 78/77,
79/78, 79/76, 79/82,
80/32, 80/79, 80/42,
81/42, 81/80,
82/81,
83/82, 83/86, 83/75, 83/84,
84/70,
85/70, 85/84, 85/65, 85/87,
86/81, 86/82,
87/86,
88/50, 88/42, 88/86, 88/87}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,88}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[LimeGreen,very thick] (p-42) -- (p-80);
\draw[LimeGreen,very thick] (p-79) -- (p-82);
\draw[LimeGreen,very thick] (p-86) -- (p-87);
\draw[LimeGreen,very thick] (p-64) -- (p-66);
\draw[LimeGreen,very thick] (p-65) -- (p-66);
\draw[LimeGreen,very thick] (p-83) -- (p-84);
\draw[LimeGreen,very thick] (p-74) -- (p-84);
\draw[LimeGreen,very thick] (p-85) -- (p-87);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
1/0.00/90.00/0.4/Blue,
10/330.00/420.00/0.4/Green,
25/240.00/330.00/0.4/Orange}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/210,
2/330,
3/150,
4/30,
5/330,
6/60,
7/210,
8/240,
9/180,
10/60,
11/270,
12/348,
13/30,
14/270,
15/30,
16/240,
17/318,
18/300,
19/240,
20/60,
21/120,
22/48,
23/330,
24/210,
25/30,
26/180,
27/258,
28/300,
29/120,
30/300,
31/60,
32/240,
33/270,
34/30,
35/210,
36/270,
37/30,
38/360,
39/90,
40/90,
41/60,
42/60,
43/60,
44/330,
45/210,
46/180,
47/150,
48/270,
49/120,
50/30,
51/180,
52/360,
53/240,
54/360,
55/92,
56/210,
57/30,
58/210,
59/60,
60/258,
61/120,
62/60,
63/240,
64/30,
65/318,
66/90,
67/270,
68/210,
69/360,
70/330,
71/120,
72/360,
73/90,
74/360,
75/120,
76/60,
77/180,
78/257,
79/123,
80/180,
81/300,
82/210,
83/270,
84/210,
85/90,
86/240,
87/360,
88/120}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
dann Button "beweglich?" - und weg sind die Winkel.
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78);</Bildtext>
%<Ausrichten von="1" nach="2"/>
%<Feinjustieren Anzahl="8,3"/>
%<Rechenweg>
%blauerWinkel=90;
%gruenerWinkel=90;
%orangerWinkel=89.99999999999994;
%P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(1,2); L(3,1,2); L(4,3,2); L(5,4,2); M(6,1,2,blauerWinkel); L(9,1,6); L(10,9,6); L(11,9,10); N(7,6,3); M(109,7,3,95.00000000000001); L(73,7,109); Q(8,7,4,ab(109,7,73,"gedreht"),D); M(110,8,4,34.99999999999997); L(37,8,110); M(111,5,2,275.00000000000006); L(38,111,5); Q(36,8,5,ab(110,8,37,"gedreht"),ab(111,5,38,"gedreht")); M(112,37,8,155.00000000000003); L(43,37,112); M(113,38,5,215); L(44,113,38); Q(40,37,38,ab(112,37,43,"gedreht"),ab(113,38,44,"gedreht")); M(114,44,38,275); M(71,114,44,125.00000000000001); M(69,71,114,125); L(116,69,71); Q(115,71,114,ab(116,71,69,"gedreht"),D); Q(72,114,44,ab(115,114,69,71,"gedreht"),D); Q(46,43,44,D,ab(114,44,69,71,72,"gedreht")); M(117,8,4,125.00000000000001); L(75,8,117); Q(74,8,43,ab(117,8,75,"gedreht"),D); M(118,73,7,215); L(77,73,118); Q(76,73,75,ab(118,73,77,"gedreht"),D); M(12,10,6,gruenerWinkel); M(119,11,9,95.00000000000006); L(14,11,119); L(15,14,119); L(16,14,15); Q(13,11,12,ab(119,11,14,15,16,"gedreht"),D); N(17,15,12); M(120,16,14,94.99999999999991); L(19,16,120); L(20,19,120); L(21,19,20); Q(18,16,17,ab(120,16,19,20,21,"gedreht"),D); N(22,20,17); M(121,21,19,95.00000000000014); L(24,21,121); L(25,24,121); L(26,24,25); Q(23,21,22,ab(121,21,24,25,26,"gedreht"),D); M(27,25,23,orangerWinkel); M(122,26,24,95); L(29,26,122); L(30,29,122); L(31,29,30); Q(28,26,27,ab(122,26,29,30,31,"gedreht"),D); N(32,30,27); M(123,31,29,95.00000000000011); L(34,31,123); M(124,32,27,244.99999999999986); L(35,124,32); Q(33,31,32,ab(123,31,34,"gedreht"),ab(124,32,35,"gedreht")); M(125,34,31,154.99999999999974); L(41,34,125); M(126,35,32,215.00000000000034); L(42,126,35); Q(39,34,35,ab(125,34,41,"gedreht"),ab(126,35,42,"gedreht")); M(127,41,34,95.00000000000016); L(47,41,127); L(48,47,127); L(49,47,48); Q(45,41,42,ab(127,41,47,48,49,"gedreht"),D); M(128,42,35,184.9999999999999); L(88,128,42); Q(50,48,42,D,ab(128,42,88,"gedreht")); M(129,49,47,95.0000000000004); L(52,49,129); L(53,52,129); L(54,52,53); Q(51,49,50,ab(129,49,52,53,54,"gedreht"),D); N(78,27,77); N(79,78,76); N(80,32,79); M(130,42,35,35.0000000000003); L(81,42,130); A(80,42,ab(130,42,81,"gedreht")); M(82,81,42,154.99999999999943); L(86,81,82); L(131,86,82); Q(83,81,75,ab(131,81,82,86,"gedreht"),D); A(79,82); M(87,86,81,275.00000000000057); L(132,86,87); A(88,86,ab(132,86,87,"gedreht")); N(55,87,53); M(133,54,52,94.9999999999983); L(57,54,133); L(58,57,133); L(59,57,58); Q(56,54,55,ab(133,54,57,58,59,"gedreht"),D); N(60,58,55); M(134,59,57,95.00000000000199); L(62,59,134); M(135,62,59,124.99999999999986); L(64,62,135); Q(63,62,134,ab(135,62,64,"gedreht"),D); Q(61,59,60,ab(134,59,62,63,64,"gedreht"),D); M(66,64,62,94.99999999999955); L(67,64,66); L(68,67,66); L(136,67,68); A(69,64,ab(136,64,66,67,68,"gedreht")); N(65,63,60); A(65,66); N(70,71,68); M(84,70,68,214.9999999999997); L(137,84,70); Q(85,70,65,ab(137,70,84,"gedreht"),D); A(83,84); A(74,84); A(85,87);
%R(42,80); // oder R(42,81);
%R(79,82);
%R(86,87); // oder R(86,88);
%R(64,66); // oder R(64,67);
%R(65,66);
%R(83,84);
%R(74,84);
%R(85,87);
%</Rechenweg>
%
%<Knopf id="Stopp_alleWinkel" color="LightGrey"/>
%
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{LimeGreen}{rgb}{0.20,0.80,0.20}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/2.73205080756887808136/0.00000000000000000000,
2/3.73205080756887808136/0.00000000000000000000,
3/3.23205080756887808136/0.86602540378443859659,
4/4.23205080756887852544/0.86602540378443859659,
5/4.73205080756887852544/0.00000000000000000000,
6/2.73205080756887808136/1.00000000000000000000,
7/3.23205080756887808136/1.86602540378443837454,
8/4.23205080756887852544/1.86602540378443881863,
9/1.86602540378443970681/0.50000000000000011102,
10/1.86602540378443970681/1.50000000000000000000,
11/1.00000000000000111022/1.00000000000000022204,
12/2.36602540378443970681/2.36602540378443837454,
13/1.50000000000000066613/1.86602540378443926272,
14/0.50000000000000055511/1.86602540378443837454,
15/1.00000000000000000000/2.73205080756887763727,
16/0.00000000000000000000/2.73205080756887674909,
17/1.86602540378443904068/3.23205080756887674909,
18/0.86602540378443904068/3.23205080756887630500,
19/0.00000000000000113687/3.73205080756887674909,
20/0.86602540378443959579/4.23205080756887674909,
21/0.00000000000000170530/4.73205080756887674909,
22/1.86602540378443970681/4.23205080756887674909,
23/1.00000000000000177636/4.73205080756887852544,
24/0.49999999999999972244/5.59807621135331512363,
25/1.49999999999999911182/5.59807621135331867634,
26/0.99999999999999633626/6.46410161513775349817,
27/2.36602540378443837454/5.09807621135331956452,
28/1.86602540378443615410/5.96410161513775616271,
29/1.86602540378443393365/6.96410161513775616271,
30/2.73205080756887452864/6.46410161513775705089,
31/2.73205080756887142002/7.46410161513775971542,
32/3.23205080756887674909/5.59807621135331956452,
33/3.23205080756886786730/6.59807621135331956452,
34/3.73205080756887053184/7.46410161513775882725,
35/4.09807621135331157092/6.09807621135332755813,
36/4.73205080756887852544/1.00000000000000000000,
37/5.23205080756887852544/1.86602540378443881863,
38/5.59807621135331689999/0.50000000000000000000,
39/4.59807621135331334727/6.96410161513776504449,
40/6.09807621135331601181/1.36602540378443837454,
41/4.59807621135330535367/7.96410161513776682085,
42/5.09807621135331157092/6.09807621135332489359,
43/6.09807621135331689999/2.36602540378443926272,
44/6.59807621135331601181/0.50000000000000011102,
45/5.09807621135330091278/7.09807621135332489359,
46/6.59807621135331601181/1.50000000000000000000,
47/5.59807621135330535367/7.96410161513776060360,
48/6.09807621135330002460/7.09807621135332045270,
49/6.59807621135330446549/7.96410161513775527453,
50/6.09807621135331157092/6.09807621135332045270,
51/6.59807621135331867634/6.96410161513775527453,
52/7.46410161513775083364/7.46410161513776682085,
53/7.46410161513776415632/6.46410161513776682085,
54/8.33012701892219631361/6.96410161513777925535,
55/6.96410161513775705089/5.59807621135332933449,
56/7.83012701892218743183/6.09807621135334532170,
57/8.83012701892218920818/6.09807621135333377538,
58/8.33012701892217499733/5.23205080756890072990,
59/9.33012701892217677369/5.23205080756888740723,
60/7.46410161513774639275/4.73205080756888474269,
61/8.46410161513774639275/4.73205080756887142002,
62/9.33012701892219098454/4.23205080756888740723,
63/8.46410161513776237996/3.73205080756887186411,
64/9.33012701892221052447/3.23205080756888740723,
65/7.46410161513776326814/3.73205080756888429860,
66/8.33012701892220164268/3.23205080756887541682,
67/8.83012701892219808997/2.36602540378443526592,
68/7.83012701892219720179/2.36602540378443926272,
69/8.33012701892219453725/1.49999999999999866773,
70/6.96410161513775971542/2.86602540378444015090,
71/7.46410161513775527453/1.99999999999999911182,
72/7.46410161513775527453/0.99999999999999966693,
73/3.73205080756887808136/2.73205080756887763727,
74/5.09807621135331689999/2.36602540378443837454,
75/4.23205080756887852544/2.86602540378443926272,
76/3.73205080756887941362/3.73205080756887763727,
77/2.86602540378443970681/3.23205080756887852544,
78/2.86602540378443526592/4.23205080756887941362,
79/3.73205080756887452864/4.73205080756887763727,
80/4.23205080756887674909/5.59807621135331512363,
81/5.09807621135332134088/5.09807621135332311724,
82/4.59807621135331689999/4.23205080756888740723,
83/5.09807621135331245910/3.36602540378444681224,
84/5.96410161513775882725/2.86602540378444547997,
85/6.46410161513776326814/3.73205080756888163407,
86/5.59807621135331601181/4.23205080756888296634,
87/6.46410161513775083364/4.73205080756889273630,
88/5.59807621135330713003/5.23205080756888474269}
\coordinate (p-\i) at (\x,\y);
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
1/2,
3/1, 3/2,
4/3, 4/2,
5/4, 5/2,
6/1,
7/6, 7/3,
8/7, 8/4,
9/1, 9/6,
10/9, 10/6,
11/9, 11/10,
12/10,
13/11, 13/12,
14/11, 14/13,
15/14, 15/13,
16/14, 16/15,
17/15, 17/12,
18/16, 18/17,
19/16, 19/18,
20/19, 20/18,
21/19, 21/20,
22/20, 22/17,
23/21, 23/22,
24/21, 24/23,
25/24, 25/23,
26/24, 26/25,
27/25,
28/26, 28/27,
29/26, 29/28,
30/29, 30/28,
31/29, 31/30,
32/30, 32/27,
33/31, 33/32,
34/31, 34/33,
35/33, 35/32,
36/8, 36/5,
37/8, 37/36,
38/36, 38/5,
39/34, 39/35,
40/37, 40/38,
41/34, 41/39,
42/39, 42/35,
43/37, 43/40,
44/40, 44/38,
45/41, 45/42,
46/43, 46/44,
47/41, 47/45,
48/47, 48/45,
49/47, 49/48,
50/48, 50/42,
51/49, 51/50,
52/49, 52/51,
53/52, 53/51,
54/52, 54/53,
55/87, 55/53,
56/54, 56/55,
57/54, 57/56,
58/57, 58/56,
59/57, 59/58,
60/58, 60/55,
61/59, 61/60,
62/59, 62/61,
63/62, 63/61,
64/62, 64/63,
65/63, 65/60, 65/66,
66/64,
67/64, 67/66,
68/67, 68/66,
69/71, 69/67, 69/68,
70/71, 70/68,
71/46,
72/69, 72/71, 72/46, 72/44,
73/7, 73/8,
74/8, 74/43, 74/84,
75/8, 75/74,
76/73, 76/75,
77/73, 77/76,
78/27, 78/77,
79/78, 79/76, 79/82,
80/32, 80/79, 80/42,
81/42, 81/80,
82/81,
83/82, 83/86, 83/75, 83/84,
84/70,
85/70, 85/84, 85/65, 85/87,
86/81, 86/82,
87/86,
88/50, 88/42, 88/86, 88/87}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,88}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[LimeGreen,very thick] (p-42) -- (p-80);
\draw[LimeGreen,very thick] (p-79) -- (p-82);
\draw[LimeGreen,very thick] (p-86) -- (p-87);
\draw[LimeGreen,very thick] (p-64) -- (p-66);
\draw[LimeGreen,very thick] (p-65) -- (p-66);
\draw[LimeGreen,very thick] (p-83) -- (p-84);
\draw[LimeGreen,very thick] (p-74) -- (p-84);
\draw[LimeGreen,very thick] (p-85) -- (p-87);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/210,
2/330,
3/150,
4/30,
5/330,
6/60,
7/210,
8/240,
9/180,
10/60,
11/270,
12/348,
13/30,
14/270,
15/30,
16/240,
17/318,
18/300,
19/240,
20/60,
21/120,
22/48,
23/330,
24/210,
25/30,
26/180,
27/258,
28/300,
29/120,
30/300,
31/60,
32/240,
33/270,
34/30,
35/210,
36/270,
37/30,
38/360,
39/90,
40/90,
41/60,
42/60,
43/60,
44/330,
45/210,
46/180,
47/150,
48/270,
49/120,
50/30,
51/180,
52/360,
53/240,
54/360,
55/92,
56/210,
57/30,
58/210,
59/60,
60/258,
61/120,
62/60,
63/240,
64/30,
65/318,
66/90,
67/270,
68/210,
69/360,
70/330,
71/120,
72/360,
73/90,
74/360,
75/120,
76/60,
77/180,
78/257,
79/123,
80/180,
81/300,
82/210,
83/270,
84/210,
85/90,
86/240,
87/360,
88/120}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/8ed9d1314fe660b94155c9fc3d44e131.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78);</Bildtext>
%<Ausrichten von=\"1\" nach=\"2\"/>
%<Feinjustieren Anzahl=\"8,3\"/>
%<Rechenweg>
%blauerWinkel=90;
%gruenerWinkel=90;
%orangerWinkel=89.99999999999994;
%P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(1,2); L(3,1,2); L(4,3,2); L(5,4,2); M(6,1,2,blauerWinkel); L(9,1,6); L(10,9,6); L(11,9,10); N(7,6,3); M(109,7,3,95.00000000000001); L(73,7,109); Q(8,7,4,ab(109,7,73,\"gedreht\"),D); M(110,8,4,34.99999999999997); L(37,8,110); M(111,5,2,275.00000000000006); L(38,111,5); Q(36,8,5,ab(110,8,37,\"gedreht\"),ab(111,5,38,\"gedreht\")); M(112,37,8,155.00000000000003); L(43,37,112); M(113,38,5,215); L(44,113,38); Q(40,37,38,ab(112,37,43,\"gedreht\"),ab(113,38,44,\"gedreht\")); M(114,44,38,275); M(71,114,44,125.00000000000001); M(69,71,114,125); L(116,69,71); Q(115,71,114,ab(116,71,69,\"gedreht\"),D); Q(72,114,44,ab(115,114,69,71,\"gedreht\"),D); Q(46,43,44,D,ab(114,44,69,71,72,\"gedreht\")); M(117,8,4,125.00000000000001); L(75,8,117); Q(74,8,43,ab(117,8,75,\"gedreht\"),D); M(118,73,7,215); L(77,73,118); Q(76,73,75,ab(118,73,77,\"gedreht\"),D); M(12,10,6,gruenerWinkel); M(119,11,9,95.00000000000006); L(14,11,119); L(15,14,119); L(16,14,15); Q(13,11,12,ab(119,11,14,15,16,\"gedreht\"),D); N(17,15,12); M(120,16,14,94.99999999999991); L(19,16,120); L(20,19,120); L(21,19,20); Q(18,16,17,ab(120,16,19,20,21,\"gedreht\"),D); N(22,20,17); M(121,21,19,95.00000000000014); L(24,21,121); L(25,24,121); L(26,24,25); Q(23,21,22,ab(121,21,24,25,26,\"gedreht\"),D); M(27,25,23,orangerWinkel); M(122,26,24,95); L(29,26,122); L(30,29,122); L(31,29,30); Q(28,26,27,ab(122,26,29,30,31,\"gedreht\"),D); N(32,30,27); M(123,31,29,95.00000000000011); L(34,31,123); M(124,32,27,244.99999999999986); L(35,124,32); Q(33,31,32,ab(123,31,34,\"gedreht\"),ab(124,32,35,\"gedreht\")); M(125,34,31,154.99999999999974); L(41,34,125); M(126,35,32,215.00000000000034); L(42,126,35); Q(39,34,35,ab(125,34,41,\"gedreht\"),ab(126,35,42,\"gedreht\")); M(127,41,34,95.00000000000016); L(47,41,127); L(48,47,127); L(49,47,48); Q(45,41,42,ab(127,41,47,48,49,\"gedreht\"),D); M(128,42,35,184.9999999999999); L(88,128,42); Q(50,48,42,D,ab(128,42,88,\"gedreht\")); M(129,49,47,95.0000000000004); L(52,49,129); L(53,52,129); L(54,52,53); Q(51,49,50,ab(129,49,52,53,54,\"gedreht\"),D); N(78,27,77); N(79,78,76); N(80,32,79); M(130,42,35,35.0000000000003); L(81,42,130); A(80,42,ab(130,42,81,\"gedreht\")); M(82,81,42,154.99999999999943); L(86,81,82); L(131,86,82); Q(83,81,75,ab(131,81,82,86,\"gedreht\"),D); A(79,82); M(87,86,81,275.00000000000057); L(132,86,87); A(88,86,ab(132,86,87,\"gedreht\")); N(55,87,53); M(133,54,52,94.9999999999983); L(57,54,133); L(58,57,133); L(59,57,58); Q(56,54,55,ab(133,54,57,58,59,\"gedreht\"),D); N(60,58,55); M(134,59,57,95.00000000000199); L(62,59,134); M(135,62,59,124.99999999999986); L(64,62,135); Q(63,62,134,ab(135,62,64,\"gedreht\"),D); Q(61,59,60,ab(134,59,62,63,64,\"gedreht\"),D); M(66,64,62,94.99999999999955); L(67,64,66); L(68,67,66); L(136,67,68); A(69,64,ab(136,64,66,67,68,\"gedreht\")); N(65,63,60); A(65,66); N(70,71,68); M(84,70,68,214.9999999999997); L(137,84,70); Q(85,70,65,ab(137,70,84,\"gedreht\"),D); A(83,84); A(74,84); A(85,87);
%R(42,80); // oder R(42,81);
%R(79,82);
%R(86,87); // oder R(86,88);
%R(64,66); // oder R(64,67);
%R(65,66);
%R(83,84);
%R(74,84);
%R(85,87);
%</Rechenweg>
%
%<Knopf id=\"Stopp_alleWinkel\" color=\"LightGrey\"/>
%
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{LimeGreen}{rgb}{0.20,0.80,0.20}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/2.73205080756887808136/0.00000000000000000000,
2/3.73205080756887808136/0.00000000000000000000,
3/3.23205080756887808136/0.86602540378443859659,
4/4.23205080756887852544/0.86602540378443859659,
5/4.73205080756887852544/0.00000000000000000000,
6/2.73205080756887808136/1.00000000000000000000,
7/3.23205080756887808136/1.86602540378443837454,
8/4.23205080756887852544/1.86602540378443881863,
9/1.86602540378443970681/0.50000000000000011102,
10/1.86602540378443970681/1.50000000000000000000,
11/1.00000000000000111022/1.00000000000000022204,
12/2.36602540378443970681/2.36602540378443837454,
13/1.50000000000000066613/1.86602540378443926272,
14/0.50000000000000055511/1.86602540378443837454,
15/1.00000000000000000000/2.73205080756887763727,
16/0.00000000000000000000/2.73205080756887674909,
17/1.86602540378443904068/3.23205080756887674909,
18/0.86602540378443904068/3.23205080756887630500,
19/0.00000000000000113687/3.73205080756887674909,
20/0.86602540378443959579/4.23205080756887674909,
21/0.00000000000000170530/4.73205080756887674909,
22/1.86602540378443970681/4.23205080756887674909,
23/1.00000000000000177636/4.73205080756887852544,
24/0.49999999999999972244/5.59807621135331512363,
25/1.49999999999999911182/5.59807621135331867634,
26/0.99999999999999633626/6.46410161513775349817,
27/2.36602540378443837454/5.09807621135331956452,
28/1.86602540378443615410/5.96410161513775616271,
29/1.86602540378443393365/6.96410161513775616271,
30/2.73205080756887452864/6.46410161513775705089,
31/2.73205080756887142002/7.46410161513775971542,
32/3.23205080756887674909/5.59807621135331956452,
33/3.23205080756886786730/6.59807621135331956452,
34/3.73205080756887053184/7.46410161513775882725,
35/4.09807621135331157092/6.09807621135332755813,
36/4.73205080756887852544/1.00000000000000000000,
37/5.23205080756887852544/1.86602540378443881863,
38/5.59807621135331689999/0.50000000000000000000,
39/4.59807621135331334727/6.96410161513776504449,
40/6.09807621135331601181/1.36602540378443837454,
41/4.59807621135330535367/7.96410161513776682085,
42/5.09807621135331157092/6.09807621135332489359,
43/6.09807621135331689999/2.36602540378443926272,
44/6.59807621135331601181/0.50000000000000011102,
45/5.09807621135330091278/7.09807621135332489359,
46/6.59807621135331601181/1.50000000000000000000,
47/5.59807621135330535367/7.96410161513776060360,
48/6.09807621135330002460/7.09807621135332045270,
49/6.59807621135330446549/7.96410161513775527453,
50/6.09807621135331157092/6.09807621135332045270,
51/6.59807621135331867634/6.96410161513775527453,
52/7.46410161513775083364/7.46410161513776682085,
53/7.46410161513776415632/6.46410161513776682085,
54/8.33012701892219631361/6.96410161513777925535,
55/6.96410161513775705089/5.59807621135332933449,
56/7.83012701892218743183/6.09807621135334532170,
57/8.83012701892218920818/6.09807621135333377538,
58/8.33012701892217499733/5.23205080756890072990,
59/9.33012701892217677369/5.23205080756888740723,
60/7.46410161513774639275/4.73205080756888474269,
61/8.46410161513774639275/4.73205080756887142002,
62/9.33012701892219098454/4.23205080756888740723,
63/8.46410161513776237996/3.73205080756887186411,
64/9.33012701892221052447/3.23205080756888740723,
65/7.46410161513776326814/3.73205080756888429860,
66/8.33012701892220164268/3.23205080756887541682,
67/8.83012701892219808997/2.36602540378443526592,
68/7.83012701892219720179/2.36602540378443926272,
69/8.33012701892219453725/1.49999999999999866773,
70/6.96410161513775971542/2.86602540378444015090,
71/7.46410161513775527453/1.99999999999999911182,
72/7.46410161513775527453/0.99999999999999966693,
73/3.73205080756887808136/2.73205080756887763727,
74/5.09807621135331689999/2.36602540378443837454,
75/4.23205080756887852544/2.86602540378443926272,
76/3.73205080756887941362/3.73205080756887763727,
77/2.86602540378443970681/3.23205080756887852544,
78/2.86602540378443526592/4.23205080756887941362,
79/3.73205080756887452864/4.73205080756887763727,
80/4.23205080756887674909/5.59807621135331512363,
81/5.09807621135332134088/5.09807621135332311724,
82/4.59807621135331689999/4.23205080756888740723,
83/5.09807621135331245910/3.36602540378444681224,
84/5.96410161513775882725/2.86602540378444547997,
85/6.46410161513776326814/3.73205080756888163407,
86/5.59807621135331601181/4.23205080756888296634,
87/6.46410161513775083364/4.73205080756889273630,
88/5.59807621135330713003/5.23205080756888474269}
\coordinate (p-\i) at (\x,\y);
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
1/2,
3/1, 3/2,
4/3, 4/2,
5/4, 5/2,
6/1,
7/6, 7/3,
8/7, 8/4,
9/1, 9/6,
10/9, 10/6,
11/9, 11/10,
12/10,
13/11, 13/12,
14/11, 14/13,
15/14, 15/13,
16/14, 16/15,
17/15, 17/12,
18/16, 18/17,
19/16, 19/18,
20/19, 20/18,
21/19, 21/20,
22/20, 22/17,
23/21, 23/22,
24/21, 24/23,
25/24, 25/23,
26/24, 26/25,
27/25,
28/26, 28/27,
29/26, 29/28,
30/29, 30/28,
31/29, 31/30,
32/30, 32/27,
33/31, 33/32,
34/31, 34/33,
35/33, 35/32,
36/8, 36/5,
37/8, 37/36,
38/36, 38/5,
39/34, 39/35,
40/37, 40/38,
41/34, 41/39,
42/39, 42/35,
43/37, 43/40,
44/40, 44/38,
45/41, 45/42,
46/43, 46/44,
47/41, 47/45,
48/47, 48/45,
49/47, 49/48,
50/48, 50/42,
51/49, 51/50,
52/49, 52/51,
53/52, 53/51,
54/52, 54/53,
55/87, 55/53,
56/54, 56/55,
57/54, 57/56,
58/57, 58/56,
59/57, 59/58,
60/58, 60/55,
61/59, 61/60,
62/59, 62/61,
63/62, 63/61,
64/62, 64/63,
65/63, 65/60, 65/66,
66/64,
67/64, 67/66,
68/67, 68/66,
69/71, 69/67, 69/68,
70/71, 70/68,
71/46,
72/69, 72/71, 72/46, 72/44,
73/7, 73/8,
74/8, 74/43, 74/84,
75/8, 75/74,
76/73, 76/75,
77/73, 77/76,
78/27, 78/77,
79/78, 79/76, 79/82,
80/32, 80/79, 80/42,
81/42, 81/80,
82/81,
83/82, 83/86, 83/75, 83/84,
84/70,
85/70, 85/84, 85/65, 85/87,
86/81, 86/82,
87/86,
88/50, 88/42, 88/86, 88/87}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,88}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[LimeGreen,very thick] (p-42) -- (p-80);
\draw[LimeGreen,very thick] (p-79) -- (p-82);
\draw[LimeGreen,very thick] (p-86) -- (p-87);
\draw[LimeGreen,very thick] (p-64) -- (p-66);
\draw[LimeGreen,very thick] (p-65) -- (p-66);
\draw[LimeGreen,very thick] (p-83) -- (p-84);
\draw[LimeGreen,very thick] (p-74) -- (p-84);
\draw[LimeGreen,very thick] (p-85) -- (p-87);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/210,
2/330,
3/150,
4/30,
5/330,
6/60,
7/210,
8/240,
9/180,
10/60,
11/270,
12/348,
13/30,
14/270,
15/30,
16/240,
17/318,
18/300,
19/240,
20/60,
21/120,
22/48,
23/330,
24/210,
25/30,
26/180,
27/258,
28/300,
29/120,
30/300,
31/60,
32/240,
33/270,
34/30,
35/210,
36/270,
37/30,
38/360,
39/90,
40/90,
41/60,
42/60,
43/60,
44/330,
45/210,
46/180,
47/150,
48/270,
49/120,
50/30,
51/180,
52/360,
53/240,
54/360,
55/92,
56/210,
57/30,
58/210,
59/60,
60/258,
61/120,
62/60,
63/240,
64/30,
65/318,
66/90,
67/270,
68/210,
69/360,
70/330,
71/120,
72/360,
73/90,
74/360,
75/120,
76/60,
77/180,
78/257,
79/123,
80/180,
81/300,
82/210,
83/270,
84/210,
85/90,
86/240,
87/360,
88/120}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
Soll heißen, das Streichholzprogramm hält den Graph für starr, was aber nicht stimmt. Aus irgendeinem Grund kommt bei nochmaligem Button neue Eingabe "wenig Winkel" eine leicht geänderte Eingabereihenfolge heraus, was ja erlaubt ist. Jedoch in der zugehörigen Ableitungsmatrix
[-1.7453229972375084e-9, -3.760648903394781e-9, -2.0153387847443582e-9],
[-2.908885798902361e-9, -2.2370962859952215e-9, 6.717787437438005e-10],
[-5.817710757582972e-10, -1.7573775767942834e-9, -1.1756151607755783e-9],
[ 0.000027487164666828434, 0.000017865575814846046,-3.781552848636238e-9],
[-0.000023807840509260103,-0.000015478709333827112,-5.038305328497472e-10],
[-0.00001587414215609151, -0.00001032160139780025, -2.0153323454508154e-9],
[ 0.00003968170818802186, 0.00002579868326224588, -7.557414694048248e-10],
[-0.000031752590419209525,-0.000020649053289911734,-4.5345052157586e-9] |
ist es beim besten Willen nicht möglich, die erwartete lineare Abhängigkeit erste minus zweite plus dritte Spalte gleich Null herauszulesen. Die Matrix genauer annähern mit kleineren Winkeländerungen bringt auch keine wesentliche Verbesserung. Das kann nur an einer ungünstigen Eingabevariante des Graphen liegen und man würde bei einem unbekannten Graph zu Recht erstmal "unbeweglich" annehmen. So gesehen ist der Button neue Eingabe "Rahmen zuerst" mit den vielen einzustellenden Winkeln vielleicht doch nicht so verkehrt, weil vom Rand ausgehend die Berechnung der inneren Kanten in relativ wenig Schritten erfolgt.
|
Profil
Quote
Link |
StefanVogel
Senior
Dabei seit: 26.11.2005
Mitteilungen: 3446
Aus: Raun
| Beitrag No.1901, eingetragen 2020-02-08 07:49
|
Nächster Graph #1894-1 nächste Programmversion Streichholzgraph-1898.htm mit Testbutton "Newtonpolynom(10)". Der Graph ist bereits als Startbild eingestellt (Graph #1894-1 markieren, ins große Eingabefenster kopieren und Button "neu zeichnen" geht auch).
Anschließend Button neue Eingabe "Rahmen zuerst" gefolgt von Button "beweglich?" ergibt
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1894-1</Bildtext>
%<Ausrichten von="1" nach="2"/>
%<Winkel size="18" color="LightCyan" id="neunterWinkel" value="104.47751218593004"/>
%<Feinjustieren Anzahl="8,9"/>
%<Rechenweg>
%blauerWinkel=148.95502437185988+(0.1410406669571719)*(neunterWinkel-(104.47751218593004));
%gruenerWinkel=135.52248781407008+(-0.6307535182062247)*(neunterWinkel-(104.47751218593004));
%orangerWinkel=104.47751218592992+(1.0000032572318647)*(neunterWinkel-(104.47751218593004));
%vierterWinkel=75.52248781407012+(-0.6307527345561197)*(neunterWinkel-(104.47751218593004));
%fuenfterWinkel=88.95502437185985+(0.14104184543139073)*(neunterWinkel-(104.47751218593004));
%sechsterWinkel=106.56746344221015+(-0.02057818663278938)*(neunterWinkel-(104.47751218593004));
%siebenterWinkel=148.95502437185982+(0.14103841595938466)*(neunterWinkel-(104.47751218593004));
%achterWinkel=135.52248781406996+(-0.6307501277441359)*(neunterWinkel-(104.47751218593004));
%P[5]=[81.1989530225137,-23.620797303099177]; P[2]=[31.54207889274424,-17.773160886543337]; D=ab(5,2); A(2,5); N(4,2,5); N(3,2,4); N(1,2,3); M(8,1,2,blauerWinkel); N(7,8,1); N(9,8,7); N(10,8,9); M(16,10,8,gruenerWinkel); N(15,16,10); N(17,16,15); N(18,16,17); M(37,18,16,orangerWinkel); N(36,18,37); N(35,36,37); N(31,36,35); M(30,31,36,vierterWinkel); N(29,31,30); N(28,29,30); N(22,29,28); M(24,22,29,fuenfterWinkel); N(23,22,24); N(25,23,24); N(26,23,25); M(43,26,23,sechsterWinkel); N(41,26,43); N(42,41,43); N(40,41,42); M(46,40,41,siebenterWinkel); N(45,46,40); N(47,46,45); N(48,46,47); M(53,48,46,achterWinkel); N(52,53,48); N(54,53,52); N(55,53,54); M(72,55,53,neunterWinkel); N(71,55,72); N(70,71,72); N(67,71,70); Q(59,67,5,2*D,2*D); A(59,67); A(59,5); H(60,5,59,2); A(60,5); L(62,5,60); H(65,67,59,2); A(65,67); L(66,65,67); A(65,59); L(64,59,65); A(64,66); A(60,59); L(61,60,59); A(62,61); N(6,3,4); N(11,7,6); N(20,37,17); N(27,25,24); N(32,27,28); N(38,35,20); N(44,42,43); N(49,45,44); N(57,72,54); N(63,62,61); N(68,63,64); N(73,70,57); N(19,20,15); N(56,57,52); N(12,11,6); N(21,20,19); N(33,27,32); N(39,38,20); N(50,49,44); N(58,57,56); N(69,63,68); N(74,73,57); N(13,69,12); N(14,39,21); N(34,33,50); N(51,74,58);
%A(14,12); R(14,12,"green");
%A(14,13); R(14,13,"green");
%A(14,33); R(14,33,"green");
%A(34,14); R(34,14,"green");
%A(51,13); R(51,13,"green");
%A(51,50); R(51,50,"green");
%A(51,34); R(51,34,"green");
%A(51,69); R(51,69,"green");
%</Rechenweg>
%
%<Knopf id="Stopp_alleWinkel" color="LightGrey"/>
%
%<Knopf id="Start_neunterWinkel" color="LightCyan"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#neunterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_neunterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LightCyan}{rgb}{0.88,1.00,1.00}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.85122958682191840474/0.23390545666223369614,
2/2.84436706941730799159/0.11695272833111684807,
3/2.44908236189626027368/1.03551138187480851194,
4/3.44221984449164963848/0.91855865354369181652,
5/3.83750455201269735639/0.00000000000000000000,
6/3.04693513697060236467/1.83711730708738363305,
7/1.98627496519078117210/1.22474487139158894067,
8/1.06066017177982319097/0.84627789235802786116,
9/1.19570555014868573629/1.83711730708738318896,
10/0.27009075673772781068/1.45865032805382210945,
11/2.12132034355964416150/2.21558428612094360233,
12/2.91188975860173870913/2.82795672181673873880,
13/3.83750455201268492189/2.44948974278314768327,
14/3.70245917364383281267/3.44032915751253476344,
15/1.06066017177982208075/2.07102276374961702388,
16/0.13504537836886390534/2.44948974278317699316,
17/0.92561479341095842521/3.06186217847897212962,
18/0.00000000000000000000/3.44032915751253165482,
19/1.98627496519077983983/2.44948974278317788134,
20/1.85122958682191640634/3.44032915751253298708,
21/2.77684438023287460950/3.06186217847897301780,
22/1.85122958682191174340/6.64675285836283347152,
23/2.84436706941730133025/6.76370558669395283147,
24/2.44908236189625583279/5.84514693315025990472,
25/3.44221984449164519759/5.96209966148137926467,
26/3.83750455201269069505/6.88065831502507219142,
27/3.04693513697060014422/5.04354100793768633793,
28/1.98627496519077717529/5.65591344363347836577,
29/1.06066017177981830599/6.03438042266703700278,
30/1.19570555014868351584/5.04354100793768278521,
31/0.27009075673772470205/5.42200798697124142222,
32/2.12132034355964282923/4.66507402890412414820,
33/2.91188975860173915322/4.05270159320833123218,
34/3.83750455201269602412/4.43116857224189519826,
35/1.06066017177982030439/4.80963555127544761802,
36/0.13504537836886276736/4.43116857224188631648,
37/0.92561479341095787010/3.81879613654609251228,
38/1.98627496519077850756/4.43116857224188809283,
39/2.77684438023287372133/3.81879613654609428863,
40/5.82377951720347031284/6.64675285836284324148,
41/4.83064203460808005985/6.76370558669395816054,
42/5.22592674212912911003/5.84514693315026701015,
43/4.23278925953373974522/5.96209966148138192921,
44/4.62807396705478879539/5.04354100793769077882,
45/5.68873413883460798957/5.65591344363348724755,
46/6.61434893224556574864/6.03438042266705032546,
47/6.47930355387670431355/5.04354100793769610789,
48/7.40491834728766207263/5.42200798697125740944,
49/5.55368876046574744265/4.66507402890413302998,
50/4.76311934542365467138/4.05270159320833567307,
51/3.97254993038155967966/3.44032915751253964842,
52/6.61434893224556752500/4.80963555127546271706,
53/7.53996372565652528408/4.43116857224190230369,
54/6.74939431061443162463/3.81879613654610761131,
55/7.67500910402539027189/3.44032915751254764203,
56/5.68873413883461065410/4.43116857224189875097,
57/5.82377951720347475373/3.44032915751254364523,
58/4.89816472379251610647/3.81879613654610272633,
59/5.82377951720347475373/0.23390545666225651122,
60/4.83064203460808716528/0.11695272833112821398,
61/5.22592674212912378096/1.03551138187482494324,
62/4.23278925953373530433/0.91855865354369670150,
63/4.62807396705477192000/1.83711730708739295892,
64/5.68873413883461687135/1.22474487139161203331,
65/6.61434893224557374225/0.84627789235804673496,
66/6.47930355387671408351/1.83711730708740250684,
67/7.40491834728767095442/1.45865032805383720849,
68/5.55368876046572612637/2.21558428612096269816,
69/4.76311934542362536149/2.82795672181674939694,
70/6.61434893224557374225/2.07102276374962901428,
71/7.53996372565652972497/2.44948974278319253628,
72/6.74939431061443340099/3.06186217847898456412,
73/5.68873413883461509499/2.44948974278318853948,
74/4.89816472379251877101/3.06186217847898056732}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
55/97.76/202.24/0.4/LightCyan}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
1/2, 1/3,
2/5,
3/2, 3/4,
4/2, 4/5,
6/3, 6/4,
7/8, 7/1,
8/1,
9/8, 9/7,
10/8, 10/9,
11/7, 11/6,
12/11, 12/6,
13/69, 13/12,
14/39, 14/21, 14/12, 14/13, 14/33,
15/16, 15/10,
16/10,
17/16, 17/15,
18/16, 18/17,
19/20, 19/15,
20/37, 20/17,
21/20, 21/19,
22/29, 22/28,
23/22, 23/24,
24/22,
25/23, 25/24,
26/23, 26/25,
27/25, 27/24,
28/29, 28/30,
29/31, 29/30,
30/31,
31/36, 31/35,
32/27, 32/28,
33/27, 33/32,
34/33, 34/50, 34/14,
35/36, 35/37,
36/18, 36/37,
37/18,
38/35, 38/20,
39/38, 39/20,
40/41, 40/42,
41/26, 41/43,
42/41, 42/43,
43/26,
44/42, 44/43,
45/46, 45/40,
46/40,
47/46, 47/45,
48/46, 48/47,
49/45, 49/44,
50/49, 50/44,
51/74, 51/58, 51/13, 51/50, 51/34, 51/69,
52/53, 52/48,
53/48,
54/53, 54/52,
55/53, 55/54,
56/57, 56/52,
57/72, 57/54,
58/57, 58/56,
60/5, 60/59,
61/60, 61/59,
62/5, 62/60, 62/61,
63/62, 63/61,
64/59, 64/65, 64/66,
65/67, 65/59,
66/65, 66/67,
67/71, 67/70,
68/63, 68/64,
69/63, 69/68,
70/71, 70/72,
71/55, 71/72,
72/55,
73/70, 73/57,
74/73, 74/57}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,74}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[Green,very thick] (p-14) -- (p-12);
\draw[Green,very thick] (p-14) -- (p-13);
\draw[Green,very thick] (p-14) -- (p-33);
\draw[Green,very thick] (p-34) -- (p-14);
\draw[Green,very thick] (p-51) -- (p-13);
\draw[Green,very thick] (p-51) -- (p-50);
\draw[Green,very thick] (p-51) -- (p-34);
\draw[Green,very thick] (p-51) -- (p-69);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
55/97.76/202.24/0.4/LightCyan}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/292,
2/323,
3/83,
4/23,
5/323,
6/308,
7/52,
8/232,
9/52,
10/172,
11/188,
12/68,
13/232,
14/68,
15/308,
16/128,
17/68,
18/128,
19/248,
20/232,
21/8,
22/68,
23/37,
24/217,
25/37,
26/37,
27/277,
28/308,
29/68,
30/248,
31/188,
32/172,
33/292,
34/52,
35/352,
36/232,
37/352,
38/112,
39/352,
40/23,
41/83,
42/263,
43/263,
44/263,
45/232,
46/52,
47/232,
48/352,
49/8,
50/248,
51/112,
52/128,
53/308,
54/248,
55/308,
56/68,
57/308,
58/188,
59/337,
60/277,
61/97,
62/157,
63/232,
64/128,
65/8,
66/128,
67/8,
68/352,
69/112,
70/172,
71/52,
72/172,
73/292,
74/172}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/264949124e884211c97a5d30a2f9ec02.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1894-1</Bildtext>
%<Ausrichten von=\"1\" nach=\"2\"/>
%<Winkel size=\"18\" color=\"LightCyan\" id=\"neunterWinkel\" value=\"104.47751218593004\"/>
%<Feinjustieren Anzahl=\"8,9\"/>
%<Rechenweg>
%blauerWinkel=148.95502437185988+(0.1410406669571719)*(neunterWinkel-(104.47751218593004));
%gruenerWinkel=135.52248781407008+(-0.6307535182062247)*(neunterWinkel-(104.47751218593004));
%orangerWinkel=104.47751218592992+(1.0000032572318647)*(neunterWinkel-(104.47751218593004));
%vierterWinkel=75.52248781407012+(-0.6307527345561197)*(neunterWinkel-(104.47751218593004));
%fuenfterWinkel=88.95502437185985+(0.14104184543139073)*(neunterWinkel-(104.47751218593004));
%sechsterWinkel=106.56746344221015+(-0.02057818663278938)*(neunterWinkel-(104.47751218593004));
%siebenterWinkel=148.95502437185982+(0.14103841595938466)*(neunterWinkel-(104.47751218593004));
%achterWinkel=135.52248781406996+(-0.6307501277441359)*(neunterWinkel-(104.47751218593004));
%P[5]=[81.1989530225137,-23.620797303099177]; P[2]=[31.54207889274424,-17.773160886543337]; D=ab(5,2); A(2,5); N(4,2,5); N(3,2,4); N(1,2,3); M(8,1,2,blauerWinkel); N(7,8,1); N(9,8,7); N(10,8,9); M(16,10,8,gruenerWinkel); N(15,16,10); N(17,16,15); N(18,16,17); M(37,18,16,orangerWinkel); N(36,18,37); N(35,36,37); N(31,36,35); M(30,31,36,vierterWinkel); N(29,31,30); N(28,29,30); N(22,29,28); M(24,22,29,fuenfterWinkel); N(23,22,24); N(25,23,24); N(26,23,25); M(43,26,23,sechsterWinkel); N(41,26,43); N(42,41,43); N(40,41,42); M(46,40,41,siebenterWinkel); N(45,46,40); N(47,46,45); N(48,46,47); M(53,48,46,achterWinkel); N(52,53,48); N(54,53,52); N(55,53,54); M(72,55,53,neunterWinkel); N(71,55,72); N(70,71,72); N(67,71,70); Q(59,67,5,2*D,2*D); A(59,67); A(59,5); H(60,5,59,2); A(60,5); L(62,5,60); H(65,67,59,2); A(65,67); L(66,65,67); A(65,59); L(64,59,65); A(64,66); A(60,59); L(61,60,59); A(62,61); N(6,3,4); N(11,7,6); N(20,37,17); N(27,25,24); N(32,27,28); N(38,35,20); N(44,42,43); N(49,45,44); N(57,72,54); N(63,62,61); N(68,63,64); N(73,70,57); N(19,20,15); N(56,57,52); N(12,11,6); N(21,20,19); N(33,27,32); N(39,38,20); N(50,49,44); N(58,57,56); N(69,63,68); N(74,73,57); N(13,69,12); N(14,39,21); N(34,33,50); N(51,74,58);
%A(14,12); R(14,12,\"green\");
%A(14,13); R(14,13,\"green\");
%A(14,33); R(14,33,\"green\");
%A(34,14); R(34,14,\"green\");
%A(51,13); R(51,13,\"green\");
%A(51,50); R(51,50,\"green\");
%A(51,34); R(51,34,\"green\");
%A(51,69); R(51,69,\"green\");
%</Rechenweg>
%
%<Knopf id=\"Stopp_alleWinkel\" color=\"LightGrey\"/>
%
%<Knopf id=\"Start_neunterWinkel\" color=\"LightCyan\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#neunterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_neunterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LightCyan}{rgb}{0.88,1.00,1.00}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.85122958682191840474/0.23390545666223369614,
2/2.84436706941730799159/0.11695272833111684807,
3/2.44908236189626027368/1.03551138187480851194,
4/3.44221984449164963848/0.91855865354369181652,
5/3.83750455201269735639/0.00000000000000000000,
6/3.04693513697060236467/1.83711730708738363305,
7/1.98627496519078117210/1.22474487139158894067,
8/1.06066017177982319097/0.84627789235802786116,
9/1.19570555014868573629/1.83711730708738318896,
10/0.27009075673772781068/1.45865032805382210945,
11/2.12132034355964416150/2.21558428612094360233,
12/2.91188975860173870913/2.82795672181673873880,
13/3.83750455201268492189/2.44948974278314768327,
14/3.70245917364383281267/3.44032915751253476344,
15/1.06066017177982208075/2.07102276374961702388,
16/0.13504537836886390534/2.44948974278317699316,
17/0.92561479341095842521/3.06186217847897212962,
18/0.00000000000000000000/3.44032915751253165482,
19/1.98627496519077983983/2.44948974278317788134,
20/1.85122958682191640634/3.44032915751253298708,
21/2.77684438023287460950/3.06186217847897301780,
22/1.85122958682191174340/6.64675285836283347152,
23/2.84436706941730133025/6.76370558669395283147,
24/2.44908236189625583279/5.84514693315025990472,
25/3.44221984449164519759/5.96209966148137926467,
26/3.83750455201269069505/6.88065831502507219142,
27/3.04693513697060014422/5.04354100793768633793,
28/1.98627496519077717529/5.65591344363347836577,
29/1.06066017177981830599/6.03438042266703700278,
30/1.19570555014868351584/5.04354100793768278521,
31/0.27009075673772470205/5.42200798697124142222,
32/2.12132034355964282923/4.66507402890412414820,
33/2.91188975860173915322/4.05270159320833123218,
34/3.83750455201269602412/4.43116857224189519826,
35/1.06066017177982030439/4.80963555127544761802,
36/0.13504537836886276736/4.43116857224188631648,
37/0.92561479341095787010/3.81879613654609251228,
38/1.98627496519077850756/4.43116857224188809283,
39/2.77684438023287372133/3.81879613654609428863,
40/5.82377951720347031284/6.64675285836284324148,
41/4.83064203460808005985/6.76370558669395816054,
42/5.22592674212912911003/5.84514693315026701015,
43/4.23278925953373974522/5.96209966148138192921,
44/4.62807396705478879539/5.04354100793769077882,
45/5.68873413883460798957/5.65591344363348724755,
46/6.61434893224556574864/6.03438042266705032546,
47/6.47930355387670431355/5.04354100793769610789,
48/7.40491834728766207263/5.42200798697125740944,
49/5.55368876046574744265/4.66507402890413302998,
50/4.76311934542365467138/4.05270159320833567307,
51/3.97254993038155967966/3.44032915751253964842,
52/6.61434893224556752500/4.80963555127546271706,
53/7.53996372565652528408/4.43116857224190230369,
54/6.74939431061443162463/3.81879613654610761131,
55/7.67500910402539027189/3.44032915751254764203,
56/5.68873413883461065410/4.43116857224189875097,
57/5.82377951720347475373/3.44032915751254364523,
58/4.89816472379251610647/3.81879613654610272633,
59/5.82377951720347475373/0.23390545666225651122,
60/4.83064203460808716528/0.11695272833112821398,
61/5.22592674212912378096/1.03551138187482494324,
62/4.23278925953373530433/0.91855865354369670150,
63/4.62807396705477192000/1.83711730708739295892,
64/5.68873413883461687135/1.22474487139161203331,
65/6.61434893224557374225/0.84627789235804673496,
66/6.47930355387671408351/1.83711730708740250684,
67/7.40491834728767095442/1.45865032805383720849,
68/5.55368876046572612637/2.21558428612096269816,
69/4.76311934542362536149/2.82795672181674939694,
70/6.61434893224557374225/2.07102276374962901428,
71/7.53996372565652972497/2.44948974278319253628,
72/6.74939431061443340099/3.06186217847898456412,
73/5.68873413883461509499/2.44948974278318853948,
74/4.89816472379251877101/3.06186217847898056732}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
55/97.76/202.24/0.4/LightCyan}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
1/2, 1/3,
2/5,
3/2, 3/4,
4/2, 4/5,
6/3, 6/4,
7/8, 7/1,
8/1,
9/8, 9/7,
10/8, 10/9,
11/7, 11/6,
12/11, 12/6,
13/69, 13/12,
14/39, 14/21, 14/12, 14/13, 14/33,
15/16, 15/10,
16/10,
17/16, 17/15,
18/16, 18/17,
19/20, 19/15,
20/37, 20/17,
21/20, 21/19,
22/29, 22/28,
23/22, 23/24,
24/22,
25/23, 25/24,
26/23, 26/25,
27/25, 27/24,
28/29, 28/30,
29/31, 29/30,
30/31,
31/36, 31/35,
32/27, 32/28,
33/27, 33/32,
34/33, 34/50, 34/14,
35/36, 35/37,
36/18, 36/37,
37/18,
38/35, 38/20,
39/38, 39/20,
40/41, 40/42,
41/26, 41/43,
42/41, 42/43,
43/26,
44/42, 44/43,
45/46, 45/40,
46/40,
47/46, 47/45,
48/46, 48/47,
49/45, 49/44,
50/49, 50/44,
51/74, 51/58, 51/13, 51/50, 51/34, 51/69,
52/53, 52/48,
53/48,
54/53, 54/52,
55/53, 55/54,
56/57, 56/52,
57/72, 57/54,
58/57, 58/56,
60/5, 60/59,
61/60, 61/59,
62/5, 62/60, 62/61,
63/62, 63/61,
64/59, 64/65, 64/66,
65/67, 65/59,
66/65, 66/67,
67/71, 67/70,
68/63, 68/64,
69/63, 69/68,
70/71, 70/72,
71/55, 71/72,
72/55,
73/70, 73/57,
74/73, 74/57}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,74}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[Green,very thick] (p-14) -- (p-12);
\draw[Green,very thick] (p-14) -- (p-13);
\draw[Green,very thick] (p-14) -- (p-33);
\draw[Green,very thick] (p-34) -- (p-14);
\draw[Green,very thick] (p-51) -- (p-13);
\draw[Green,very thick] (p-51) -- (p-50);
\draw[Green,very thick] (p-51) -- (p-34);
\draw[Green,very thick] (p-51) -- (p-69);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
55/97.76/202.24/0.4/LightCyan}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/292,
2/323,
3/83,
4/23,
5/323,
6/308,
7/52,
8/232,
9/52,
10/172,
11/188,
12/68,
13/232,
14/68,
15/308,
16/128,
17/68,
18/128,
19/248,
20/232,
21/8,
22/68,
23/37,
24/217,
25/37,
26/37,
27/277,
28/308,
29/68,
30/248,
31/188,
32/172,
33/292,
34/52,
35/352,
36/232,
37/352,
38/112,
39/352,
40/23,
41/83,
42/263,
43/263,
44/263,
45/232,
46/52,
47/232,
48/352,
49/8,
50/248,
51/112,
52/128,
53/308,
54/248,
55/308,
56/68,
57/308,
58/188,
59/337,
60/277,
61/97,
62/157,
63/232,
64/128,
65/8,
66/128,
67/8,
68/352,
69/112,
70/172,
71/52,
72/172,
73/292,
74/172}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
mit einem frei beweglichen Winkel, der Graph ist beweglich. Wird dieser Winkel mit Buttons "+1" oder "-1" verstellt, so entstehen recht schnell unpassende Kanten. Die lineare Annäherung der Winkeländerung (aus der Ableitunsmatrix abgekesen) ist zu ungenau. Nach jeder Winkeländerung um +1 müsste der Graph neu zurechtgezogen werden. Das habe ich für 10 Winkeländerungen durchgeführt und die entstehenden Winkeländerungen in Newtonpolynome gepackt. Wer das im Streichholzprogramm selber ausprobieren will, nochmal mit #1894-1 starten, dann Button neue Eingabe "Rahmen zuerst", dann Testbutton "Newtonpolynom(10)" (befindet sich bei den Testfunktionen und -Graphen) und nach etlichen Sekunden wird am Seitenende eine Liste von Newtonpolynomen ausgegeben. Diese in obigen Graph (der nach Button "beweglich?") anstelle der linearen Polynome blauerWinkel=... einsetzen, dann noch die Animationswinkelbereiche und -zeit anpassen (15 s von neunterWinkel+25° bis neunterWinkel-35°) dann Button "neu zeichnen" und man erhält
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1894-1</Bildtext>
%<Ausrichten von="1" nach="2"/>
%<Winkel size="18" color="LightCyan" id="neunterWinkel" value="104.47751218593004"/>
%<Feinjustieren Anzahl="8,9"/>
%<Rechenweg>
%blauerWinkel=148.88671009447805+(neunterWinkel-104)/1*((0.1408448774476483)+(neunterWinkel-105)/2*((-0.008544615548174761)+(neunterWinkel-106)/3*((-0.00010376917674648212)+(neunterWinkel-107)/4*((0.00000560396125592888)+(neunterWinkel-108)/5*((3.061999223064049e-7)+(neunterWinkel-109)/6*((-1.3431559864329756e-8)+(neunterWinkel-110)/7*((-1.8478090169082861e-9)+(neunterWinkel-111)/8*((4.780531526193954e-11)+(neunterWinkel-112)/9*((5.6559201766503975e-12))))))))));
%gruenerWinkel=135.82460766621898+(neunterWinkel-104)/1*((-0.6305662265546346)+(neunterWinkel-105)/2*((0.008175628854985462)+(neunterWinkel-106)/3*((0.000047319122813860304)+(neunterWinkel-107)/4*((-0.0000025056787364974298)+(neunterWinkel-108)/5*((-1.4848583873572352e-7)+(neunterWinkel-109)/6*((6.16401507613773e-9)+(neunterWinkel-110)/7*((9.677592061052565e-10)+(neunterWinkel-111)/8*((-5.150013748789206e-11)+(neunterWinkel-112)/9*((6.076561476220377e-11))))))))));
%orangerWinkel=104.00000000000078+(neunterWinkel-104)/1*((1.0000000000006537)+(neunterWinkel-105)/2*((-5.087485988042317e-12)+(neunterWinkel-106)/3*((1.1453948900452815e-11)+(neunterWinkel-107)/4*((-1.6839862837514374e-11)+(neunterWinkel-108)/5*((1.7564616427989677e-11)+(neunterWinkel-109)/6*((-9.15179043659009e-12)+(neunterWinkel-110)/7*((-1.3642420526593924e-11)+(neunterWinkel-111)/8*((5.5862869885459077e-11)+(neunterWinkel-112)/9*((-1.2396128568070708e-10))))))))));
%vierterWinkel=75.82460766621898+(neunterWinkel-104)/1*((-0.6305662265546061)+(neunterWinkel-105)/2*((0.008175628854914407)+(neunterWinkel-106)/3*((0.000047319122970179706)+(neunterWinkel-107)/4*((-0.000002505679034925379)+(neunterWinkel-108)/5*((-1.4848531293409906e-7)+(neunterWinkel-109)/6*((6.163105581435957e-9)+(neunterWinkel-110)/7*((9.693650326880743e-10)+(neunterWinkel-111)/8*((-5.441336270450847e-11)+(neunterWinkel-112)/9*((6.609468528040452e-11))))))))));
%fuenfterWinkel=88.88671009447798+(neunterWinkel-104)/1*((0.1408448774476767)+(neunterWinkel-105)/2*((-0.008544615548217394)+(neunterWinkel-106)/3*((-0.00010376917664700613)+(neunterWinkel-107)/4*((0.000005603961028555204)+(neunterWinkel-108)/5*((3.0620041968631995e-7)+(neunterWinkel-109)/6*((-1.343258304586925e-8)+(neunterWinkel-110)/7*((-1.845833708102873e-9)+(neunterWinkel-111)/8*((4.4224179873708636e-11)+(neunterWinkel-112)/9*((1.1667111721180845e-11))))))))));
%sechsterWinkel=106.57736447860536+(neunterWinkel-104)/1*((-0.02055730178675219)+(neunterWinkel-105)/2*((0.0007379733913097652)+(neunterWinkel-106)/3*((0.00011290009688025293)+(neunterWinkel-107)/4*((-0.000006196548966386217)+(neunterWinkel-108)/5*((-3.1544495016078145e-7)+(neunterWinkel-109)/6*((1.4544255577675358e-8)+(neunterWinkel-110)/7*((1.7711556665744865e-9)+(neunterWinkel-111)/8*((-3.9676706364843994e-11)+(neunterWinkel-112)/9*((-3.133493464702042e-11))))))))));
%siebenterWinkel=148.88671009447785+(neunterWinkel-104)/1*((0.14084487744770513)+(neunterWinkel-105)/2*((-0.008544615547720014)+(neunterWinkel-106)/3*((-0.00010376917805388075)+(neunterWinkel-107)/4*((0.000005603963501243925)+(neunterWinkel-108)/5*((3.06197023292043e-7)+(neunterWinkel-109)/6*((-1.3428717693386716e-8)+(neunterWinkel-110)/7*((-1.8495143194741104e-9)+(neunterWinkel-111)/8*((4.723688107333146e-11)+(neunterWinkel-112)/9*((9.208633855450898e-12))))))))));
%achterWinkel=135.82460766621944+(neunterWinkel-104)/1*((-0.6305662265542082)+(neunterWinkel-105)/2*((0.008175628851887495)+(neunterWinkel-106)/3*((0.000047319129691913986)+(neunterWinkel-107)/4*((-0.00000250568871251744)+(neunterWinkel-108)/5*((-1.484757206071663e-7)+(neunterWinkel-109)/6*((6.159467602628865e-9)+(neunterWinkel-110)/7*((9.578400295140455e-10)+(neunterWinkel-111)/8*((-1.5262457964126952e-11)+(neunterWinkel-112)/9*((-1.6967760529951192e-11))))))))));
%P[5]=[81.1989530225137,-23.620797303099177]; P[2]=[31.54207889274424,-17.773160886543337]; D=ab(5,2); A(2,5); N(4,2,5); N(3,2,4); N(1,2,3); M(8,1,2,blauerWinkel); N(7,8,1); N(9,8,7); N(10,8,9); M(16,10,8,gruenerWinkel); N(15,16,10); N(17,16,15); N(18,16,17); M(37,18,16,orangerWinkel); N(36,18,37); N(35,36,37); N(31,36,35); M(30,31,36,vierterWinkel); N(29,31,30); N(28,29,30); N(22,29,28); M(24,22,29,fuenfterWinkel); N(23,22,24); N(25,23,24); N(26,23,25); M(43,26,23,sechsterWinkel); N(41,26,43); N(42,41,43); N(40,41,42); M(46,40,41,siebenterWinkel); N(45,46,40); N(47,46,45); N(48,46,47); M(53,48,46,achterWinkel); N(52,53,48); N(54,53,52); N(55,53,54); M(72,55,53,neunterWinkel); N(71,55,72); N(70,71,72); N(67,71,70); Q(59,67,5,2*D,2*D); A(59,67); A(59,5); H(60,5,59,2); A(60,5); L(62,5,60); H(65,67,59,2); A(65,67); L(66,65,67); A(65,59); L(64,59,65); A(64,66); A(60,59); L(61,60,59); A(62,61); N(6,3,4); N(11,7,6); N(20,37,17); N(27,25,24); N(32,27,28); N(38,35,20); N(44,42,43); N(49,45,44); N(57,72,54); N(63,62,61); N(68,63,64); N(73,70,57); N(19,20,15); N(56,57,52); N(12,11,6); N(21,20,19); N(33,27,32); N(39,38,20); N(50,49,44); N(58,57,56); N(69,63,68); N(74,73,57); N(13,69,12); N(14,39,21); N(34,33,50); N(51,74,58);
%A(14,12); R(14,12,"green");
%A(14,13); R(14,13,"green");
%A(14,33); R(14,33,"green");
%A(34,14); R(34,14,"green");
%A(51,13); R(51,13,"green");
%A(51,50); R(51,50,"green");
%A(51,34); R(51,34,"green");
%A(51,69); R(51,69,"green");
%</Rechenweg>
%
%<Knopf id="Stopp_alleWinkel" color="LightGrey"/>
%
%<Knopf id="Start_neunterWinkel" color="LightCyan"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#neunterWinkel" attributeName="value" values="0;25;0;-35;0" dur="15" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_neunterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LightCyan}{rgb}{0.88,1.00,1.00}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.85122958682189819868/0.23390545666223369614,
2/2.84436706941728756348/0.11695272833111684807,
3/2.44908236189623984558/1.03551138187480851194,
4/3.44221984449163009856/0.91855865354369181652,
5/3.83750455201267737237/0.00000000000000000000,
6/3.04693513697058193657/1.83711730708738363305,
7/1.98627496519075608106/1.22474487139158938476,
8/1.06066017177980009834/0.84627789235802408641,
9/1.19570555014865798071/1.83711730708737985829,
10/0.27009075673770166492/1.45865032805381455994,
11/2.12132034355962373340/2.21558428612094360233,
12/2.91188975860171872512/2.82795672181673873880,
13/3.83750455201269602412/2.44948974278322628706,
14/3.70245917364381194048/3.44032915751253076664,
15/1.06066017177980409514/2.07102276374959926031,
16/0.13504537836885083246/2.44948974278317122000,
17/0.92561479341095298512/3.06186217847895569832,
18/0.00000000000000000000/3.44032915751252765801,
19/1.98627496519075696924/2.44948974278317255227,
20/1.85122958682190597024/3.44032915751252899028,
21/2.77684438023285951047/3.06186217847895703059,
22/1.85122958682188731849/6.64675285836283169516,
23/2.84436706941727601716/6.76370558669395638418,
24/2.44908236189623629286/5.84514693315026256926,
25/3.44221984449162521358/5.96209966148138637010,
26/3.83750455201266493788/6.88065831502508196138,
27/3.04693513697058415701/5.04354100793769166700,
28/1.98627496519075075199/5.65591344363347658941,
29/1.06066017177979254882/6.03438042266703700278,
30/1.19570555014865620436/5.04354100793768189703,
31/0.27009075673769800119/5.42200798697124142222,
32/2.12132034355962950656/4.66507402890412414820,
33/2.91188975860172893917/4.05270159320833656125,
34/3.83750455201267914873/4.43116857224191651454,
35/1.06066017177980209674/4.80963555127545827617,
36/0.13504537836884941693/4.43116857224188454012,
37/0.92561479341095276308/3.81879613654610139406,
38/1.98627496519075497083/4.43116857224188542830,
39/2.77684438023285906638/3.81879613654610228224,
40/5.82377951720344544384/6.64675285836285478780,
41/4.83064203460805519086/6.76370558669396881868,
42/5.22592674212910690557/5.84514693315027766829,
43/4.23278925953371576441/5.96209966148139081099,
44/4.62807396705476747911/5.04354100793770232514,
45/5.68873413883458223239/5.65591344363350057023,
46/6.61434893224553910329/6.03438042266705920724,
47/6.47930355387667589184/5.04354100793770410149,
48/7.40491834728763365092/5.42200798697126362669,
49/5.55368876046572612637/4.66507402890414457630,
50/4.76311934542363335510/4.05270159320834721939,
51/3.97254993038151438256/3.44032915751257428738,
52/6.61434893224553288604/4.80963555127547603973,
53/7.53996372565648798059/4.43116857224190940912,
54/6.74939431061438899206/3.81879613654612048990,
55/7.67500910402534497479/3.44032915751255341519,
56/5.68873413883457246243/4.43116857224192006726,
57/5.82377951720342945663/3.44032915751256407333,
58/4.89816472379247436209/3.81879613654613025986,
59/5.82377951720346143105/0.23390545666220380339,
60/4.83064203460806940171/0.11695272833110192945,
61/5.22592674212913177456/1.03551138187478763975,
62/4.23278925953373885704/0.91855865354368582132,
63/4.62807396705480122989/1.83711730708737164264,
64/5.68873413883456446882/1.22474487139155430171,
65/6.61434893224553466240/0.84627789235802430845,
66/6.47930355387663947653/1.83711730708737452922,
67/7.40491834728761055828/1.45865032805384498005,
68/5.55368876046576609440/2.21558428612091784515,
69/4.76311934542367954037/2.82795672181672452794,
70/6.61434893224551689883/2.07102276374964278105,
71/7.53996372565647643427/2.44948974278319964171,
72/6.74939431061438455117/3.06186217847899699862,
73/5.68873413883456180429/2.44948974278320985576,
74/4.89816472379246992119/3.06186217847900854494}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
55/97.76/202.24/0.4/LightCyan}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
1/2, 1/3,
2/5,
3/2, 3/4,
4/2, 4/5,
6/3, 6/4,
7/8, 7/1,
8/1,
9/8, 9/7,
10/8, 10/9,
11/7, 11/6,
12/11, 12/6,
13/69, 13/12,
14/39, 14/21, 14/12, 14/13, 14/33,
15/16, 15/10,
16/10,
17/16, 17/15,
18/16, 18/17,
19/20, 19/15,
20/37, 20/17,
21/20, 21/19,
22/29, 22/28,
23/22, 23/24,
24/22,
25/23, 25/24,
26/23, 26/25,
27/25, 27/24,
28/29, 28/30,
29/31, 29/30,
30/31,
31/36, 31/35,
32/27, 32/28,
33/27, 33/32,
34/33, 34/50, 34/14,
35/36, 35/37,
36/18, 36/37,
37/18,
38/35, 38/20,
39/38, 39/20,
40/41, 40/42,
41/26, 41/43,
42/41, 42/43,
43/26,
44/42, 44/43,
45/46, 45/40,
46/40,
47/46, 47/45,
48/46, 48/47,
49/45, 49/44,
50/49, 50/44,
51/74, 51/58, 51/13, 51/50, 51/34, 51/69,
52/53, 52/48,
53/48,
54/53, 54/52,
55/53, 55/54,
56/57, 56/52,
57/72, 57/54,
58/57, 58/56,
60/5, 60/59,
61/60, 61/59,
62/5, 62/60, 62/61,
63/62, 63/61,
64/59, 64/65, 64/66,
65/67, 65/59,
66/65, 66/67,
67/71, 67/70,
68/63, 68/64,
69/63, 69/68,
70/71, 70/72,
71/55, 71/72,
72/55,
73/70, 73/57,
74/73, 74/57}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,74}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[Green,very thick] (p-14) -- (p-12);
\draw[Green,very thick] (p-14) -- (p-13);
\draw[Green,very thick] (p-14) -- (p-33);
\draw[Green,very thick] (p-34) -- (p-14);
\draw[Green,very thick] (p-51) -- (p-13);
\draw[Green,very thick] (p-51) -- (p-50);
\draw[Green,very thick] (p-51) -- (p-34);
\draw[Green,very thick] (p-51) -- (p-69);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
55/97.76/202.24/0.4/LightCyan}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/203,
2/323,
3/83,
4/23,
5/217,
6/83,
7/352,
8/172,
9/112,
10/172,
11/188,
12/188,
13/308,
14/292,
15/308,
16/188,
17/68,
18/128,
19/248,
20/128,
21/8,
22/157,
23/157,
24/157,
25/337,
26/37,
27/277,
28/308,
29/68,
30/308,
31/112,
32/172,
33/292,
34/52,
35/352,
36/112,
37/292,
38/112,
39/352,
40/112,
41/143,
42/23,
43/263,
44/128,
45/232,
46/112,
47/292,
48/68,
49/8,
50/8,
51/112,
52/188,
53/8,
54/188,
55/52,
56/68,
57/52,
58/188,
59/337,
60/337,
61/37,
62/217,
63/232,
64/128,
65/8,
66/128,
67/8,
68/352,
69/352,
70/232,
71/352,
72/172,
73/292,
74/172}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/e977daea57989e8a95170dba3df91402.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1894-1</Bildtext>
%<Ausrichten von=\"1\" nach=\"2\"/>
%<Winkel size=\"18\" color=\"LightCyan\" id=\"neunterWinkel\" value=\"104.47751218593004\"/>
%<Feinjustieren Anzahl=\"8,9\"/>
%<Rechenweg>
%blauerWinkel=148.88671009447805+(neunterWinkel-104)/1*((0.1408448774476483)+(neunterWinkel-105)/2*((-0.008544615548174761)+(neunterWinkel-106)/3*((-0.00010376917674648212)+(neunterWinkel-107)/4*((0.00000560396125592888)+(neunterWinkel-108)/5*((3.061999223064049e-7)+(neunterWinkel-109)/6*((-1.3431559864329756e-8)+(neunterWinkel-110)/7*((-1.8478090169082861e-9)+(neunterWinkel-111)/8*((4.780531526193954e-11)+(neunterWinkel-112)/9*((5.6559201766503975e-12))))))))));
%gruenerWinkel=135.82460766621898+(neunterWinkel-104)/1*((-0.6305662265546346)+(neunterWinkel-105)/2*((0.008175628854985462)+(neunterWinkel-106)/3*((0.000047319122813860304)+(neunterWinkel-107)/4*((-0.0000025056787364974298)+(neunterWinkel-108)/5*((-1.4848583873572352e-7)+(neunterWinkel-109)/6*((6.16401507613773e-9)+(neunterWinkel-110)/7*((9.677592061052565e-10)+(neunterWinkel-111)/8*((-5.150013748789206e-11)+(neunterWinkel-112)/9*((6.076561476220377e-11))))))))));
%orangerWinkel=104.00000000000078+(neunterWinkel-104)/1*((1.0000000000006537)+(neunterWinkel-105)/2*((-5.087485988042317e-12)+(neunterWinkel-106)/3*((1.1453948900452815e-11)+(neunterWinkel-107)/4*((-1.6839862837514374e-11)+(neunterWinkel-108)/5*((1.7564616427989677e-11)+(neunterWinkel-109)/6*((-9.15179043659009e-12)+(neunterWinkel-110)/7*((-1.3642420526593924e-11)+(neunterWinkel-111)/8*((5.5862869885459077e-11)+(neunterWinkel-112)/9*((-1.2396128568070708e-10))))))))));
%vierterWinkel=75.82460766621898+(neunterWinkel-104)/1*((-0.6305662265546061)+(neunterWinkel-105)/2*((0.008175628854914407)+(neunterWinkel-106)/3*((0.000047319122970179706)+(neunterWinkel-107)/4*((-0.000002505679034925379)+(neunterWinkel-108)/5*((-1.4848531293409906e-7)+(neunterWinkel-109)/6*((6.163105581435957e-9)+(neunterWinkel-110)/7*((9.693650326880743e-10)+(neunterWinkel-111)/8*((-5.441336270450847e-11)+(neunterWinkel-112)/9*((6.609468528040452e-11))))))))));
%fuenfterWinkel=88.88671009447798+(neunterWinkel-104)/1*((0.1408448774476767)+(neunterWinkel-105)/2*((-0.008544615548217394)+(neunterWinkel-106)/3*((-0.00010376917664700613)+(neunterWinkel-107)/4*((0.000005603961028555204)+(neunterWinkel-108)/5*((3.0620041968631995e-7)+(neunterWinkel-109)/6*((-1.343258304586925e-8)+(neunterWinkel-110)/7*((-1.845833708102873e-9)+(neunterWinkel-111)/8*((4.4224179873708636e-11)+(neunterWinkel-112)/9*((1.1667111721180845e-11))))))))));
%sechsterWinkel=106.57736447860536+(neunterWinkel-104)/1*((-0.02055730178675219)+(neunterWinkel-105)/2*((0.0007379733913097652)+(neunterWinkel-106)/3*((0.00011290009688025293)+(neunterWinkel-107)/4*((-0.000006196548966386217)+(neunterWinkel-108)/5*((-3.1544495016078145e-7)+(neunterWinkel-109)/6*((1.4544255577675358e-8)+(neunterWinkel-110)/7*((1.7711556665744865e-9)+(neunterWinkel-111)/8*((-3.9676706364843994e-11)+(neunterWinkel-112)/9*((-3.133493464702042e-11))))))))));
%siebenterWinkel=148.88671009447785+(neunterWinkel-104)/1*((0.14084487744770513)+(neunterWinkel-105)/2*((-0.008544615547720014)+(neunterWinkel-106)/3*((-0.00010376917805388075)+(neunterWinkel-107)/4*((0.000005603963501243925)+(neunterWinkel-108)/5*((3.06197023292043e-7)+(neunterWinkel-109)/6*((-1.3428717693386716e-8)+(neunterWinkel-110)/7*((-1.8495143194741104e-9)+(neunterWinkel-111)/8*((4.723688107333146e-11)+(neunterWinkel-112)/9*((9.208633855450898e-12))))))))));
%achterWinkel=135.82460766621944+(neunterWinkel-104)/1*((-0.6305662265542082)+(neunterWinkel-105)/2*((0.008175628851887495)+(neunterWinkel-106)/3*((0.000047319129691913986)+(neunterWinkel-107)/4*((-0.00000250568871251744)+(neunterWinkel-108)/5*((-1.484757206071663e-7)+(neunterWinkel-109)/6*((6.159467602628865e-9)+(neunterWinkel-110)/7*((9.578400295140455e-10)+(neunterWinkel-111)/8*((-1.5262457964126952e-11)+(neunterWinkel-112)/9*((-1.6967760529951192e-11))))))))));
%P[5]=[81.1989530225137,-23.620797303099177]; P[2]=[31.54207889274424,-17.773160886543337]; D=ab(5,2); A(2,5); N(4,2,5); N(3,2,4); N(1,2,3); M(8,1,2,blauerWinkel); N(7,8,1); N(9,8,7); N(10,8,9); M(16,10,8,gruenerWinkel); N(15,16,10); N(17,16,15); N(18,16,17); M(37,18,16,orangerWinkel); N(36,18,37); N(35,36,37); N(31,36,35); M(30,31,36,vierterWinkel); N(29,31,30); N(28,29,30); N(22,29,28); M(24,22,29,fuenfterWinkel); N(23,22,24); N(25,23,24); N(26,23,25); M(43,26,23,sechsterWinkel); N(41,26,43); N(42,41,43); N(40,41,42); M(46,40,41,siebenterWinkel); N(45,46,40); N(47,46,45); N(48,46,47); M(53,48,46,achterWinkel); N(52,53,48); N(54,53,52); N(55,53,54); M(72,55,53,neunterWinkel); N(71,55,72); N(70,71,72); N(67,71,70); Q(59,67,5,2*D,2*D); A(59,67); A(59,5); H(60,5,59,2); A(60,5); L(62,5,60); H(65,67,59,2); A(65,67); L(66,65,67); A(65,59); L(64,59,65); A(64,66); A(60,59); L(61,60,59); A(62,61); N(6,3,4); N(11,7,6); N(20,37,17); N(27,25,24); N(32,27,28); N(38,35,20); N(44,42,43); N(49,45,44); N(57,72,54); N(63,62,61); N(68,63,64); N(73,70,57); N(19,20,15); N(56,57,52); N(12,11,6); N(21,20,19); N(33,27,32); N(39,38,20); N(50,49,44); N(58,57,56); N(69,63,68); N(74,73,57); N(13,69,12); N(14,39,21); N(34,33,50); N(51,74,58);
%A(14,12); R(14,12,\"green\");
%A(14,13); R(14,13,\"green\");
%A(14,33); R(14,33,\"green\");
%A(34,14); R(34,14,\"green\");
%A(51,13); R(51,13,\"green\");
%A(51,50); R(51,50,\"green\");
%A(51,34); R(51,34,\"green\");
%A(51,69); R(51,69,\"green\");
%</Rechenweg>
%
%<Knopf id=\"Stopp_alleWinkel\" color=\"LightGrey\"/>
%
%<Knopf id=\"Start_neunterWinkel\" color=\"LightCyan\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#neunterWinkel\" attributeName=\"value\" values=\"0;25;0;-35;0\" dur=\"15\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_neunterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LightCyan}{rgb}{0.88,1.00,1.00}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.85122958682189819868/0.23390545666223369614,
2/2.84436706941728756348/0.11695272833111684807,
3/2.44908236189623984558/1.03551138187480851194,
4/3.44221984449163009856/0.91855865354369181652,
5/3.83750455201267737237/0.00000000000000000000,
6/3.04693513697058193657/1.83711730708738363305,
7/1.98627496519075608106/1.22474487139158938476,
8/1.06066017177980009834/0.84627789235802408641,
9/1.19570555014865798071/1.83711730708737985829,
10/0.27009075673770166492/1.45865032805381455994,
11/2.12132034355962373340/2.21558428612094360233,
12/2.91188975860171872512/2.82795672181673873880,
13/3.83750455201269602412/2.44948974278322628706,
14/3.70245917364381194048/3.44032915751253076664,
15/1.06066017177980409514/2.07102276374959926031,
16/0.13504537836885083246/2.44948974278317122000,
17/0.92561479341095298512/3.06186217847895569832,
18/0.00000000000000000000/3.44032915751252765801,
19/1.98627496519075696924/2.44948974278317255227,
20/1.85122958682190597024/3.44032915751252899028,
21/2.77684438023285951047/3.06186217847895703059,
22/1.85122958682188731849/6.64675285836283169516,
23/2.84436706941727601716/6.76370558669395638418,
24/2.44908236189623629286/5.84514693315026256926,
25/3.44221984449162521358/5.96209966148138637010,
26/3.83750455201266493788/6.88065831502508196138,
27/3.04693513697058415701/5.04354100793769166700,
28/1.98627496519075075199/5.65591344363347658941,
29/1.06066017177979254882/6.03438042266703700278,
30/1.19570555014865620436/5.04354100793768189703,
31/0.27009075673769800119/5.42200798697124142222,
32/2.12132034355962950656/4.66507402890412414820,
33/2.91188975860172893917/4.05270159320833656125,
34/3.83750455201267914873/4.43116857224191651454,
35/1.06066017177980209674/4.80963555127545827617,
36/0.13504537836884941693/4.43116857224188454012,
37/0.92561479341095276308/3.81879613654610139406,
38/1.98627496519075497083/4.43116857224188542830,
39/2.77684438023285906638/3.81879613654610228224,
40/5.82377951720344544384/6.64675285836285478780,
41/4.83064203460805519086/6.76370558669396881868,
42/5.22592674212910690557/5.84514693315027766829,
43/4.23278925953371576441/5.96209966148139081099,
44/4.62807396705476747911/5.04354100793770232514,
45/5.68873413883458223239/5.65591344363350057023,
46/6.61434893224553910329/6.03438042266705920724,
47/6.47930355387667589184/5.04354100793770410149,
48/7.40491834728763365092/5.42200798697126362669,
49/5.55368876046572612637/4.66507402890414457630,
50/4.76311934542363335510/4.05270159320834721939,
51/3.97254993038151438256/3.44032915751257428738,
52/6.61434893224553288604/4.80963555127547603973,
53/7.53996372565648798059/4.43116857224190940912,
54/6.74939431061438899206/3.81879613654612048990,
55/7.67500910402534497479/3.44032915751255341519,
56/5.68873413883457246243/4.43116857224192006726,
57/5.82377951720342945663/3.44032915751256407333,
58/4.89816472379247436209/3.81879613654613025986,
59/5.82377951720346143105/0.23390545666220380339,
60/4.83064203460806940171/0.11695272833110192945,
61/5.22592674212913177456/1.03551138187478763975,
62/4.23278925953373885704/0.91855865354368582132,
63/4.62807396705480122989/1.83711730708737164264,
64/5.68873413883456446882/1.22474487139155430171,
65/6.61434893224553466240/0.84627789235802430845,
66/6.47930355387663947653/1.83711730708737452922,
67/7.40491834728761055828/1.45865032805384498005,
68/5.55368876046576609440/2.21558428612091784515,
69/4.76311934542367954037/2.82795672181672452794,
70/6.61434893224551689883/2.07102276374964278105,
71/7.53996372565647643427/2.44948974278319964171,
72/6.74939431061438455117/3.06186217847899699862,
73/5.68873413883456180429/2.44948974278320985576,
74/4.89816472379246992119/3.06186217847900854494}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
55/97.76/202.24/0.4/LightCyan}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
1/2, 1/3,
2/5,
3/2, 3/4,
4/2, 4/5,
6/3, 6/4,
7/8, 7/1,
8/1,
9/8, 9/7,
10/8, 10/9,
11/7, 11/6,
12/11, 12/6,
13/69, 13/12,
14/39, 14/21, 14/12, 14/13, 14/33,
15/16, 15/10,
16/10,
17/16, 17/15,
18/16, 18/17,
19/20, 19/15,
20/37, 20/17,
21/20, 21/19,
22/29, 22/28,
23/22, 23/24,
24/22,
25/23, 25/24,
26/23, 26/25,
27/25, 27/24,
28/29, 28/30,
29/31, 29/30,
30/31,
31/36, 31/35,
32/27, 32/28,
33/27, 33/32,
34/33, 34/50, 34/14,
35/36, 35/37,
36/18, 36/37,
37/18,
38/35, 38/20,
39/38, 39/20,
40/41, 40/42,
41/26, 41/43,
42/41, 42/43,
43/26,
44/42, 44/43,
45/46, 45/40,
46/40,
47/46, 47/45,
48/46, 48/47,
49/45, 49/44,
50/49, 50/44,
51/74, 51/58, 51/13, 51/50, 51/34, 51/69,
52/53, 52/48,
53/48,
54/53, 54/52,
55/53, 55/54,
56/57, 56/52,
57/72, 57/54,
58/57, 58/56,
60/5, 60/59,
61/60, 61/59,
62/5, 62/60, 62/61,
63/62, 63/61,
64/59, 64/65, 64/66,
65/67, 65/59,
66/65, 66/67,
67/71, 67/70,
68/63, 68/64,
69/63, 69/68,
70/71, 70/72,
71/55, 71/72,
72/55,
73/70, 73/57,
74/73, 74/57}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,74}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[Green,very thick] (p-14) -- (p-12);
\draw[Green,very thick] (p-14) -- (p-13);
\draw[Green,very thick] (p-14) -- (p-33);
\draw[Green,very thick] (p-34) -- (p-14);
\draw[Green,very thick] (p-51) -- (p-13);
\draw[Green,very thick] (p-51) -- (p-50);
\draw[Green,very thick] (p-51) -- (p-34);
\draw[Green,very thick] (p-51) -- (p-69);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
55/97.76/202.24/0.4/LightCyan}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/203,
2/323,
3/83,
4/23,
5/217,
6/83,
7/352,
8/172,
9/112,
10/172,
11/188,
12/188,
13/308,
14/292,
15/308,
16/188,
17/68,
18/128,
19/248,
20/128,
21/8,
22/157,
23/157,
24/157,
25/337,
26/37,
27/277,
28/308,
29/68,
30/308,
31/112,
32/172,
33/292,
34/52,
35/352,
36/112,
37/292,
38/112,
39/352,
40/112,
41/143,
42/23,
43/263,
44/128,
45/232,
46/112,
47/292,
48/68,
49/8,
50/8,
51/112,
52/188,
53/8,
54/188,
55/52,
56/68,
57/52,
58/188,
59/337,
60/337,
61/37,
62/217,
63/232,
64/128,
65/8,
66/128,
67/8,
68/352,
69/352,
70/232,
71/352,
72/172,
73/292,
74/172}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
Äußerlich kein Unterschied, nur in der Eingabe sind die Polynome ersetzt. Anstelle der Umformungsschritte kann man den Graph auch von hier aus ins Streichholzprogramm kopieren.
Anschließend mit Button "Kanten" die Beschriftung ausschalten und mit Knopf "Start_neunterWinkel" links vom Graph die Animation starten.
Button "Newtonpolynom(10)" hat noch viele viele Mängel und ist auch nicht als endgültige Lösung gedacht, deshalb nur Testbutton. Es soll nur ein Test sein, ob das ein halbwegs brauchbares Ergebnis liefert, dass man wenigstens ungefähr die Beweglichkeit im Blick hat und so Kanten zum Um- und Einsetzen suchen kann.
|
Profil
Quote
Link |
StefanVogel
Senior
Dabei seit: 26.11.2005
Mitteilungen: 3446
Aus: Raun
| Beitrag No.1902, eingetragen 2020-02-15 05:55
|
Weitere Newtonpolynome:
Im letzten Graph setze ich Kante P9-P11 ein und entferne dafür Kante P4-P6 und ebenso alle dazu symmetrischen Kanten. Dann Button neue Eingabe "Rahmen zuerst" und vor dem Testbutton "Newtonpolynom(10)" setze ich noch blauerWinkel an das Ende der Liste der Winkel, damit dieser als Parameter in den Newtonpolynomen erscheint. neunterWinkel als Parameter ergab kein brauchbares Ergebnis und nach verschiedenen anderen Versuchen habe ich schließlich folgenden Graph erhalten
74 Knoten, 16×Grad 3, 54×Grad 4, 4×Grad 6, 0 Überschneidungen
144 Kanten, minimal 0.99999999999990096811, maximal 1.00000000000010635937
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1902_1a = #1894-1 mit 4 umgelegten Kanten, dann blauerWinkel+10*1</Bildtext>
%<Ausrichten von="18" nach="55"/>
%<Winkel size="18" color="blue" id="blauerWinkel" value="148.95502437185988"/>
%<Feinjustieren Anzahl="1"/>
%<Rechenweg>
%gruenerWinkel=135.52248781407005+(blauerWinkel-148.95502437185988)*((-0.13401954390838)+(blauerWinkel-149.95502437185988)*((-0.01563260986196724)+(blauerWinkel-150.95502437185988)*((0.00017091138651418683)+(blauerWinkel-151.95502437185988)*((-0.000001846049790070005)+(blauerWinkel-152.95502437185988)*((2.2553862777385804e-9)+(blauerWinkel-153.95502437185988)*((3.220487580294345e-11)+(blauerWinkel-154.95502437185988)*((-5.102390467712281e-12)+(blauerWinkel-155.95502437185988)*((5.0566958004057103e-14)+(blauerWinkel-156.95502437185988)*((-2.4870562162008914e-15)+(blauerWinkel-157.95502437185988)*((1.4262547123617674e-17)))))))))));
%orangerWinkel=104.47751218592991+(blauerWinkel-148.95502437185988)*((0.13357316342579395)+(blauerWinkel-149.95502437185988)*((0.01520338351935635)+(blauerWinkel-150.95502437185988)*((-0.00016144706818484641)+(blauerWinkel-151.95502437185988)*((0.0000021058598237052236)+(blauerWinkel-152.95502437185988)*((-1.0005154749137547e-8)+(blauerWinkel-153.95502437185988)*((2.0668908559974283e-10)+(blauerWinkel-154.95502437185988)*((3.64730327071304e-12)+(blauerWinkel-155.95502437185988)*((-5.0157761548087156e-14)+(blauerWinkel-156.95502437185988)*((4.0883228625250085e-15)+(blauerWinkel-157.95502437185988)*((-3.432488515719872e-17)))))))))));
%vierterWinkel=75.52248781407012+(blauerWinkel-148.95502437185988)*((-0.13401954390846527)+(blauerWinkel-149.95502437185988)*((-0.015632609861931712)+(blauerWinkel-150.95502437185988)*((0.00017091138651655532)+(blauerWinkel-151.95502437185988)*((-0.0000018460497977675557)+(blauerWinkel-152.95502437185988)*((2.2553906594196878e-9)+(blauerWinkel-153.95502437185988)*((3.220323760711625e-11)+(blauerWinkel-154.95502437185988)*((-5.101933690271561e-12)+(blauerWinkel-155.95502437185988)*((5.046298475415152e-14)+(blauerWinkel-156.95502437185988)*((-2.465439180228494e-15)+(blauerWinkel-157.95502437185988)*((9.825572171682454e-18)))))))))));
%fuenfterWinkel=88.95502437185979+(blauerWinkel-148.95502437185988)*((0.9999999999984368)+(blauerWinkel-149.95502437185988)*((1.8474111129762605e-12)+(blauerWinkel-150.95502437185988)*((-1.0444978215673473e-12)+(blauerWinkel-151.95502437185988)*((3.8487731520338763e-13)+(blauerWinkel-152.95502437185988)*((-1.1013412404281553e-13)+(blauerWinkel-153.95502437185988)*((2.7257208835686063e-14)+(blauerWinkel-154.95502437185988)*((-6.132660516977055e-15)+(blauerWinkel-155.95502437185988)*((1.284686642780538e-15)+(blauerWinkel-156.95502437185988)*((-2.5587997329455987e-16)+(blauerWinkel-157.95502437185988)*((4.881065177752363e-17)))))))))));
%sechsterWinkel=106.56746344221033+(blauerWinkel-148.95502437185988)*((-1.8655340756059786)+(blauerWinkel-149.95502437185988)*((0.016061836201068047)+(blauerWinkel-150.95502437185988)*((-0.000180375702915588)+(blauerWinkel-151.95502437185988)*((0.0000015862390672083393)+(blauerWinkel-152.95502437185988)*((5.494573921775703e-9)+(blauerWinkel-153.95502437185988)*((-2.711455159165118e-10)+(blauerWinkel-154.95502437185988)*((6.568025840994326e-12)+(blauerWinkel-155.95502437185988)*((-5.323466533701143e-14)+(blauerWinkel-156.95502437185988)*((1.3469139527593563e-15)+(blauerWinkel-157.95502437185988)*((-8.337050312758024e-17)))))))))));
%siebenterWinkel=148.95502437185985+(blauerWinkel-148.95502437185988)*((0.9999999999983515)+(blauerWinkel-149.95502437185988)*((1.9184653865522705e-12)+(blauerWinkel-150.95502437185988)*((-1.0705510552118842e-12)+(blauerWinkel-151.95502437185988)*((3.943512183468556e-13)+(blauerWinkel-152.95502437185988)*((-1.1558161835030962e-13)+(blauerWinkel-153.95502437185988)*((3.0000693287648675e-14)+(blauerWinkel-154.95502437185988)*((-7.156180410155296e-15)+(blauerWinkel-155.95502437185988)*((1.5803936642600644e-15)+(blauerWinkel-156.95502437185988)*((-3.253521301088466e-16)+(blauerWinkel-157.95502437185988)*((6.255627017764463e-17)))))))))));
%achterWinkel=135.52248781407008+(blauerWinkel-148.95502437185988)*((-0.13401954390860737)+(blauerWinkel-149.95502437185988)*((-0.015632609861739866)+(blauerWinkel-150.95502437185988)*((0.00017091138641471085)+(blauerWinkel-151.95502437185988)*((-0.0000018460497687537228)+(blauerWinkel-152.95502437185988)*((2.2553872251279913e-9)+(blauerWinkel-153.95502437185988)*((3.220227048003076e-11)+(blauerWinkel-154.95502437185988)*((-5.101200590709603e-12)+(blauerWinkel-155.95502437185988)*((5.0189834646261943e-14)+(blauerWinkel-156.95502437185988)*((-2.3890746299755062e-15)+(blauerWinkel-157.95502437185988)*((-7.675616697290482e-18)))))))))));
%neunterWinkel=104.47751218592991+(blauerWinkel-148.95502437185988)*((0.1335731634261208)+(blauerWinkel-149.95502437185988)*((0.015203383518979763)+(blauerWinkel-150.95502437185988)*((-0.0001614470679811575)+(blauerWinkel-151.95502437185988)*((0.000002105859759164254)+(blauerWinkel-152.95502437185988)*((-1.0005143143605743e-8)+(blauerWinkel-153.95502437185988)*((2.0668863164203418e-10)+(blauerWinkel-154.95502437185988)*((3.646880328511662e-12)+(blauerWinkel-155.95502437185988)*((-4.9992461642598194e-14)+(blauerWinkel-156.95502437185988)*((4.048221676833542e-15)+(blauerWinkel-157.95502437185988)*((-2.6508286772677843e-17)))))))))));
%P[5]=[81.19895302251417,-23.62079730309884]; P[2]=[31.542078892744694,-17.773160886543025]; D=ab(5,2); A(2,5); N(4,2,5); N(3,2,4); N(1,2,3); M(8,1,2,blauerWinkel); N(7,8,1); N(9,8,7); N(10,8,9); M(16,10,8,gruenerWinkel); N(15,16,10); N(17,16,15); N(18,16,17); M(37,18,16,orangerWinkel); N(36,18,37); N(35,36,37); N(31,36,35); M(30,31,36,vierterWinkel); N(29,31,30); N(28,29,30); N(22,29,28); M(24,22,29,fuenfterWinkel); N(23,22,24); N(25,23,24); N(26,23,25); M(43,26,23,sechsterWinkel); N(41,26,43); N(42,41,43); N(40,41,42); M(46,40,41,siebenterWinkel); N(45,46,40); N(47,46,45); N(48,46,47); M(53,48,46,achterWinkel); N(52,53,48); N(54,53,52); N(55,53,54); M(72,55,53,neunterWinkel); N(71,55,72); N(70,71,72); N(67,71,70); Q(59,67,5,2*D,2*D); A(59,67); A(59,5); H(60,5,59,2); A(60,5); L(62,5,60); H(65,67,59,2); A(65,67); L(66,65,67); A(65,59); L(64,59,65); A(64,66); A(60,59); L(61,60,59); A(62,61); N(11,9,7); N(20,37,17); N(32,28,30); N(38,35,20); N(49,47,45); N(57,72,54); N(68,64,66); N(73,70,57); N(6,11,3); N(19,20,15); N(27,24,32); N(44,49,42); N(56,57,52); N(63,61,68); N(12,11,6); N(21,20,19); N(33,27,32); N(39,38,20); N(50,49,44); N(58,57,56); N(69,63,68); N(74,73,57); N(13,69,12); N(14,33,13); N(34,14,50); N(51,69,34);
%A(14,39); R(14,39,"green");
%A(14,21); R(14,21,"green");
%A(14,12); R(14,12,"green");
%A(34,33); R(34,33,"green");
%A(51,74); R(51,74,"green");
%A(51,58); R(51,58,"green");
%A(51,13); R(51,13,"green");
%A(51,50); R(51,50,"green");
%</Rechenweg>
%
%<Knopf id="Stopp_alleWinkel" color="LightGrey"/>
%
%<Knopf id="Start_blauerWinkel" color="blue"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#blauerWinkel" attributeName="value" values="0;28;0;-25;0" dur="10" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_blauerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.85/0.23,
2/2.84/0.12,
3/2.45/1.04,
4/3.44/0.92,
5/3.84/0.00,
6/3.05/1.84,
7/1.99/1.22,
8/1.06/0.85,
9/1.20/1.84,
10/0.27/1.46,
11/2.12/2.22,
12/2.91/2.83,
13/3.84/2.45,
14/3.70/3.44,
15/1.06/2.07,
16/0.14/2.45,
17/0.93/3.06,
18/0.00/3.44,
19/1.99/2.45,
20/1.85/3.44,
21/2.78/3.06,
22/1.85/6.65,
23/2.84/6.76,
24/2.45/5.85,
25/3.44/5.96,
26/3.84/6.88,
27/3.05/5.04,
28/1.99/5.66,
29/1.06/6.03,
30/1.20/5.04,
31/0.27/5.42,
32/2.12/4.67,
33/2.91/4.05,
34/3.84/4.43,
35/1.06/4.81,
36/0.14/4.43,
37/0.93/3.82,
38/1.99/4.43,
39/2.78/3.82,
40/5.82/6.65,
41/4.83/6.76,
42/5.23/5.85,
43/4.23/5.96,
44/4.63/5.04,
45/5.69/5.66,
46/6.61/6.03,
47/6.48/5.04,
48/7.40/5.42,
49/5.55/4.67,
50/4.76/4.05,
51/3.97/3.44,
52/6.61/4.81,
53/7.54/4.43,
54/6.75/3.82,
55/7.68/3.44,
56/5.69/4.43,
57/5.82/3.44,
58/4.90/3.82,
59/5.82/0.23,
60/4.83/0.12,
61/5.23/1.04,
62/4.23/0.92,
63/4.63/1.84,
64/5.69/1.22,
65/6.61/0.85,
66/6.48/1.84,
67/7.40/1.46,
68/5.55/2.22,
69/4.76/2.83,
70/6.61/2.07,
71/7.54/2.45,
72/6.75/3.06,
73/5.69/2.45,
74/4.90/3.06}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
1/353.28/502.24/0.4/Blue}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
1/2, 1/3,
2/5,
3/2, 3/4,
4/2, 4/5,
6/11, 6/3,
7/8, 7/1,
8/1,
9/8, 9/7,
10/8, 10/9,
11/9, 11/7,
12/11, 12/6,
13/69, 13/12,
14/33, 14/13, 14/39, 14/21, 14/12,
15/16, 15/10,
16/10,
17/16, 17/15,
18/16, 18/17,
19/20, 19/15,
20/37, 20/17,
21/20, 21/19,
22/29, 22/28,
23/22, 23/24,
24/22,
25/23, 25/24,
26/23, 26/25,
27/24, 27/32,
28/29, 28/30,
29/31, 29/30,
30/31,
31/36, 31/35,
32/28, 32/30,
33/27, 33/32,
34/14, 34/50, 34/33,
35/36, 35/37,
36/18, 36/37,
37/18,
38/35, 38/20,
39/38, 39/20,
40/41, 40/42,
41/26, 41/43,
42/41, 42/43,
43/26,
44/49, 44/42,
45/46, 45/40,
46/40,
47/46, 47/45,
48/46, 48/47,
49/47, 49/45,
50/49, 50/44,
51/69, 51/34, 51/74, 51/58, 51/13, 51/50,
52/53, 52/48,
53/48,
54/53, 54/52,
55/53, 55/54,
56/57, 56/52,
57/72, 57/54,
58/57, 58/56,
60/5, 60/59,
61/60, 61/59,
62/5, 62/60, 62/61,
63/61, 63/68,
64/59, 64/65, 64/66,
65/67, 65/59,
66/65, 66/67,
67/71, 67/70,
68/64, 68/66,
69/63, 69/68,
70/71, 70/72,
71/55, 71/72,
72/55,
73/70, 73/57,
74/73, 74/57}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,74}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
1/353.28/502.24/0.4/Blue}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/203,
2/263,
3/83,
4/23,
5/217,
6/308,
7/292,
8/172,
9/112,
10/172,
11/52,
12/188,
13/232,
14/68,
15/308,
16/248,
17/68,
18/232,
19/248,
20/128,
21/8,
22/68,
23/97,
24/217,
25/277,
26/37,
27/52,
28/68,
29/68,
30/248,
31/112,
32/308,
33/172,
34/128,
35/52,
36/232,
37/352,
38/112,
39/352,
40/112,
41/143,
42/263,
43/263,
44/128,
45/232,
46/52,
47/232,
48/68,
49/8,
50/248,
51/112,
52/188,
53/308,
54/248,
55/52,
56/68,
57/308,
58/188,
59/337,
60/277,
61/37,
62/97,
63/232,
64/128,
65/308,
66/8,
67/292,
68/128,
69/112,
70/172,
71/292,
72/112,
73/292,
74/172}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/57230efa08037acdb8e2449a4e9fbdd5.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1902_1a = #1894-1 mit 4 umgelegten Kanten, dann blauerWinkel+10*1</Bildtext>
%<Ausrichten von=\"18\" nach=\"55\"/>
%<Winkel size=\"18\" color=\"blue\" id=\"blauerWinkel\" value=\"148.95502437185988\"/>
%<Feinjustieren Anzahl=\"1\"/>
%<Rechenweg>
%gruenerWinkel=135.52248781407005+(blauerWinkel-148.95502437185988)*((-0.13401954390838)+(blauerWinkel-149.95502437185988)*((-0.01563260986196724)+(blauerWinkel-150.95502437185988)*((0.00017091138651418683)+(blauerWinkel-151.95502437185988)*((-0.000001846049790070005)+(blauerWinkel-152.95502437185988)*((2.2553862777385804e-9)+(blauerWinkel-153.95502437185988)*((3.220487580294345e-11)+(blauerWinkel-154.95502437185988)*((-5.102390467712281e-12)+(blauerWinkel-155.95502437185988)*((5.0566958004057103e-14)+(blauerWinkel-156.95502437185988)*((-2.4870562162008914e-15)+(blauerWinkel-157.95502437185988)*((1.4262547123617674e-17)))))))))));
%orangerWinkel=104.47751218592991+(blauerWinkel-148.95502437185988)*((0.13357316342579395)+(blauerWinkel-149.95502437185988)*((0.01520338351935635)+(blauerWinkel-150.95502437185988)*((-0.00016144706818484641)+(blauerWinkel-151.95502437185988)*((0.0000021058598237052236)+(blauerWinkel-152.95502437185988)*((-1.0005154749137547e-8)+(blauerWinkel-153.95502437185988)*((2.0668908559974283e-10)+(blauerWinkel-154.95502437185988)*((3.64730327071304e-12)+(blauerWinkel-155.95502437185988)*((-5.0157761548087156e-14)+(blauerWinkel-156.95502437185988)*((4.0883228625250085e-15)+(blauerWinkel-157.95502437185988)*((-3.432488515719872e-17)))))))))));
%vierterWinkel=75.52248781407012+(blauerWinkel-148.95502437185988)*((-0.13401954390846527)+(blauerWinkel-149.95502437185988)*((-0.015632609861931712)+(blauerWinkel-150.95502437185988)*((0.00017091138651655532)+(blauerWinkel-151.95502437185988)*((-0.0000018460497977675557)+(blauerWinkel-152.95502437185988)*((2.2553906594196878e-9)+(blauerWinkel-153.95502437185988)*((3.220323760711625e-11)+(blauerWinkel-154.95502437185988)*((-5.101933690271561e-12)+(blauerWinkel-155.95502437185988)*((5.046298475415152e-14)+(blauerWinkel-156.95502437185988)*((-2.465439180228494e-15)+(blauerWinkel-157.95502437185988)*((9.825572171682454e-18)))))))))));
%fuenfterWinkel=88.95502437185979+(blauerWinkel-148.95502437185988)*((0.9999999999984368)+(blauerWinkel-149.95502437185988)*((1.8474111129762605e-12)+(blauerWinkel-150.95502437185988)*((-1.0444978215673473e-12)+(blauerWinkel-151.95502437185988)*((3.8487731520338763e-13)+(blauerWinkel-152.95502437185988)*((-1.1013412404281553e-13)+(blauerWinkel-153.95502437185988)*((2.7257208835686063e-14)+(blauerWinkel-154.95502437185988)*((-6.132660516977055e-15)+(blauerWinkel-155.95502437185988)*((1.284686642780538e-15)+(blauerWinkel-156.95502437185988)*((-2.5587997329455987e-16)+(blauerWinkel-157.95502437185988)*((4.881065177752363e-17)))))))))));
%sechsterWinkel=106.56746344221033+(blauerWinkel-148.95502437185988)*((-1.8655340756059786)+(blauerWinkel-149.95502437185988)*((0.016061836201068047)+(blauerWinkel-150.95502437185988)*((-0.000180375702915588)+(blauerWinkel-151.95502437185988)*((0.0000015862390672083393)+(blauerWinkel-152.95502437185988)*((5.494573921775703e-9)+(blauerWinkel-153.95502437185988)*((-2.711455159165118e-10)+(blauerWinkel-154.95502437185988)*((6.568025840994326e-12)+(blauerWinkel-155.95502437185988)*((-5.323466533701143e-14)+(blauerWinkel-156.95502437185988)*((1.3469139527593563e-15)+(blauerWinkel-157.95502437185988)*((-8.337050312758024e-17)))))))))));
%siebenterWinkel=148.95502437185985+(blauerWinkel-148.95502437185988)*((0.9999999999983515)+(blauerWinkel-149.95502437185988)*((1.9184653865522705e-12)+(blauerWinkel-150.95502437185988)*((-1.0705510552118842e-12)+(blauerWinkel-151.95502437185988)*((3.943512183468556e-13)+(blauerWinkel-152.95502437185988)*((-1.1558161835030962e-13)+(blauerWinkel-153.95502437185988)*((3.0000693287648675e-14)+(blauerWinkel-154.95502437185988)*((-7.156180410155296e-15)+(blauerWinkel-155.95502437185988)*((1.5803936642600644e-15)+(blauerWinkel-156.95502437185988)*((-3.253521301088466e-16)+(blauerWinkel-157.95502437185988)*((6.255627017764463e-17)))))))))));
%achterWinkel=135.52248781407008+(blauerWinkel-148.95502437185988)*((-0.13401954390860737)+(blauerWinkel-149.95502437185988)*((-0.015632609861739866)+(blauerWinkel-150.95502437185988)*((0.00017091138641471085)+(blauerWinkel-151.95502437185988)*((-0.0000018460497687537228)+(blauerWinkel-152.95502437185988)*((2.2553872251279913e-9)+(blauerWinkel-153.95502437185988)*((3.220227048003076e-11)+(blauerWinkel-154.95502437185988)*((-5.101200590709603e-12)+(blauerWinkel-155.95502437185988)*((5.0189834646261943e-14)+(blauerWinkel-156.95502437185988)*((-2.3890746299755062e-15)+(blauerWinkel-157.95502437185988)*((-7.675616697290482e-18)))))))))));
%neunterWinkel=104.47751218592991+(blauerWinkel-148.95502437185988)*((0.1335731634261208)+(blauerWinkel-149.95502437185988)*((0.015203383518979763)+(blauerWinkel-150.95502437185988)*((-0.0001614470679811575)+(blauerWinkel-151.95502437185988)*((0.000002105859759164254)+(blauerWinkel-152.95502437185988)*((-1.0005143143605743e-8)+(blauerWinkel-153.95502437185988)*((2.0668863164203418e-10)+(blauerWinkel-154.95502437185988)*((3.646880328511662e-12)+(blauerWinkel-155.95502437185988)*((-4.9992461642598194e-14)+(blauerWinkel-156.95502437185988)*((4.048221676833542e-15)+(blauerWinkel-157.95502437185988)*((-2.6508286772677843e-17)))))))))));
%P[5]=[81.19895302251417,-23.62079730309884]; P[2]=[31.542078892744694,-17.773160886543025]; D=ab(5,2); A(2,5); N(4,2,5); N(3,2,4); N(1,2,3); M(8,1,2,blauerWinkel); N(7,8,1); N(9,8,7); N(10,8,9); M(16,10,8,gruenerWinkel); N(15,16,10); N(17,16,15); N(18,16,17); M(37,18,16,orangerWinkel); N(36,18,37); N(35,36,37); N(31,36,35); M(30,31,36,vierterWinkel); N(29,31,30); N(28,29,30); N(22,29,28); M(24,22,29,fuenfterWinkel); N(23,22,24); N(25,23,24); N(26,23,25); M(43,26,23,sechsterWinkel); N(41,26,43); N(42,41,43); N(40,41,42); M(46,40,41,siebenterWinkel); N(45,46,40); N(47,46,45); N(48,46,47); M(53,48,46,achterWinkel); N(52,53,48); N(54,53,52); N(55,53,54); M(72,55,53,neunterWinkel); N(71,55,72); N(70,71,72); N(67,71,70); Q(59,67,5,2*D,2*D); A(59,67); A(59,5); H(60,5,59,2); A(60,5); L(62,5,60); H(65,67,59,2); A(65,67); L(66,65,67); A(65,59); L(64,59,65); A(64,66); A(60,59); L(61,60,59); A(62,61); N(11,9,7); N(20,37,17); N(32,28,30); N(38,35,20); N(49,47,45); N(57,72,54); N(68,64,66); N(73,70,57); N(6,11,3); N(19,20,15); N(27,24,32); N(44,49,42); N(56,57,52); N(63,61,68); N(12,11,6); N(21,20,19); N(33,27,32); N(39,38,20); N(50,49,44); N(58,57,56); N(69,63,68); N(74,73,57); N(13,69,12); N(14,33,13); N(34,14,50); N(51,69,34);
%A(14,39); R(14,39,\"green\");
%A(14,21); R(14,21,\"green\");
%A(14,12); R(14,12,\"green\");
%A(34,33); R(34,33,\"green\");
%A(51,74); R(51,74,\"green\");
%A(51,58); R(51,58,\"green\");
%A(51,13); R(51,13,\"green\");
%A(51,50); R(51,50,\"green\");
%</Rechenweg>
%
%<Knopf id=\"Stopp_alleWinkel\" color=\"LightGrey\"/>
%
%<Knopf id=\"Start_blauerWinkel\" color=\"blue\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#blauerWinkel\" attributeName=\"value\" values=\"0;28;0;-25;0\" dur=\"10\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_blauerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.85/0.23,
2/2.84/0.12,
3/2.45/1.04,
4/3.44/0.92,
5/3.84/0.00,
6/3.05/1.84,
7/1.99/1.22,
8/1.06/0.85,
9/1.20/1.84,
10/0.27/1.46,
11/2.12/2.22,
12/2.91/2.83,
13/3.84/2.45,
14/3.70/3.44,
15/1.06/2.07,
16/0.14/2.45,
17/0.93/3.06,
18/0.00/3.44,
19/1.99/2.45,
20/1.85/3.44,
21/2.78/3.06,
22/1.85/6.65,
23/2.84/6.76,
24/2.45/5.85,
25/3.44/5.96,
26/3.84/6.88,
27/3.05/5.04,
28/1.99/5.66,
29/1.06/6.03,
30/1.20/5.04,
31/0.27/5.42,
32/2.12/4.67,
33/2.91/4.05,
34/3.84/4.43,
35/1.06/4.81,
36/0.14/4.43,
37/0.93/3.82,
38/1.99/4.43,
39/2.78/3.82,
40/5.82/6.65,
41/4.83/6.76,
42/5.23/5.85,
43/4.23/5.96,
44/4.63/5.04,
45/5.69/5.66,
46/6.61/6.03,
47/6.48/5.04,
48/7.40/5.42,
49/5.55/4.67,
50/4.76/4.05,
51/3.97/3.44,
52/6.61/4.81,
53/7.54/4.43,
54/6.75/3.82,
55/7.68/3.44,
56/5.69/4.43,
57/5.82/3.44,
58/4.90/3.82,
59/5.82/0.23,
60/4.83/0.12,
61/5.23/1.04,
62/4.23/0.92,
63/4.63/1.84,
64/5.69/1.22,
65/6.61/0.85,
66/6.48/1.84,
67/7.40/1.46,
68/5.55/2.22,
69/4.76/2.83,
70/6.61/2.07,
71/7.54/2.45,
72/6.75/3.06,
73/5.69/2.45,
74/4.90/3.06}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
1/353.28/502.24/0.4/Blue}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
1/2, 1/3,
2/5,
3/2, 3/4,
4/2, 4/5,
6/11, 6/3,
7/8, 7/1,
8/1,
9/8, 9/7,
10/8, 10/9,
11/9, 11/7,
12/11, 12/6,
13/69, 13/12,
14/33, 14/13, 14/39, 14/21, 14/12,
15/16, 15/10,
16/10,
17/16, 17/15,
18/16, 18/17,
19/20, 19/15,
20/37, 20/17,
21/20, 21/19,
22/29, 22/28,
23/22, 23/24,
24/22,
25/23, 25/24,
26/23, 26/25,
27/24, 27/32,
28/29, 28/30,
29/31, 29/30,
30/31,
31/36, 31/35,
32/28, 32/30,
33/27, 33/32,
34/14, 34/50, 34/33,
35/36, 35/37,
36/18, 36/37,
37/18,
38/35, 38/20,
39/38, 39/20,
40/41, 40/42,
41/26, 41/43,
42/41, 42/43,
43/26,
44/49, 44/42,
45/46, 45/40,
46/40,
47/46, 47/45,
48/46, 48/47,
49/47, 49/45,
50/49, 50/44,
51/69, 51/34, 51/74, 51/58, 51/13, 51/50,
52/53, 52/48,
53/48,
54/53, 54/52,
55/53, 55/54,
56/57, 56/52,
57/72, 57/54,
58/57, 58/56,
60/5, 60/59,
61/60, 61/59,
62/5, 62/60, 62/61,
63/61, 63/68,
64/59, 64/65, 64/66,
65/67, 65/59,
66/65, 66/67,
67/71, 67/70,
68/64, 68/66,
69/63, 69/68,
70/71, 70/72,
71/55, 71/72,
72/55,
73/70, 73/57,
74/73, 74/57}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,74}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
1/353.28/502.24/0.4/Blue}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/203,
2/263,
3/83,
4/23,
5/217,
6/308,
7/292,
8/172,
9/112,
10/172,
11/52,
12/188,
13/232,
14/68,
15/308,
16/248,
17/68,
18/232,
19/248,
20/128,
21/8,
22/68,
23/97,
24/217,
25/277,
26/37,
27/52,
28/68,
29/68,
30/248,
31/112,
32/308,
33/172,
34/128,
35/52,
36/232,
37/352,
38/112,
39/352,
40/112,
41/143,
42/263,
43/263,
44/128,
45/232,
46/52,
47/232,
48/68,
49/8,
50/248,
51/112,
52/188,
53/308,
54/248,
55/52,
56/68,
57/308,
58/188,
59/337,
60/277,
61/37,
62/97,
63/232,
64/128,
65/308,
66/8,
67/292,
68/128,
69/112,
70/172,
71/292,
72/112,
73/292,
74/172}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
[Graph ins große Eingabefenster des Streichholzprogramms kopieren, dann Buttons "neu zeichnen", "Ausrichten", "Kanten" und schließlich Animationsknopf "Start_blauerWinkel" links neben dem Graph"]
Zwei Bilder für größeren und kleineren blauerWinkel:
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1902_1a = #1894-1 mit 4 umgelegten Kanten, dann blauerWinkel+10*1</Bildtext>
%<Ausrichten von="18" nach="55"/>
%<Winkel size="18" color="blue" id="blauerWinkel" value="168.95502437185988"/>
%<Feinjustieren Anzahl="1"/>
%<Rechenweg>
%gruenerWinkel=135.52248781407005+(blauerWinkel-148.95502437185988)*((-0.13401954390838)+(blauerWinkel-149.95502437185988)*((-0.01563260986196724)+(blauerWinkel-150.95502437185988)*((0.00017091138651418683)+(blauerWinkel-151.95502437185988)*((-0.000001846049790070005)+(blauerWinkel-152.95502437185988)*((2.2553862777385804e-9)+(blauerWinkel-153.95502437185988)*((3.220487580294345e-11)+(blauerWinkel-154.95502437185988)*((-5.102390467712281e-12)+(blauerWinkel-155.95502437185988)*((5.0566958004057103e-14)+(blauerWinkel-156.95502437185988)*((-2.4870562162008914e-15)+(blauerWinkel-157.95502437185988)*((1.4262547123617674e-17)))))))))));
%orangerWinkel=104.47751218592991+(blauerWinkel-148.95502437185988)*((0.13357316342579395)+(blauerWinkel-149.95502437185988)*((0.01520338351935635)+(blauerWinkel-150.95502437185988)*((-0.00016144706818484641)+(blauerWinkel-151.95502437185988)*((0.0000021058598237052236)+(blauerWinkel-152.95502437185988)*((-1.0005154749137547e-8)+(blauerWinkel-153.95502437185988)*((2.0668908559974283e-10)+(blauerWinkel-154.95502437185988)*((3.64730327071304e-12)+(blauerWinkel-155.95502437185988)*((-5.0157761548087156e-14)+(blauerWinkel-156.95502437185988)*((4.0883228625250085e-15)+(blauerWinkel-157.95502437185988)*((-3.432488515719872e-17)))))))))));
%vierterWinkel=75.52248781407012+(blauerWinkel-148.95502437185988)*((-0.13401954390846527)+(blauerWinkel-149.95502437185988)*((-0.015632609861931712)+(blauerWinkel-150.95502437185988)*((0.00017091138651655532)+(blauerWinkel-151.95502437185988)*((-0.0000018460497977675557)+(blauerWinkel-152.95502437185988)*((2.2553906594196878e-9)+(blauerWinkel-153.95502437185988)*((3.220323760711625e-11)+(blauerWinkel-154.95502437185988)*((-5.101933690271561e-12)+(blauerWinkel-155.95502437185988)*((5.046298475415152e-14)+(blauerWinkel-156.95502437185988)*((-2.465439180228494e-15)+(blauerWinkel-157.95502437185988)*((9.825572171682454e-18)))))))))));
%fuenfterWinkel=88.95502437185979+(blauerWinkel-148.95502437185988)*((0.9999999999984368)+(blauerWinkel-149.95502437185988)*((1.8474111129762605e-12)+(blauerWinkel-150.95502437185988)*((-1.0444978215673473e-12)+(blauerWinkel-151.95502437185988)*((3.8487731520338763e-13)+(blauerWinkel-152.95502437185988)*((-1.1013412404281553e-13)+(blauerWinkel-153.95502437185988)*((2.7257208835686063e-14)+(blauerWinkel-154.95502437185988)*((-6.132660516977055e-15)+(blauerWinkel-155.95502437185988)*((1.284686642780538e-15)+(blauerWinkel-156.95502437185988)*((-2.5587997329455987e-16)+(blauerWinkel-157.95502437185988)*((4.881065177752363e-17)))))))))));
%sechsterWinkel=106.56746344221033+(blauerWinkel-148.95502437185988)*((-1.8655340756059786)+(blauerWinkel-149.95502437185988)*((0.016061836201068047)+(blauerWinkel-150.95502437185988)*((-0.000180375702915588)+(blauerWinkel-151.95502437185988)*((0.0000015862390672083393)+(blauerWinkel-152.95502437185988)*((5.494573921775703e-9)+(blauerWinkel-153.95502437185988)*((-2.711455159165118e-10)+(blauerWinkel-154.95502437185988)*((6.568025840994326e-12)+(blauerWinkel-155.95502437185988)*((-5.323466533701143e-14)+(blauerWinkel-156.95502437185988)*((1.3469139527593563e-15)+(blauerWinkel-157.95502437185988)*((-8.337050312758024e-17)))))))))));
%siebenterWinkel=148.95502437185985+(blauerWinkel-148.95502437185988)*((0.9999999999983515)+(blauerWinkel-149.95502437185988)*((1.9184653865522705e-12)+(blauerWinkel-150.95502437185988)*((-1.0705510552118842e-12)+(blauerWinkel-151.95502437185988)*((3.943512183468556e-13)+(blauerWinkel-152.95502437185988)*((-1.1558161835030962e-13)+(blauerWinkel-153.95502437185988)*((3.0000693287648675e-14)+(blauerWinkel-154.95502437185988)*((-7.156180410155296e-15)+(blauerWinkel-155.95502437185988)*((1.5803936642600644e-15)+(blauerWinkel-156.95502437185988)*((-3.253521301088466e-16)+(blauerWinkel-157.95502437185988)*((6.255627017764463e-17)))))))))));
%achterWinkel=135.52248781407008+(blauerWinkel-148.95502437185988)*((-0.13401954390860737)+(blauerWinkel-149.95502437185988)*((-0.015632609861739866)+(blauerWinkel-150.95502437185988)*((0.00017091138641471085)+(blauerWinkel-151.95502437185988)*((-0.0000018460497687537228)+(blauerWinkel-152.95502437185988)*((2.2553872251279913e-9)+(blauerWinkel-153.95502437185988)*((3.220227048003076e-11)+(blauerWinkel-154.95502437185988)*((-5.101200590709603e-12)+(blauerWinkel-155.95502437185988)*((5.0189834646261943e-14)+(blauerWinkel-156.95502437185988)*((-2.3890746299755062e-15)+(blauerWinkel-157.95502437185988)*((-7.675616697290482e-18)))))))))));
%neunterWinkel=104.47751218592991+(blauerWinkel-148.95502437185988)*((0.1335731634261208)+(blauerWinkel-149.95502437185988)*((0.015203383518979763)+(blauerWinkel-150.95502437185988)*((-0.0001614470679811575)+(blauerWinkel-151.95502437185988)*((0.000002105859759164254)+(blauerWinkel-152.95502437185988)*((-1.0005143143605743e-8)+(blauerWinkel-153.95502437185988)*((2.0668863164203418e-10)+(blauerWinkel-154.95502437185988)*((3.646880328511662e-12)+(blauerWinkel-155.95502437185988)*((-4.9992461642598194e-14)+(blauerWinkel-156.95502437185988)*((4.048221676833542e-15)+(blauerWinkel-157.95502437185988)*((-2.6508286772677843e-17)))))))))));
%P[5]=[31.74219649117,-79.36949187458876]; P[2]=[-14.33674095819476,-59.95991888759268]; D=ab(5,2); A(2,5); N(4,2,5); N(3,2,4); N(1,2,3); M(8,1,2,blauerWinkel); N(7,8,1); N(9,8,7); N(10,8,9); M(16,10,8,gruenerWinkel); N(15,16,10); N(17,16,15); N(18,16,17); M(37,18,16,orangerWinkel); N(36,18,37); N(35,36,37); N(31,36,35); M(30,31,36,vierterWinkel); N(29,31,30); N(28,29,30); N(22,29,28); M(24,22,29,fuenfterWinkel); N(23,22,24); N(25,23,24); N(26,23,25); M(43,26,23,sechsterWinkel); N(41,26,43); N(42,41,43); N(40,41,42); M(46,40,41,siebenterWinkel); N(45,46,40); N(47,46,45); N(48,46,47); M(53,48,46,achterWinkel); N(52,53,48); N(54,53,52); N(55,53,54); M(72,55,53,neunterWinkel); N(71,55,72); N(70,71,72); N(67,71,70); Q(59,67,5,2*D,2*D); A(59,67); A(59,5); H(60,5,59,2); A(60,5); L(62,5,60); H(65,67,59,2); A(65,67); L(66,65,67); A(65,59); L(64,59,65); A(64,66); A(60,59); L(61,60,59); A(62,61); N(11,9,7); N(20,37,17); N(32,28,30); N(38,35,20); N(49,47,45); N(57,72,54); N(68,64,66); N(73,70,57); N(6,11,3); N(19,20,15); N(27,24,32); N(44,49,42); N(56,57,52); N(63,61,68); N(12,11,6); N(21,20,19); N(33,27,32); N(39,38,20); N(50,49,44); N(58,57,56); N(69,63,68); N(74,73,57); N(13,69,12); N(14,33,13); N(34,14,50); N(51,69,34);
%A(14,39); R(14,39,"green");
%A(14,21); R(14,21,"green");
%A(14,12); R(14,12,"green");
%A(34,33); R(34,33,"green");
%A(51,74); R(51,74,"green");
%A(51,58); R(51,58,"green");
%A(51,13); R(51,13,"green");
%A(51,50); R(51,50,"green");
%</Rechenweg>
%
%<Knopf id="Stopp_alleWinkel" color="LightGrey"/>
%
%<Knopf id="Start_blauerWinkel" color="blue"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#blauerWinkel" attributeName="value" values="0;28;0;-25;0" dur="10" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_blauerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.80/0.78,
2/2.72/0.39,
3/2.60/1.38,
4/3.52/0.99,
5/3.64/0.00,
6/2.84/2.35,
7/1.87/1.77,
8/0.97/1.33,
9/1.04/2.33,
10/0.14/1.89,
11/1.93/2.77,
12/2.75/3.35,
13/3.64/2.89,
14/3.594/3.887,
15/0.97/2.45,
16/0.07/2.89,
17/0.90/3.45,
18/0.00/3.89,
19/1.87/2.89,
20/1.80/3.89,
21/2.70/3.45,
22/1.80/7.00,
23/2.72/7.39,
24/2.60/6.39,
25/3.52/6.78,
26/3.64/7.77,
27/2.84/5.42,
28/1.87/6.00,
29/0.97/6.44,
30/1.04/5.44,
31/0.14/5.88,
32/1.93/5.00,
33/2.75/4.43,
34/3.64/4.89,
35/0.97/5.32,
36/0.07/4.88,
37/0.90/4.33,
38/1.87/4.88,
39/2.70/4.33,
40/5.49/7.00,
41/4.56/7.39,
42/4.69/6.39,
43/3.77/6.78,
44/4.44/5.42,
45/5.42/6.00,
46/6.32/6.44,
47/6.25/5.44,
48/7.15/5.88,
49/5.35/5.00,
50/4.53/4.43,
51/3.690/3.887,
52/6.32/5.32,
53/7.21/4.88,
54/6.39/4.33,
55/7.28/3.89,
56/5.42/4.88,
57/5.49/3.89,
58/4.59/4.33,
59/5.49/0.78,
60/4.56/0.39,
61/4.69/1.38,
62/3.77/0.99,
63/4.44/2.35,
64/5.42/1.77,
65/6.32/1.33,
66/6.25/2.33,
67/7.15/1.89,
68/5.35/2.77,
69/4.53/3.35,
70/6.32/2.45,
71/7.21/2.89,
72/6.39/3.45,
73/5.42/2.89,
74/4.59/3.45}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
1/337.16/506.11/0.4/Blue}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
1/2, 1/3,
2/5,
3/2, 3/4,
4/2, 4/5,
6/11, 6/3,
7/8, 7/1,
8/1,
9/8, 9/7,
10/8, 10/9,
11/9, 11/7,
12/11, 12/6,
13/69, 13/12,
14/33, 14/13, 14/39, 14/21, 14/12,
15/16, 15/10,
16/10,
17/16, 17/15,
18/16, 18/17,
19/20, 19/15,
20/37, 20/17,
21/20, 21/19,
22/29, 22/28,
23/22, 23/24,
24/22,
25/23, 25/24,
26/23, 26/25,
27/24, 27/32,
28/29, 28/30,
29/31, 29/30,
30/31,
31/36, 31/35,
32/28, 32/30,
33/27, 33/32,
34/14, 34/50, 34/33,
35/36, 35/37,
36/18, 36/37,
37/18,
38/35, 38/20,
39/38, 39/20,
40/41, 40/42,
41/26, 41/43,
42/41, 42/43,
43/26,
44/49, 44/42,
45/46, 45/40,
46/40,
47/46, 47/45,
48/46, 48/47,
49/47, 49/45,
50/49, 50/44,
51/69, 51/34, 51/74, 51/58, 51/13, 51/50,
52/53, 52/48,
53/48,
54/53, 54/52,
55/53, 55/54,
56/57, 56/52,
57/72, 57/54,
58/57, 58/56,
60/5, 60/59,
61/60, 61/59,
62/5, 62/60, 62/61,
63/61, 63/68,
64/59, 64/65, 64/66,
65/67, 65/59,
66/65, 66/67,
67/71, 67/70,
68/64, 68/66,
69/63, 69/68,
70/71, 70/72,
71/55, 71/72,
72/55,
73/70, 73/57,
74/73, 74/57}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,74}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
1/337.16/506.11/0.4/Blue}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/187,
2/187,
3/127,
4/7,
5/233,
6/305,
7/356,
8/176,
9/116,
10/176,
11/56,
12/65,
13/303,
14/297,
15/4,
16/184,
17/4,
18/124,
19/244,
20/124,
21/4,
22/173,
23/173,
24/293,
25/353,
26/127,
27/55,
28/4,
29/124,
30/184,
31/184,
32/175,
33/295,
34/57,
35/356,
36/116,
37/356,
38/116,
39/356,
40/7,
41/7,
42/307,
43/187,
44/125,
45/116,
46/116,
47/356,
48/64,
49/5,
50/3,
51/243,
52/124,
53/4,
54/184,
55/56,
56/64,
57/56,
58/184,
59/353,
60/353,
61/53,
62/173,
63/235,
64/124,
65/304,
66/124,
67/296,
68/124,
69/357,
70/176,
71/356,
72/116,
73/296,
74/176}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/4a18f9ce9a681b4de8ccfe12a6ae365a.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1902_1a = #1894-1 mit 4 umgelegten Kanten, dann blauerWinkel+10*1</Bildtext>
%<Ausrichten von=\"18\" nach=\"55\"/>
%<Winkel size=\"18\" color=\"blue\" id=\"blauerWinkel\" value=\"168.95502437185988\"/>
%<Feinjustieren Anzahl=\"1\"/>
%<Rechenweg>
%gruenerWinkel=135.52248781407005+(blauerWinkel-148.95502437185988)*((-0.13401954390838)+(blauerWinkel-149.95502437185988)*((-0.01563260986196724)+(blauerWinkel-150.95502437185988)*((0.00017091138651418683)+(blauerWinkel-151.95502437185988)*((-0.000001846049790070005)+(blauerWinkel-152.95502437185988)*((2.2553862777385804e-9)+(blauerWinkel-153.95502437185988)*((3.220487580294345e-11)+(blauerWinkel-154.95502437185988)*((-5.102390467712281e-12)+(blauerWinkel-155.95502437185988)*((5.0566958004057103e-14)+(blauerWinkel-156.95502437185988)*((-2.4870562162008914e-15)+(blauerWinkel-157.95502437185988)*((1.4262547123617674e-17)))))))))));
%orangerWinkel=104.47751218592991+(blauerWinkel-148.95502437185988)*((0.13357316342579395)+(blauerWinkel-149.95502437185988)*((0.01520338351935635)+(blauerWinkel-150.95502437185988)*((-0.00016144706818484641)+(blauerWinkel-151.95502437185988)*((0.0000021058598237052236)+(blauerWinkel-152.95502437185988)*((-1.0005154749137547e-8)+(blauerWinkel-153.95502437185988)*((2.0668908559974283e-10)+(blauerWinkel-154.95502437185988)*((3.64730327071304e-12)+(blauerWinkel-155.95502437185988)*((-5.0157761548087156e-14)+(blauerWinkel-156.95502437185988)*((4.0883228625250085e-15)+(blauerWinkel-157.95502437185988)*((-3.432488515719872e-17)))))))))));
%vierterWinkel=75.52248781407012+(blauerWinkel-148.95502437185988)*((-0.13401954390846527)+(blauerWinkel-149.95502437185988)*((-0.015632609861931712)+(blauerWinkel-150.95502437185988)*((0.00017091138651655532)+(blauerWinkel-151.95502437185988)*((-0.0000018460497977675557)+(blauerWinkel-152.95502437185988)*((2.2553906594196878e-9)+(blauerWinkel-153.95502437185988)*((3.220323760711625e-11)+(blauerWinkel-154.95502437185988)*((-5.101933690271561e-12)+(blauerWinkel-155.95502437185988)*((5.046298475415152e-14)+(blauerWinkel-156.95502437185988)*((-2.465439180228494e-15)+(blauerWinkel-157.95502437185988)*((9.825572171682454e-18)))))))))));
%fuenfterWinkel=88.95502437185979+(blauerWinkel-148.95502437185988)*((0.9999999999984368)+(blauerWinkel-149.95502437185988)*((1.8474111129762605e-12)+(blauerWinkel-150.95502437185988)*((-1.0444978215673473e-12)+(blauerWinkel-151.95502437185988)*((3.8487731520338763e-13)+(blauerWinkel-152.95502437185988)*((-1.1013412404281553e-13)+(blauerWinkel-153.95502437185988)*((2.7257208835686063e-14)+(blauerWinkel-154.95502437185988)*((-6.132660516977055e-15)+(blauerWinkel-155.95502437185988)*((1.284686642780538e-15)+(blauerWinkel-156.95502437185988)*((-2.5587997329455987e-16)+(blauerWinkel-157.95502437185988)*((4.881065177752363e-17)))))))))));
%sechsterWinkel=106.56746344221033+(blauerWinkel-148.95502437185988)*((-1.8655340756059786)+(blauerWinkel-149.95502437185988)*((0.016061836201068047)+(blauerWinkel-150.95502437185988)*((-0.000180375702915588)+(blauerWinkel-151.95502437185988)*((0.0000015862390672083393)+(blauerWinkel-152.95502437185988)*((5.494573921775703e-9)+(blauerWinkel-153.95502437185988)*((-2.711455159165118e-10)+(blauerWinkel-154.95502437185988)*((6.568025840994326e-12)+(blauerWinkel-155.95502437185988)*((-5.323466533701143e-14)+(blauerWinkel-156.95502437185988)*((1.3469139527593563e-15)+(blauerWinkel-157.95502437185988)*((-8.337050312758024e-17)))))))))));
%siebenterWinkel=148.95502437185985+(blauerWinkel-148.95502437185988)*((0.9999999999983515)+(blauerWinkel-149.95502437185988)*((1.9184653865522705e-12)+(blauerWinkel-150.95502437185988)*((-1.0705510552118842e-12)+(blauerWinkel-151.95502437185988)*((3.943512183468556e-13)+(blauerWinkel-152.95502437185988)*((-1.1558161835030962e-13)+(blauerWinkel-153.95502437185988)*((3.0000693287648675e-14)+(blauerWinkel-154.95502437185988)*((-7.156180410155296e-15)+(blauerWinkel-155.95502437185988)*((1.5803936642600644e-15)+(blauerWinkel-156.95502437185988)*((-3.253521301088466e-16)+(blauerWinkel-157.95502437185988)*((6.255627017764463e-17)))))))))));
%achterWinkel=135.52248781407008+(blauerWinkel-148.95502437185988)*((-0.13401954390860737)+(blauerWinkel-149.95502437185988)*((-0.015632609861739866)+(blauerWinkel-150.95502437185988)*((0.00017091138641471085)+(blauerWinkel-151.95502437185988)*((-0.0000018460497687537228)+(blauerWinkel-152.95502437185988)*((2.2553872251279913e-9)+(blauerWinkel-153.95502437185988)*((3.220227048003076e-11)+(blauerWinkel-154.95502437185988)*((-5.101200590709603e-12)+(blauerWinkel-155.95502437185988)*((5.0189834646261943e-14)+(blauerWinkel-156.95502437185988)*((-2.3890746299755062e-15)+(blauerWinkel-157.95502437185988)*((-7.675616697290482e-18)))))))))));
%neunterWinkel=104.47751218592991+(blauerWinkel-148.95502437185988)*((0.1335731634261208)+(blauerWinkel-149.95502437185988)*((0.015203383518979763)+(blauerWinkel-150.95502437185988)*((-0.0001614470679811575)+(blauerWinkel-151.95502437185988)*((0.000002105859759164254)+(blauerWinkel-152.95502437185988)*((-1.0005143143605743e-8)+(blauerWinkel-153.95502437185988)*((2.0668863164203418e-10)+(blauerWinkel-154.95502437185988)*((3.646880328511662e-12)+(blauerWinkel-155.95502437185988)*((-4.9992461642598194e-14)+(blauerWinkel-156.95502437185988)*((4.048221676833542e-15)+(blauerWinkel-157.95502437185988)*((-2.6508286772677843e-17)))))))))));
%P[5]=[31.74219649117,-79.36949187458876]; P[2]=[-14.33674095819476,-59.95991888759268]; D=ab(5,2); A(2,5); N(4,2,5); N(3,2,4); N(1,2,3); M(8,1,2,blauerWinkel); N(7,8,1); N(9,8,7); N(10,8,9); M(16,10,8,gruenerWinkel); N(15,16,10); N(17,16,15); N(18,16,17); M(37,18,16,orangerWinkel); N(36,18,37); N(35,36,37); N(31,36,35); M(30,31,36,vierterWinkel); N(29,31,30); N(28,29,30); N(22,29,28); M(24,22,29,fuenfterWinkel); N(23,22,24); N(25,23,24); N(26,23,25); M(43,26,23,sechsterWinkel); N(41,26,43); N(42,41,43); N(40,41,42); M(46,40,41,siebenterWinkel); N(45,46,40); N(47,46,45); N(48,46,47); M(53,48,46,achterWinkel); N(52,53,48); N(54,53,52); N(55,53,54); M(72,55,53,neunterWinkel); N(71,55,72); N(70,71,72); N(67,71,70); Q(59,67,5,2*D,2*D); A(59,67); A(59,5); H(60,5,59,2); A(60,5); L(62,5,60); H(65,67,59,2); A(65,67); L(66,65,67); A(65,59); L(64,59,65); A(64,66); A(60,59); L(61,60,59); A(62,61); N(11,9,7); N(20,37,17); N(32,28,30); N(38,35,20); N(49,47,45); N(57,72,54); N(68,64,66); N(73,70,57); N(6,11,3); N(19,20,15); N(27,24,32); N(44,49,42); N(56,57,52); N(63,61,68); N(12,11,6); N(21,20,19); N(33,27,32); N(39,38,20); N(50,49,44); N(58,57,56); N(69,63,68); N(74,73,57); N(13,69,12); N(14,33,13); N(34,14,50); N(51,69,34);
%A(14,39); R(14,39,\"green\");
%A(14,21); R(14,21,\"green\");
%A(14,12); R(14,12,\"green\");
%A(34,33); R(34,33,\"green\");
%A(51,74); R(51,74,\"green\");
%A(51,58); R(51,58,\"green\");
%A(51,13); R(51,13,\"green\");
%A(51,50); R(51,50,\"green\");
%</Rechenweg>
%
%<Knopf id=\"Stopp_alleWinkel\" color=\"LightGrey\"/>
%
%<Knopf id=\"Start_blauerWinkel\" color=\"blue\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#blauerWinkel\" attributeName=\"value\" values=\"0;28;0;-25;0\" dur=\"10\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_blauerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.80/0.78,
2/2.72/0.39,
3/2.60/1.38,
4/3.52/0.99,
5/3.64/0.00,
6/2.84/2.35,
7/1.87/1.77,
8/0.97/1.33,
9/1.04/2.33,
10/0.14/1.89,
11/1.93/2.77,
12/2.75/3.35,
13/3.64/2.89,
14/3.594/3.887,
15/0.97/2.45,
16/0.07/2.89,
17/0.90/3.45,
18/0.00/3.89,
19/1.87/2.89,
20/1.80/3.89,
21/2.70/3.45,
22/1.80/7.00,
23/2.72/7.39,
24/2.60/6.39,
25/3.52/6.78,
26/3.64/7.77,
27/2.84/5.42,
28/1.87/6.00,
29/0.97/6.44,
30/1.04/5.44,
31/0.14/5.88,
32/1.93/5.00,
33/2.75/4.43,
34/3.64/4.89,
35/0.97/5.32,
36/0.07/4.88,
37/0.90/4.33,
38/1.87/4.88,
39/2.70/4.33,
40/5.49/7.00,
41/4.56/7.39,
42/4.69/6.39,
43/3.77/6.78,
44/4.44/5.42,
45/5.42/6.00,
46/6.32/6.44,
47/6.25/5.44,
48/7.15/5.88,
49/5.35/5.00,
50/4.53/4.43,
51/3.690/3.887,
52/6.32/5.32,
53/7.21/4.88,
54/6.39/4.33,
55/7.28/3.89,
56/5.42/4.88,
57/5.49/3.89,
58/4.59/4.33,
59/5.49/0.78,
60/4.56/0.39,
61/4.69/1.38,
62/3.77/0.99,
63/4.44/2.35,
64/5.42/1.77,
65/6.32/1.33,
66/6.25/2.33,
67/7.15/1.89,
68/5.35/2.77,
69/4.53/3.35,
70/6.32/2.45,
71/7.21/2.89,
72/6.39/3.45,
73/5.42/2.89,
74/4.59/3.45}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
1/337.16/506.11/0.4/Blue}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
1/2, 1/3,
2/5,
3/2, 3/4,
4/2, 4/5,
6/11, 6/3,
7/8, 7/1,
8/1,
9/8, 9/7,
10/8, 10/9,
11/9, 11/7,
12/11, 12/6,
13/69, 13/12,
14/33, 14/13, 14/39, 14/21, 14/12,
15/16, 15/10,
16/10,
17/16, 17/15,
18/16, 18/17,
19/20, 19/15,
20/37, 20/17,
21/20, 21/19,
22/29, 22/28,
23/22, 23/24,
24/22,
25/23, 25/24,
26/23, 26/25,
27/24, 27/32,
28/29, 28/30,
29/31, 29/30,
30/31,
31/36, 31/35,
32/28, 32/30,
33/27, 33/32,
34/14, 34/50, 34/33,
35/36, 35/37,
36/18, 36/37,
37/18,
38/35, 38/20,
39/38, 39/20,
40/41, 40/42,
41/26, 41/43,
42/41, 42/43,
43/26,
44/49, 44/42,
45/46, 45/40,
46/40,
47/46, 47/45,
48/46, 48/47,
49/47, 49/45,
50/49, 50/44,
51/69, 51/34, 51/74, 51/58, 51/13, 51/50,
52/53, 52/48,
53/48,
54/53, 54/52,
55/53, 55/54,
56/57, 56/52,
57/72, 57/54,
58/57, 58/56,
60/5, 60/59,
61/60, 61/59,
62/5, 62/60, 62/61,
63/61, 63/68,
64/59, 64/65, 64/66,
65/67, 65/59,
66/65, 66/67,
67/71, 67/70,
68/64, 68/66,
69/63, 69/68,
70/71, 70/72,
71/55, 71/72,
72/55,
73/70, 73/57,
74/73, 74/57}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,74}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
1/337.16/506.11/0.4/Blue}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/187,
2/187,
3/127,
4/7,
5/233,
6/305,
7/356,
8/176,
9/116,
10/176,
11/56,
12/65,
13/303,
14/297,
15/4,
16/184,
17/4,
18/124,
19/244,
20/124,
21/4,
22/173,
23/173,
24/293,
25/353,
26/127,
27/55,
28/4,
29/124,
30/184,
31/184,
32/175,
33/295,
34/57,
35/356,
36/116,
37/356,
38/116,
39/356,
40/7,
41/7,
42/307,
43/187,
44/125,
45/116,
46/116,
47/356,
48/64,
49/5,
50/3,
51/243,
52/124,
53/4,
54/184,
55/56,
56/64,
57/56,
58/184,
59/353,
60/353,
61/53,
62/173,
63/235,
64/124,
65/304,
66/124,
67/296,
68/124,
69/357,
70/176,
71/356,
72/116,
73/296,
74/176}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1902_1a = #1894-1 mit 4 umgelegten Kanten, dann blauerWinkel+10*1</Bildtext>
%<Ausrichten von="18" nach="55"/>
%<Winkel size="18" color="blue" id="blauerWinkel" value="138.95502437185988"/>
%<Feinjustieren Anzahl="1"/>
%<Rechenweg>
%gruenerWinkel=135.52248781407005+(blauerWinkel-148.95502437185988)*((-0.13401954390838)+(blauerWinkel-149.95502437185988)*((-0.01563260986196724)+(blauerWinkel-150.95502437185988)*((0.00017091138651418683)+(blauerWinkel-151.95502437185988)*((-0.000001846049790070005)+(blauerWinkel-152.95502437185988)*((2.2553862777385804e-9)+(blauerWinkel-153.95502437185988)*((3.220487580294345e-11)+(blauerWinkel-154.95502437185988)*((-5.102390467712281e-12)+(blauerWinkel-155.95502437185988)*((5.0566958004057103e-14)+(blauerWinkel-156.95502437185988)*((-2.4870562162008914e-15)+(blauerWinkel-157.95502437185988)*((1.4262547123617674e-17)))))))))));
%orangerWinkel=104.47751218592991+(blauerWinkel-148.95502437185988)*((0.13357316342579395)+(blauerWinkel-149.95502437185988)*((0.01520338351935635)+(blauerWinkel-150.95502437185988)*((-0.00016144706818484641)+(blauerWinkel-151.95502437185988)*((0.0000021058598237052236)+(blauerWinkel-152.95502437185988)*((-1.0005154749137547e-8)+(blauerWinkel-153.95502437185988)*((2.0668908559974283e-10)+(blauerWinkel-154.95502437185988)*((3.64730327071304e-12)+(blauerWinkel-155.95502437185988)*((-5.0157761548087156e-14)+(blauerWinkel-156.95502437185988)*((4.0883228625250085e-15)+(blauerWinkel-157.95502437185988)*((-3.432488515719872e-17)))))))))));
%vierterWinkel=75.52248781407012+(blauerWinkel-148.95502437185988)*((-0.13401954390846527)+(blauerWinkel-149.95502437185988)*((-0.015632609861931712)+(blauerWinkel-150.95502437185988)*((0.00017091138651655532)+(blauerWinkel-151.95502437185988)*((-0.0000018460497977675557)+(blauerWinkel-152.95502437185988)*((2.2553906594196878e-9)+(blauerWinkel-153.95502437185988)*((3.220323760711625e-11)+(blauerWinkel-154.95502437185988)*((-5.101933690271561e-12)+(blauerWinkel-155.95502437185988)*((5.046298475415152e-14)+(blauerWinkel-156.95502437185988)*((-2.465439180228494e-15)+(blauerWinkel-157.95502437185988)*((9.825572171682454e-18)))))))))));
%fuenfterWinkel=88.95502437185979+(blauerWinkel-148.95502437185988)*((0.9999999999984368)+(blauerWinkel-149.95502437185988)*((1.8474111129762605e-12)+(blauerWinkel-150.95502437185988)*((-1.0444978215673473e-12)+(blauerWinkel-151.95502437185988)*((3.8487731520338763e-13)+(blauerWinkel-152.95502437185988)*((-1.1013412404281553e-13)+(blauerWinkel-153.95502437185988)*((2.7257208835686063e-14)+(blauerWinkel-154.95502437185988)*((-6.132660516977055e-15)+(blauerWinkel-155.95502437185988)*((1.284686642780538e-15)+(blauerWinkel-156.95502437185988)*((-2.5587997329455987e-16)+(blauerWinkel-157.95502437185988)*((4.881065177752363e-17)))))))))));
%sechsterWinkel=106.56746344221033+(blauerWinkel-148.95502437185988)*((-1.8655340756059786)+(blauerWinkel-149.95502437185988)*((0.016061836201068047)+(blauerWinkel-150.95502437185988)*((-0.000180375702915588)+(blauerWinkel-151.95502437185988)*((0.0000015862390672083393)+(blauerWinkel-152.95502437185988)*((5.494573921775703e-9)+(blauerWinkel-153.95502437185988)*((-2.711455159165118e-10)+(blauerWinkel-154.95502437185988)*((6.568025840994326e-12)+(blauerWinkel-155.95502437185988)*((-5.323466533701143e-14)+(blauerWinkel-156.95502437185988)*((1.3469139527593563e-15)+(blauerWinkel-157.95502437185988)*((-8.337050312758024e-17)))))))))));
%siebenterWinkel=148.95502437185985+(blauerWinkel-148.95502437185988)*((0.9999999999983515)+(blauerWinkel-149.95502437185988)*((1.9184653865522705e-12)+(blauerWinkel-150.95502437185988)*((-1.0705510552118842e-12)+(blauerWinkel-151.95502437185988)*((3.943512183468556e-13)+(blauerWinkel-152.95502437185988)*((-1.1558161835030962e-13)+(blauerWinkel-153.95502437185988)*((3.0000693287648675e-14)+(blauerWinkel-154.95502437185988)*((-7.156180410155296e-15)+(blauerWinkel-155.95502437185988)*((1.5803936642600644e-15)+(blauerWinkel-156.95502437185988)*((-3.253521301088466e-16)+(blauerWinkel-157.95502437185988)*((6.255627017764463e-17)))))))))));
%achterWinkel=135.52248781407008+(blauerWinkel-148.95502437185988)*((-0.13401954390860737)+(blauerWinkel-149.95502437185988)*((-0.015632609861739866)+(blauerWinkel-150.95502437185988)*((0.00017091138641471085)+(blauerWinkel-151.95502437185988)*((-0.0000018460497687537228)+(blauerWinkel-152.95502437185988)*((2.2553872251279913e-9)+(blauerWinkel-153.95502437185988)*((3.220227048003076e-11)+(blauerWinkel-154.95502437185988)*((-5.101200590709603e-12)+(blauerWinkel-155.95502437185988)*((5.0189834646261943e-14)+(blauerWinkel-156.95502437185988)*((-2.3890746299755062e-15)+(blauerWinkel-157.95502437185988)*((-7.675616697290482e-18)))))))))));
%neunterWinkel=104.47751218592991+(blauerWinkel-148.95502437185988)*((0.1335731634261208)+(blauerWinkel-149.95502437185988)*((0.015203383518979763)+(blauerWinkel-150.95502437185988)*((-0.0001614470679811575)+(blauerWinkel-151.95502437185988)*((0.000002105859759164254)+(blauerWinkel-152.95502437185988)*((-1.0005143143605743e-8)+(blauerWinkel-153.95502437185988)*((2.0668863164203418e-10)+(blauerWinkel-154.95502437185988)*((3.646880328511662e-12)+(blauerWinkel-155.95502437185988)*((-4.9992461642598194e-14)+(blauerWinkel-156.95502437185988)*((4.048221676833542e-15)+(blauerWinkel-157.95502437185988)*((-2.6508286772677843e-17)))))))))));
%P[5]=[120.71208750145257,-10.495143621012147]; P[2]=[70.81218587654718,-13.657392476614973]; D=ab(5,2); A(2,5); N(4,2,5); N(3,2,4); N(1,2,3); M(8,1,2,blauerWinkel); N(7,8,1); N(9,8,7); N(10,8,9); M(16,10,8,gruenerWinkel); N(15,16,10); N(17,16,15); N(18,16,17); M(37,18,16,orangerWinkel); N(36,18,37); N(35,36,37); N(31,36,35); M(30,31,36,vierterWinkel); N(29,31,30); N(28,29,30); N(22,29,28); M(24,22,29,fuenfterWinkel); N(23,22,24); N(25,23,24); N(26,23,25); M(43,26,23,sechsterWinkel); N(41,26,43); N(42,41,43); N(40,41,42); M(46,40,41,siebenterWinkel); N(45,46,40); N(47,46,45); N(48,46,47); M(53,48,46,achterWinkel); N(52,53,48); N(54,53,52); N(55,53,54); M(72,55,53,neunterWinkel); N(71,55,72); N(70,71,72); N(67,71,70); Q(59,67,5,2*D,2*D); A(59,67); A(59,5); H(60,5,59,2); A(60,5); L(62,5,60); H(65,67,59,2); A(65,67); L(66,65,67); A(65,59); L(64,59,65); A(64,66); A(60,59); L(61,60,59); A(62,61); N(11,9,7); N(20,37,17); N(32,28,30); N(38,35,20); N(49,47,45); N(57,72,54); N(68,64,66); N(73,70,57); N(6,11,3); N(19,20,15); N(27,24,32); N(44,49,42); N(56,57,52); N(63,61,68); N(12,11,6); N(21,20,19); N(33,27,32); N(39,38,20); N(50,49,44); N(58,57,56); N(69,63,68); N(74,73,57); N(13,69,12); N(14,33,13); N(34,14,50); N(51,69,34);
%A(14,39); R(14,39,"green");
%A(14,21); R(14,21,"green");
%A(14,12); R(14,12,"green");
%A(34,33); R(34,33,"green");
%A(51,74); R(51,74,"green");
%A(51,58); R(51,58,"green");
%A(51,13); R(51,13,"green");
%A(51,50); R(51,50,"green");
%</Rechenweg>
%
%<Knopf id="Stopp_alleWinkel" color="LightGrey"/>
%
%<Knopf id="Start_blauerWinkel" color="blue"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#blauerWinkel" attributeName="value" values="0;28;0;-25;0" dur="10" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_blauerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.85/0.00,
2/2.85/0.06,
3/2.29/0.90,
4/3.29/0.96,
5/3.84/0.13,
6/3.02/1.58,
7/1.98/0.99,
8/1.05/0.61,
9/1.18/1.60,
10/0.26/1.22,
11/2.11/1.98,
12/2.91/2.57,
13/3.84/2.21,
14/3.69/3.20,
15/1.05/1.82,
16/0.13/2.21,
17/0.92/2.82,
18/0.00/3.20,
19/1.98/2.21,
20/1.85/3.20,
21/2.77/2.82,
22/1.85/6.40,
23/2.85/6.33,
24/2.29/5.50,
25/3.29/5.44,
26/3.84/6.27,
27/3.02/4.82,
28/1.98/5.41,
29/1.05/5.79,
30/1.18/4.80,
31/0.26/5.18,
32/2.11/4.41,
33/2.91/3.82,
34/3.84/4.19,
35/1.05/4.57,
36/0.13/4.19,
37/0.92/3.58,
38/1.98/4.19,
39/2.77/3.58,
40/5.84/6.40,
41/4.84/6.33,
42/5.40/5.50,
43/4.40/5.44,
44/4.67/4.82,
45/5.71/5.41,
46/6.63/5.79,
47/6.51/4.80,
48/7.43/5.18,
49/5.58/4.41,
50/4.78/3.82,
51/3.99/3.20,
52/6.64/4.57,
53/7.56/4.19,
54/6.77/3.58,
55/7.69/3.20,
56/5.71/4.19,
57/5.84/3.20,
58/4.92/3.58,
59/5.84/0.00,
60/4.84/0.06,
61/5.40/0.90,
62/4.40/0.96,
63/4.67/1.58,
64/5.71/0.99,
65/6.63/0.61,
66/6.51/1.60,
67/7.43/1.22,
68/5.58/1.98,
69/4.78/2.57,
70/6.64/1.82,
71/7.56/2.21,
72/6.77/2.82,
73/5.71/2.21,
74/4.92/2.82}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
1/3.63/142.58/0.4/Blue}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
1/2, 1/3,
2/5,
3/2, 3/4,
4/2, 4/5,
6/11, 6/3,
7/8, 7/1,
8/1,
9/8, 9/7,
10/8, 10/9,
11/9, 11/7,
12/11, 12/6,
13/69, 13/12,
14/33, 14/13, 14/39, 14/21, 14/12,
15/16, 15/10,
16/10,
17/16, 17/15,
18/16, 18/17,
19/20, 19/15,
20/37, 20/17,
21/20, 21/19,
22/29, 22/28,
23/22, 23/24,
24/22,
25/23, 25/24,
26/23, 26/25,
27/24, 27/32,
28/29, 28/30,
29/31, 29/30,
30/31,
31/36, 31/35,
32/28, 32/30,
33/27, 33/32,
34/14, 34/50, 34/33,
35/36, 35/37,
36/18, 36/37,
37/18,
38/35, 38/20,
39/38, 39/20,
40/41, 40/42,
41/26, 41/43,
42/41, 42/43,
43/26,
44/49, 44/42,
45/46, 45/40,
46/40,
47/46, 47/45,
48/46, 48/47,
49/47, 49/45,
50/49, 50/44,
51/69, 51/34, 51/74, 51/58, 51/13, 51/50,
52/53, 52/48,
53/48,
54/53, 54/52,
55/53, 55/54,
56/57, 56/52,
57/72, 57/54,
58/57, 58/56,
60/5, 60/59,
61/60, 61/59,
62/5, 62/60, 62/61,
63/61, 63/68,
64/59, 64/65, 64/66,
65/67, 65/59,
66/65, 66/67,
67/71, 67/70,
68/64, 68/66,
69/63, 69/68,
70/71, 70/72,
71/55, 71/72,
72/55,
73/70, 73/57,
74/73, 74/57}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,74}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
1/3.63/142.58/0.4/Blue}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/214,
2/334,
3/154,
4/34,
5/334,
6/306,
7/53,
8/173,
9/113,
10/173,
11/53,
12/189,
13/231,
14/69,
15/307,
16/187,
17/67,
18/127,
19/247,
20/233,
21/7,
22/146,
23/146,
24/266,
25/326,
26/154,
27/54,
28/67,
29/67,
30/187,
31/113,
32/307,
33/171,
34/129,
35/353,
36/233,
37/293,
38/113,
39/353,
40/113,
41/154,
42/334,
43/214,
44/126,
45/233,
46/113,
47/353,
48/67,
49/233,
50/246,
51/111,
52/127,
53/67,
54/247,
55/307,
56/67,
57/53,
58/187,
59/247,
60/206,
61/26,
62/86,
63/234,
64/127,
65/307,
66/127,
67/293,
68/127,
69/114,
70/173,
71/293,
72/173,
73/293,
74/173}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/fcf1e561b954deb65fc7020eaf337c67.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1902_1a = #1894-1 mit 4 umgelegten Kanten, dann blauerWinkel+10*1</Bildtext>
%<Ausrichten von=\"18\" nach=\"55\"/>
%<Winkel size=\"18\" color=\"blue\" id=\"blauerWinkel\" value=\"138.95502437185988\"/>
%<Feinjustieren Anzahl=\"1\"/>
%<Rechenweg>
%gruenerWinkel=135.52248781407005+(blauerWinkel-148.95502437185988)*((-0.13401954390838)+(blauerWinkel-149.95502437185988)*((-0.01563260986196724)+(blauerWinkel-150.95502437185988)*((0.00017091138651418683)+(blauerWinkel-151.95502437185988)*((-0.000001846049790070005)+(blauerWinkel-152.95502437185988)*((2.2553862777385804e-9)+(blauerWinkel-153.95502437185988)*((3.220487580294345e-11)+(blauerWinkel-154.95502437185988)*((-5.102390467712281e-12)+(blauerWinkel-155.95502437185988)*((5.0566958004057103e-14)+(blauerWinkel-156.95502437185988)*((-2.4870562162008914e-15)+(blauerWinkel-157.95502437185988)*((1.4262547123617674e-17)))))))))));
%orangerWinkel=104.47751218592991+(blauerWinkel-148.95502437185988)*((0.13357316342579395)+(blauerWinkel-149.95502437185988)*((0.01520338351935635)+(blauerWinkel-150.95502437185988)*((-0.00016144706818484641)+(blauerWinkel-151.95502437185988)*((0.0000021058598237052236)+(blauerWinkel-152.95502437185988)*((-1.0005154749137547e-8)+(blauerWinkel-153.95502437185988)*((2.0668908559974283e-10)+(blauerWinkel-154.95502437185988)*((3.64730327071304e-12)+(blauerWinkel-155.95502437185988)*((-5.0157761548087156e-14)+(blauerWinkel-156.95502437185988)*((4.0883228625250085e-15)+(blauerWinkel-157.95502437185988)*((-3.432488515719872e-17)))))))))));
%vierterWinkel=75.52248781407012+(blauerWinkel-148.95502437185988)*((-0.13401954390846527)+(blauerWinkel-149.95502437185988)*((-0.015632609861931712)+(blauerWinkel-150.95502437185988)*((0.00017091138651655532)+(blauerWinkel-151.95502437185988)*((-0.0000018460497977675557)+(blauerWinkel-152.95502437185988)*((2.2553906594196878e-9)+(blauerWinkel-153.95502437185988)*((3.220323760711625e-11)+(blauerWinkel-154.95502437185988)*((-5.101933690271561e-12)+(blauerWinkel-155.95502437185988)*((5.046298475415152e-14)+(blauerWinkel-156.95502437185988)*((-2.465439180228494e-15)+(blauerWinkel-157.95502437185988)*((9.825572171682454e-18)))))))))));
%fuenfterWinkel=88.95502437185979+(blauerWinkel-148.95502437185988)*((0.9999999999984368)+(blauerWinkel-149.95502437185988)*((1.8474111129762605e-12)+(blauerWinkel-150.95502437185988)*((-1.0444978215673473e-12)+(blauerWinkel-151.95502437185988)*((3.8487731520338763e-13)+(blauerWinkel-152.95502437185988)*((-1.1013412404281553e-13)+(blauerWinkel-153.95502437185988)*((2.7257208835686063e-14)+(blauerWinkel-154.95502437185988)*((-6.132660516977055e-15)+(blauerWinkel-155.95502437185988)*((1.284686642780538e-15)+(blauerWinkel-156.95502437185988)*((-2.5587997329455987e-16)+(blauerWinkel-157.95502437185988)*((4.881065177752363e-17)))))))))));
%sechsterWinkel=106.56746344221033+(blauerWinkel-148.95502437185988)*((-1.8655340756059786)+(blauerWinkel-149.95502437185988)*((0.016061836201068047)+(blauerWinkel-150.95502437185988)*((-0.000180375702915588)+(blauerWinkel-151.95502437185988)*((0.0000015862390672083393)+(blauerWinkel-152.95502437185988)*((5.494573921775703e-9)+(blauerWinkel-153.95502437185988)*((-2.711455159165118e-10)+(blauerWinkel-154.95502437185988)*((6.568025840994326e-12)+(blauerWinkel-155.95502437185988)*((-5.323466533701143e-14)+(blauerWinkel-156.95502437185988)*((1.3469139527593563e-15)+(blauerWinkel-157.95502437185988)*((-8.337050312758024e-17)))))))))));
%siebenterWinkel=148.95502437185985+(blauerWinkel-148.95502437185988)*((0.9999999999983515)+(blauerWinkel-149.95502437185988)*((1.9184653865522705e-12)+(blauerWinkel-150.95502437185988)*((-1.0705510552118842e-12)+(blauerWinkel-151.95502437185988)*((3.943512183468556e-13)+(blauerWinkel-152.95502437185988)*((-1.1558161835030962e-13)+(blauerWinkel-153.95502437185988)*((3.0000693287648675e-14)+(blauerWinkel-154.95502437185988)*((-7.156180410155296e-15)+(blauerWinkel-155.95502437185988)*((1.5803936642600644e-15)+(blauerWinkel-156.95502437185988)*((-3.253521301088466e-16)+(blauerWinkel-157.95502437185988)*((6.255627017764463e-17)))))))))));
%achterWinkel=135.52248781407008+(blauerWinkel-148.95502437185988)*((-0.13401954390860737)+(blauerWinkel-149.95502437185988)*((-0.015632609861739866)+(blauerWinkel-150.95502437185988)*((0.00017091138641471085)+(blauerWinkel-151.95502437185988)*((-0.0000018460497687537228)+(blauerWinkel-152.95502437185988)*((2.2553872251279913e-9)+(blauerWinkel-153.95502437185988)*((3.220227048003076e-11)+(blauerWinkel-154.95502437185988)*((-5.101200590709603e-12)+(blauerWinkel-155.95502437185988)*((5.0189834646261943e-14)+(blauerWinkel-156.95502437185988)*((-2.3890746299755062e-15)+(blauerWinkel-157.95502437185988)*((-7.675616697290482e-18)))))))))));
%neunterWinkel=104.47751218592991+(blauerWinkel-148.95502437185988)*((0.1335731634261208)+(blauerWinkel-149.95502437185988)*((0.015203383518979763)+(blauerWinkel-150.95502437185988)*((-0.0001614470679811575)+(blauerWinkel-151.95502437185988)*((0.000002105859759164254)+(blauerWinkel-152.95502437185988)*((-1.0005143143605743e-8)+(blauerWinkel-153.95502437185988)*((2.0668863164203418e-10)+(blauerWinkel-154.95502437185988)*((3.646880328511662e-12)+(blauerWinkel-155.95502437185988)*((-4.9992461642598194e-14)+(blauerWinkel-156.95502437185988)*((4.048221676833542e-15)+(blauerWinkel-157.95502437185988)*((-2.6508286772677843e-17)))))))))));
%P[5]=[120.71208750145257,-10.495143621012147]; P[2]=[70.81218587654718,-13.657392476614973]; D=ab(5,2); A(2,5); N(4,2,5); N(3,2,4); N(1,2,3); M(8,1,2,blauerWinkel); N(7,8,1); N(9,8,7); N(10,8,9); M(16,10,8,gruenerWinkel); N(15,16,10); N(17,16,15); N(18,16,17); M(37,18,16,orangerWinkel); N(36,18,37); N(35,36,37); N(31,36,35); M(30,31,36,vierterWinkel); N(29,31,30); N(28,29,30); N(22,29,28); M(24,22,29,fuenfterWinkel); N(23,22,24); N(25,23,24); N(26,23,25); M(43,26,23,sechsterWinkel); N(41,26,43); N(42,41,43); N(40,41,42); M(46,40,41,siebenterWinkel); N(45,46,40); N(47,46,45); N(48,46,47); M(53,48,46,achterWinkel); N(52,53,48); N(54,53,52); N(55,53,54); M(72,55,53,neunterWinkel); N(71,55,72); N(70,71,72); N(67,71,70); Q(59,67,5,2*D,2*D); A(59,67); A(59,5); H(60,5,59,2); A(60,5); L(62,5,60); H(65,67,59,2); A(65,67); L(66,65,67); A(65,59); L(64,59,65); A(64,66); A(60,59); L(61,60,59); A(62,61); N(11,9,7); N(20,37,17); N(32,28,30); N(38,35,20); N(49,47,45); N(57,72,54); N(68,64,66); N(73,70,57); N(6,11,3); N(19,20,15); N(27,24,32); N(44,49,42); N(56,57,52); N(63,61,68); N(12,11,6); N(21,20,19); N(33,27,32); N(39,38,20); N(50,49,44); N(58,57,56); N(69,63,68); N(74,73,57); N(13,69,12); N(14,33,13); N(34,14,50); N(51,69,34);
%A(14,39); R(14,39,\"green\");
%A(14,21); R(14,21,\"green\");
%A(14,12); R(14,12,\"green\");
%A(34,33); R(34,33,\"green\");
%A(51,74); R(51,74,\"green\");
%A(51,58); R(51,58,\"green\");
%A(51,13); R(51,13,\"green\");
%A(51,50); R(51,50,\"green\");
%</Rechenweg>
%
%<Knopf id=\"Stopp_alleWinkel\" color=\"LightGrey\"/>
%
%<Knopf id=\"Start_blauerWinkel\" color=\"blue\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#blauerWinkel\" attributeName=\"value\" values=\"0;28;0;-25;0\" dur=\"10\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_blauerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.85/0.00,
2/2.85/0.06,
3/2.29/0.90,
4/3.29/0.96,
5/3.84/0.13,
6/3.02/1.58,
7/1.98/0.99,
8/1.05/0.61,
9/1.18/1.60,
10/0.26/1.22,
11/2.11/1.98,
12/2.91/2.57,
13/3.84/2.21,
14/3.69/3.20,
15/1.05/1.82,
16/0.13/2.21,
17/0.92/2.82,
18/0.00/3.20,
19/1.98/2.21,
20/1.85/3.20,
21/2.77/2.82,
22/1.85/6.40,
23/2.85/6.33,
24/2.29/5.50,
25/3.29/5.44,
26/3.84/6.27,
27/3.02/4.82,
28/1.98/5.41,
29/1.05/5.79,
30/1.18/4.80,
31/0.26/5.18,
32/2.11/4.41,
33/2.91/3.82,
34/3.84/4.19,
35/1.05/4.57,
36/0.13/4.19,
37/0.92/3.58,
38/1.98/4.19,
39/2.77/3.58,
40/5.84/6.40,
41/4.84/6.33,
42/5.40/5.50,
43/4.40/5.44,
44/4.67/4.82,
45/5.71/5.41,
46/6.63/5.79,
47/6.51/4.80,
48/7.43/5.18,
49/5.58/4.41,
50/4.78/3.82,
51/3.99/3.20,
52/6.64/4.57,
53/7.56/4.19,
54/6.77/3.58,
55/7.69/3.20,
56/5.71/4.19,
57/5.84/3.20,
58/4.92/3.58,
59/5.84/0.00,
60/4.84/0.06,
61/5.40/0.90,
62/4.40/0.96,
63/4.67/1.58,
64/5.71/0.99,
65/6.63/0.61,
66/6.51/1.60,
67/7.43/1.22,
68/5.58/1.98,
69/4.78/2.57,
70/6.64/1.82,
71/7.56/2.21,
72/6.77/2.82,
73/5.71/2.21,
74/4.92/2.82}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
1/3.63/142.58/0.4/Blue}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
1/2, 1/3,
2/5,
3/2, 3/4,
4/2, 4/5,
6/11, 6/3,
7/8, 7/1,
8/1,
9/8, 9/7,
10/8, 10/9,
11/9, 11/7,
12/11, 12/6,
13/69, 13/12,
14/33, 14/13, 14/39, 14/21, 14/12,
15/16, 15/10,
16/10,
17/16, 17/15,
18/16, 18/17,
19/20, 19/15,
20/37, 20/17,
21/20, 21/19,
22/29, 22/28,
23/22, 23/24,
24/22,
25/23, 25/24,
26/23, 26/25,
27/24, 27/32,
28/29, 28/30,
29/31, 29/30,
30/31,
31/36, 31/35,
32/28, 32/30,
33/27, 33/32,
34/14, 34/50, 34/33,
35/36, 35/37,
36/18, 36/37,
37/18,
38/35, 38/20,
39/38, 39/20,
40/41, 40/42,
41/26, 41/43,
42/41, 42/43,
43/26,
44/49, 44/42,
45/46, 45/40,
46/40,
47/46, 47/45,
48/46, 48/47,
49/47, 49/45,
50/49, 50/44,
51/69, 51/34, 51/74, 51/58, 51/13, 51/50,
52/53, 52/48,
53/48,
54/53, 54/52,
55/53, 55/54,
56/57, 56/52,
57/72, 57/54,
58/57, 58/56,
60/5, 60/59,
61/60, 61/59,
62/5, 62/60, 62/61,
63/61, 63/68,
64/59, 64/65, 64/66,
65/67, 65/59,
66/65, 66/67,
67/71, 67/70,
68/64, 68/66,
69/63, 69/68,
70/71, 70/72,
71/55, 71/72,
72/55,
73/70, 73/57,
74/73, 74/57}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,74}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
1/3.63/142.58/0.4/Blue}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/214,
2/334,
3/154,
4/34,
5/334,
6/306,
7/53,
8/173,
9/113,
10/173,
11/53,
12/189,
13/231,
14/69,
15/307,
16/187,
17/67,
18/127,
19/247,
20/233,
21/7,
22/146,
23/146,
24/266,
25/326,
26/154,
27/54,
28/67,
29/67,
30/187,
31/113,
32/307,
33/171,
34/129,
35/353,
36/233,
37/293,
38/113,
39/353,
40/113,
41/154,
42/334,
43/214,
44/126,
45/233,
46/113,
47/353,
48/67,
49/233,
50/246,
51/111,
52/127,
53/67,
54/247,
55/307,
56/67,
57/53,
58/187,
59/247,
60/206,
61/26,
62/86,
63/234,
64/127,
65/307,
66/127,
67/293,
68/127,
69/114,
70/173,
71/293,
72/173,
73/293,
74/173}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
Zufällig habe ich dann noch eine Bewegungsmöglichkeit gefunden, bei der der oberste Knoten P26 nach außen und der unterste Knoten P5 nach innen bewegt wird.
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1902_1c = #1894-1 mit 4 umgelegten Kanten, dann blauerWinkel=138+10*1</Bildtext>
%<Ausrichten von="18" nach="55"/>
%<Winkel size="18" color="blue" id="blauerWinkel" value="138"/>
%<Feinjustieren Anzahl="8,8"/>
%<Rechenweg>
%gruenerWinkel=134.02217398627073+(blauerWinkel-138)*((0.33863056790141854)+(blauerWinkel-139)*((-0.020425597796361217)+(blauerWinkel-140)*((0.00012591747007206777)+(blauerWinkel-141)*((-1.6782361456080253e-7)+(blauerWinkel-142)*((-5.10587625512926e-9)+(blauerWinkel-143)*((-5.73784378035447e-10)+(blauerWinkel-144)*((1.7203660718255866e-11)+(blauerWinkel-145)*((-1.8288228075388755e-13)+(blauerWinkel-146)*((-2.8274462916897133e-15)+(blauerWinkel-147)*((-1.0871584379996863e-8)))))))))));
%orangerWinkel=105.9584582600583+(blauerWinkel-138)*((-0.3354217042569161)+(blauerWinkel-139)*((0.020273471044319535)+(blauerWinkel-140)*((-0.00012750497954291026)+(blauerWinkel-141)*((5.102121741392337e-7)+(blauerWinkel-142)*((-8.54838795305568e-9)+(blauerWinkel-143)*((8.758419767217454e-10)+(blauerWinkel-144)*((-2.0858201938099876e-11)+(blauerWinkel-145)*((1.7920761875748829e-13)+(blauerWinkel-146)*((4.136334622017823e-15)+(blauerWinkel-147)*((1.0964366102717062e-8)))))))))));
%vierterWinkel=74.03945099335755+(blauerWinkel-138)*((0.3360019979627964)+(blauerWinkel-139)*((-0.020307756998917625)+(blauerWinkel-140)*((0.00012447453548247722)+(blauerWinkel-141)*((-5.133324603908348e-7)+(blauerWinkel-142)*((9.860567710500534e-9)+(blauerWinkel-143)*((-8.274150352529208e-10)+(blauerWinkel-144)*((1.9842588242755387e-11)+(blauerWinkel-145)*((-1.5015713541300292e-13)+(blauerWinkel-146)*((-4.670925608277748e-15)+(blauerWinkel-147)*((-1.0660105930766685e-8)))))))))));
%fuenfterWinkel=97.43016871071936+(blauerWinkel-138)*((-1.1229762192709387)+(blauerWinkel-139)*((0.007160463156708374)+(blauerWinkel-140)*((-0.000012708070556755047)+(blauerWinkel-141)*((-0.0000010831081874348074)+(blauerWinkel-142)*((5.5091601799024e-9)+(blauerWinkel-143)*((3.796474246087483e-10)+(blauerWinkel-144)*((-3.5389032092830534e-12)+(blauerWinkel-145)*((-2.770482256302422e-13)+(blauerWinkel-146)*((1.246617937249165e-14)+(blauerWinkel-147)*((3.2229361552503416e-7)))))))))));
%sechsterWinkel=92.05994788126162+(blauerWinkel-138)*((1.8225329525087233)+(blauerWinkel-139)*((0.003217098771855831)+(blauerWinkel-140)*((0.00005680942219044027)+(blauerWinkel-141)*((4.0591844966778903e-7)+(blauerWinkel-142)*((1.76164661525039e-8)+(blauerWinkel-143)*((-3.7049346306947657e-10)+(blauerWinkel-144)*((-4.971467329474287e-12)+(blauerWinkel-145)*((4.764041013444236e-13)+(blauerWinkel-146)*((-1.3956032095490156e-14)+(blauerWinkel-147)*((-6.16767933321335e-7)))))))))));
%siebenterWinkel=157.4301687107192+(blauerWinkel-138)*((-1.1229762192706403)+(blauerWinkel-139)*((0.007160463156424157)+(blauerWinkel-140)*((-0.000012708070438331257)+(blauerWinkel-141)*((-0.0000010831082176328741)+(blauerWinkel-142)*((5.509167522177534e-9)+(blauerWinkel-143)*((3.79645273243191e-10)+(blauerWinkel-144)*((-3.53830545109976e-12)+(blauerWinkel-145)*((-2.7718568181449936e-13)+(blauerWinkel-146)*((1.2493944737976288e-14)+(blauerWinkel-147)*((3.222936155195046e-7)))))))))));
%achterWinkel=134.03945099335772+(blauerWinkel-138)*((0.33600199796262586)+(blauerWinkel-139)*((-0.02030775699883236)+(blauerWinkel-140)*((0.00012447453548247722)+(blauerWinkel-141)*((-5.133324746016895e-7)+(blauerWinkel-142)*((9.860573631689773e-9)+(blauerWinkel-143)*((-8.274163181772673e-10)+(blauerWinkel-144)*((1.984272922346768e-11)+(blauerWinkel-145)*((-1.5014092263971942e-13)+(blauerWinkel-146)*((-4.685023675967204e-15)+(blauerWinkel-147)*((-1.0660105926090826e-8)))))))))));
%neunterWinkel=105.95845826005805+(blauerWinkel-138)*((-0.33542170425687345)+(blauerWinkel-139)*((0.020273471044440328)+(blauerWinkel-140)*((-0.00012750497965186014)+(blauerWinkel-141)*((5.10212214995441e-7)+(blauerWinkel-142)*((-8.548394466364995e-9)+(blauerWinkel-143)*((8.758412859166843e-10)+(blauerWinkel-144)*((-2.0857513952367783e-11)+(blauerWinkel-145)*((1.7898804132962844e-13)+(blauerWinkel-146)*((4.184698833487993e-15)+(blauerWinkel-147)*((1.0964366094332629e-8)))))))))));
%P[5]=[113.53195298149822,13.1016955924527]; P[2]=[63.687443166521255,9.161538069629813]; D=ab(5,2); A(2,5); N(4,2,5); N(3,2,4); N(1,2,3); M(8,1,2,blauerWinkel); N(7,8,1); N(9,8,7); N(10,8,9); M(16,10,8,gruenerWinkel); N(15,16,10); N(17,16,15); N(18,16,17); M(37,18,16,orangerWinkel); N(36,18,37); N(35,36,37); N(31,36,35); M(30,31,36,vierterWinkel); N(29,31,30); N(28,29,30); N(22,29,28); M(24,22,29,fuenfterWinkel); N(23,22,24); N(25,23,24); N(26,23,25); M(43,26,23,sechsterWinkel); N(41,26,43); N(42,41,43); N(40,41,42); M(46,40,41,siebenterWinkel); N(45,46,40); N(47,46,45); N(48,46,47); M(53,48,46,achterWinkel); N(52,53,48); N(54,53,52); N(55,53,54); M(72,55,53,neunterWinkel); N(71,55,72); N(70,71,72); N(67,71,70); Q(59,67,5,2*D,2*D); A(59,67); A(59,5); H(60,5,59,2); A(60,5); L(62,5,60); H(65,67,59,2); A(65,67); L(66,65,67); A(65,59); L(64,59,65); A(64,66); A(60,59); L(61,60,59); A(62,61); N(11,9,7); N(20,37,17); N(32,28,30); N(38,35,20); N(49,47,45); N(57,72,54); N(68,64,66); N(73,70,57); N(6,11,3); N(19,20,15); N(27,24,32); N(44,49,42); N(56,57,52); N(63,61,68); N(12,11,6); N(21,20,19); N(33,27,32); N(39,38,20); N(50,49,44); N(58,57,56); N(69,63,68); N(74,73,57); N(13,69,12); N(14,33,13); N(34,14,50); N(51,69,34);
%A(14,39); R(14,39,"green");
%A(14,21); R(14,21,"green");
%A(14,12); R(14,12,"green");
%A(34,33); R(34,33,"green");
%A(51,74); R(51,74,"green");
%A(51,58); R(51,58,"green");
%A(51,13); R(51,13,"green");
%A(51,50); R(51,50,"green");
%</Rechenweg>
%
%<Knopf id="Stopp_alleWinkel" color="LightGrey"/>
%
%<Knopf id="Start_blauerWinkel" color="blue"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#blauerWinkel" attributeName="value" values="0;10;0;10;0" dur="15" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_blauerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.81/0.00,
2/2.81/0.08,
3/2.25/0.90,
4/3.24/0.98,
5/3.81/0.16,
6/2.99/1.57,
7/1.95/0.99,
8/1.02/0.61,
9/1.15/1.60,
10/0.23/1.22,
11/2.08/1.98,
12/2.89/2.57,
13/3.81/2.18,
14/3.68/3.17,
15/1.03/1.81,
16/0.11/2.21,
17/0.92/2.81,
18/0.00/3.20,
19/1.96/2.20,
20/1.84/3.19,
21/2.76/2.79,
22/1.87/6.38,
23/2.84/6.62,
24/2.56/5.66,
25/3.53/5.90,
26/3.81/6.86,
27/3.02/4.77,
28/1.98/5.38,
29/1.06/5.78,
30/1.18/4.79,
31/0.26/5.19,
32/2.10/4.39,
33/2.89/3.78,
34/3.81/4.17,
35/1.05/4.58,
36/0.13/4.20,
37/0.92/3.59,
38/1.97/4.18,
39/2.77/3.57,
40/5.75/6.38,
41/4.78/6.62,
42/5.06/5.66,
43/4.08/5.90,
44/4.60/4.77,
45/5.64/5.38,
46/6.55/5.78,
47/6.44/4.79,
48/7.36/5.19,
49/5.52/4.39,
50/4.73/3.78,
51/3.94/3.17,
52/6.56/4.58,
53/7.49/4.20,
54/6.69/3.59,
55/7.62/3.20,
56/5.65/4.18,
57/5.78/3.19,
58/4.85/3.57,
59/5.80/0.00,
60/4.81/0.08,
61/5.37/0.90,
62/4.38/0.98,
63/4.63/1.57,
64/5.67/0.99,
65/6.60/0.61,
66/6.47/1.60,
67/7.39/1.22,
68/5.54/1.98,
69/4.73/2.57,
70/6.59/1.81,
71/7.50/2.21,
72/6.70/2.81,
73/5.66/2.20,
74/4.86/2.79}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
1/4.52/142.52/0.4/Blue}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
1/2, 1/3,
2/5,
3/2, 3/4,
4/2, 4/5,
6/11, 6/3,
7/8, 7/1,
8/1,
9/8, 9/7,
10/8, 10/9,
11/9, 11/7,
12/11, 12/6,
13/69, 13/12,
14/33, 14/13, 14/39, 14/21, 14/12,
15/16, 15/10,
16/10,
17/16, 17/15,
18/16, 18/17,
19/20, 19/15,
20/37, 20/17,
21/20, 21/19,
22/29, 22/28,
23/22, 23/24,
24/22,
25/23, 25/24,
26/23, 26/25,
27/24, 27/32,
28/29, 28/30,
29/31, 29/30,
30/31,
31/36, 31/35,
32/28, 32/30,
33/27, 33/32,
34/14, 34/50, 34/33,
35/36, 35/37,
36/18, 36/37,
37/18,
38/35, 38/20,
39/38, 39/20,
40/41, 40/42,
41/26, 41/43,
42/41, 42/43,
43/26,
44/49, 44/42,
45/46, 45/40,
46/40,
47/46, 47/45,
48/46, 48/47,
49/47, 49/45,
50/49, 50/44,
51/69, 51/34, 51/74, 51/58, 51/13, 51/50,
52/53, 52/48,
53/48,
54/53, 54/52,
55/53, 55/54,
56/57, 56/52,
57/72, 57/54,
58/57, 58/56,
60/5, 60/59,
61/60, 61/59,
62/5, 62/60, 62/61,
63/61, 63/68,
64/59, 64/65, 64/66,
65/67, 65/59,
66/65, 66/67,
67/71, 67/70,
68/64, 68/66,
69/63, 69/68,
70/71, 70/72,
71/55, 71/72,
72/55,
73/70, 73/57,
74/73, 74/57}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,74}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
1/4.52/142.52/0.4/Blue}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/293,
2/335,
3/155,
4/35,
5/335,
6/306,
7/293,
8/293,
9/53,
10/173,
11/53,
12/187,
13/233,
14/67,
15/307,
16/127,
17/7,
18/233,
19/247,
20/127,
21/7,
22/164,
23/164,
24/284,
25/344,
26/136,
27/52,
28/307,
29/187,
30/307,
31/113,
32/307,
33/173,
34/127,
35/353,
36/173,
37/353,
38/113,
39/353,
40/113,
41/76,
42/256,
43/256,
44/128,
45/233,
46/53,
47/353,
48/353,
49/8,
50/248,
51/113,
52/187,
53/307,
54/187,
55/53,
56/67,
57/307,
58/187,
59/325,
60/325,
61/25,
62/145,
63/234,
64/127,
65/7,
66/127,
67/293,
68/127,
69/114,
70/173,
71/353,
72/113,
73/293,
74/173}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/bfa0ea018ff2c3c90341f94679c83449.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1902_1c = #1894-1 mit 4 umgelegten Kanten, dann blauerWinkel=138+10*1</Bildtext>
%<Ausrichten von=\"18\" nach=\"55\"/>
%<Winkel size=\"18\" color=\"blue\" id=\"blauerWinkel\" value=\"138\"/>
%<Feinjustieren Anzahl=\"8,8\"/>
%<Rechenweg>
%gruenerWinkel=134.02217398627073+(blauerWinkel-138)*((0.33863056790141854)+(blauerWinkel-139)*((-0.020425597796361217)+(blauerWinkel-140)*((0.00012591747007206777)+(blauerWinkel-141)*((-1.6782361456080253e-7)+(blauerWinkel-142)*((-5.10587625512926e-9)+(blauerWinkel-143)*((-5.73784378035447e-10)+(blauerWinkel-144)*((1.7203660718255866e-11)+(blauerWinkel-145)*((-1.8288228075388755e-13)+(blauerWinkel-146)*((-2.8274462916897133e-15)+(blauerWinkel-147)*((-1.0871584379996863e-8)))))))))));
%orangerWinkel=105.9584582600583+(blauerWinkel-138)*((-0.3354217042569161)+(blauerWinkel-139)*((0.020273471044319535)+(blauerWinkel-140)*((-0.00012750497954291026)+(blauerWinkel-141)*((5.102121741392337e-7)+(blauerWinkel-142)*((-8.54838795305568e-9)+(blauerWinkel-143)*((8.758419767217454e-10)+(blauerWinkel-144)*((-2.0858201938099876e-11)+(blauerWinkel-145)*((1.7920761875748829e-13)+(blauerWinkel-146)*((4.136334622017823e-15)+(blauerWinkel-147)*((1.0964366102717062e-8)))))))))));
%vierterWinkel=74.03945099335755+(blauerWinkel-138)*((0.3360019979627964)+(blauerWinkel-139)*((-0.020307756998917625)+(blauerWinkel-140)*((0.00012447453548247722)+(blauerWinkel-141)*((-5.133324603908348e-7)+(blauerWinkel-142)*((9.860567710500534e-9)+(blauerWinkel-143)*((-8.274150352529208e-10)+(blauerWinkel-144)*((1.9842588242755387e-11)+(blauerWinkel-145)*((-1.5015713541300292e-13)+(blauerWinkel-146)*((-4.670925608277748e-15)+(blauerWinkel-147)*((-1.0660105930766685e-8)))))))))));
%fuenfterWinkel=97.43016871071936+(blauerWinkel-138)*((-1.1229762192709387)+(blauerWinkel-139)*((0.007160463156708374)+(blauerWinkel-140)*((-0.000012708070556755047)+(blauerWinkel-141)*((-0.0000010831081874348074)+(blauerWinkel-142)*((5.5091601799024e-9)+(blauerWinkel-143)*((3.796474246087483e-10)+(blauerWinkel-144)*((-3.5389032092830534e-12)+(blauerWinkel-145)*((-2.770482256302422e-13)+(blauerWinkel-146)*((1.246617937249165e-14)+(blauerWinkel-147)*((3.2229361552503416e-7)))))))))));
%sechsterWinkel=92.05994788126162+(blauerWinkel-138)*((1.8225329525087233)+(blauerWinkel-139)*((0.003217098771855831)+(blauerWinkel-140)*((0.00005680942219044027)+(blauerWinkel-141)*((4.0591844966778903e-7)+(blauerWinkel-142)*((1.76164661525039e-8)+(blauerWinkel-143)*((-3.7049346306947657e-10)+(blauerWinkel-144)*((-4.971467329474287e-12)+(blauerWinkel-145)*((4.764041013444236e-13)+(blauerWinkel-146)*((-1.3956032095490156e-14)+(blauerWinkel-147)*((-6.16767933321335e-7)))))))))));
%siebenterWinkel=157.4301687107192+(blauerWinkel-138)*((-1.1229762192706403)+(blauerWinkel-139)*((0.007160463156424157)+(blauerWinkel-140)*((-0.000012708070438331257)+(blauerWinkel-141)*((-0.0000010831082176328741)+(blauerWinkel-142)*((5.509167522177534e-9)+(blauerWinkel-143)*((3.79645273243191e-10)+(blauerWinkel-144)*((-3.53830545109976e-12)+(blauerWinkel-145)*((-2.7718568181449936e-13)+(blauerWinkel-146)*((1.2493944737976288e-14)+(blauerWinkel-147)*((3.222936155195046e-7)))))))))));
%achterWinkel=134.03945099335772+(blauerWinkel-138)*((0.33600199796262586)+(blauerWinkel-139)*((-0.02030775699883236)+(blauerWinkel-140)*((0.00012447453548247722)+(blauerWinkel-141)*((-5.133324746016895e-7)+(blauerWinkel-142)*((9.860573631689773e-9)+(blauerWinkel-143)*((-8.274163181772673e-10)+(blauerWinkel-144)*((1.984272922346768e-11)+(blauerWinkel-145)*((-1.5014092263971942e-13)+(blauerWinkel-146)*((-4.685023675967204e-15)+(blauerWinkel-147)*((-1.0660105926090826e-8)))))))))));
%neunterWinkel=105.95845826005805+(blauerWinkel-138)*((-0.33542170425687345)+(blauerWinkel-139)*((0.020273471044440328)+(blauerWinkel-140)*((-0.00012750497965186014)+(blauerWinkel-141)*((5.10212214995441e-7)+(blauerWinkel-142)*((-8.548394466364995e-9)+(blauerWinkel-143)*((8.758412859166843e-10)+(blauerWinkel-144)*((-2.0857513952367783e-11)+(blauerWinkel-145)*((1.7898804132962844e-13)+(blauerWinkel-146)*((4.184698833487993e-15)+(blauerWinkel-147)*((1.0964366094332629e-8)))))))))));
%P[5]=[113.53195298149822,13.1016955924527]; P[2]=[63.687443166521255,9.161538069629813]; D=ab(5,2); A(2,5); N(4,2,5); N(3,2,4); N(1,2,3); M(8,1,2,blauerWinkel); N(7,8,1); N(9,8,7); N(10,8,9); M(16,10,8,gruenerWinkel); N(15,16,10); N(17,16,15); N(18,16,17); M(37,18,16,orangerWinkel); N(36,18,37); N(35,36,37); N(31,36,35); M(30,31,36,vierterWinkel); N(29,31,30); N(28,29,30); N(22,29,28); M(24,22,29,fuenfterWinkel); N(23,22,24); N(25,23,24); N(26,23,25); M(43,26,23,sechsterWinkel); N(41,26,43); N(42,41,43); N(40,41,42); M(46,40,41,siebenterWinkel); N(45,46,40); N(47,46,45); N(48,46,47); M(53,48,46,achterWinkel); N(52,53,48); N(54,53,52); N(55,53,54); M(72,55,53,neunterWinkel); N(71,55,72); N(70,71,72); N(67,71,70); Q(59,67,5,2*D,2*D); A(59,67); A(59,5); H(60,5,59,2); A(60,5); L(62,5,60); H(65,67,59,2); A(65,67); L(66,65,67); A(65,59); L(64,59,65); A(64,66); A(60,59); L(61,60,59); A(62,61); N(11,9,7); N(20,37,17); N(32,28,30); N(38,35,20); N(49,47,45); N(57,72,54); N(68,64,66); N(73,70,57); N(6,11,3); N(19,20,15); N(27,24,32); N(44,49,42); N(56,57,52); N(63,61,68); N(12,11,6); N(21,20,19); N(33,27,32); N(39,38,20); N(50,49,44); N(58,57,56); N(69,63,68); N(74,73,57); N(13,69,12); N(14,33,13); N(34,14,50); N(51,69,34);
%A(14,39); R(14,39,\"green\");
%A(14,21); R(14,21,\"green\");
%A(14,12); R(14,12,\"green\");
%A(34,33); R(34,33,\"green\");
%A(51,74); R(51,74,\"green\");
%A(51,58); R(51,58,\"green\");
%A(51,13); R(51,13,\"green\");
%A(51,50); R(51,50,\"green\");
%</Rechenweg>
%
%<Knopf id=\"Stopp_alleWinkel\" color=\"LightGrey\"/>
%
%<Knopf id=\"Start_blauerWinkel\" color=\"blue\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#blauerWinkel\" attributeName=\"value\" values=\"0;10;0;10;0\" dur=\"15\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_blauerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.81/0.00,
2/2.81/0.08,
3/2.25/0.90,
4/3.24/0.98,
5/3.81/0.16,
6/2.99/1.57,
7/1.95/0.99,
8/1.02/0.61,
9/1.15/1.60,
10/0.23/1.22,
11/2.08/1.98,
12/2.89/2.57,
13/3.81/2.18,
14/3.68/3.17,
15/1.03/1.81,
16/0.11/2.21,
17/0.92/2.81,
18/0.00/3.20,
19/1.96/2.20,
20/1.84/3.19,
21/2.76/2.79,
22/1.87/6.38,
23/2.84/6.62,
24/2.56/5.66,
25/3.53/5.90,
26/3.81/6.86,
27/3.02/4.77,
28/1.98/5.38,
29/1.06/5.78,
30/1.18/4.79,
31/0.26/5.19,
32/2.10/4.39,
33/2.89/3.78,
34/3.81/4.17,
35/1.05/4.58,
36/0.13/4.20,
37/0.92/3.59,
38/1.97/4.18,
39/2.77/3.57,
40/5.75/6.38,
41/4.78/6.62,
42/5.06/5.66,
43/4.08/5.90,
44/4.60/4.77,
45/5.64/5.38,
46/6.55/5.78,
47/6.44/4.79,
48/7.36/5.19,
49/5.52/4.39,
50/4.73/3.78,
51/3.94/3.17,
52/6.56/4.58,
53/7.49/4.20,
54/6.69/3.59,
55/7.62/3.20,
56/5.65/4.18,
57/5.78/3.19,
58/4.85/3.57,
59/5.80/0.00,
60/4.81/0.08,
61/5.37/0.90,
62/4.38/0.98,
63/4.63/1.57,
64/5.67/0.99,
65/6.60/0.61,
66/6.47/1.60,
67/7.39/1.22,
68/5.54/1.98,
69/4.73/2.57,
70/6.59/1.81,
71/7.50/2.21,
72/6.70/2.81,
73/5.66/2.20,
74/4.86/2.79}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
1/4.52/142.52/0.4/Blue}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
1/2, 1/3,
2/5,
3/2, 3/4,
4/2, 4/5,
6/11, 6/3,
7/8, 7/1,
8/1,
9/8, 9/7,
10/8, 10/9,
11/9, 11/7,
12/11, 12/6,
13/69, 13/12,
14/33, 14/13, 14/39, 14/21, 14/12,
15/16, 15/10,
16/10,
17/16, 17/15,
18/16, 18/17,
19/20, 19/15,
20/37, 20/17,
21/20, 21/19,
22/29, 22/28,
23/22, 23/24,
24/22,
25/23, 25/24,
26/23, 26/25,
27/24, 27/32,
28/29, 28/30,
29/31, 29/30,
30/31,
31/36, 31/35,
32/28, 32/30,
33/27, 33/32,
34/14, 34/50, 34/33,
35/36, 35/37,
36/18, 36/37,
37/18,
38/35, 38/20,
39/38, 39/20,
40/41, 40/42,
41/26, 41/43,
42/41, 42/43,
43/26,
44/49, 44/42,
45/46, 45/40,
46/40,
47/46, 47/45,
48/46, 48/47,
49/47, 49/45,
50/49, 50/44,
51/69, 51/34, 51/74, 51/58, 51/13, 51/50,
52/53, 52/48,
53/48,
54/53, 54/52,
55/53, 55/54,
56/57, 56/52,
57/72, 57/54,
58/57, 58/56,
60/5, 60/59,
61/60, 61/59,
62/5, 62/60, 62/61,
63/61, 63/68,
64/59, 64/65, 64/66,
65/67, 65/59,
66/65, 66/67,
67/71, 67/70,
68/64, 68/66,
69/63, 69/68,
70/71, 70/72,
71/55, 71/72,
72/55,
73/70, 73/57,
74/73, 74/57}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,74}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
1/4.52/142.52/0.4/Blue}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/293,
2/335,
3/155,
4/35,
5/335,
6/306,
7/293,
8/293,
9/53,
10/173,
11/53,
12/187,
13/233,
14/67,
15/307,
16/127,
17/7,
18/233,
19/247,
20/127,
21/7,
22/164,
23/164,
24/284,
25/344,
26/136,
27/52,
28/307,
29/187,
30/307,
31/113,
32/307,
33/173,
34/127,
35/353,
36/173,
37/353,
38/113,
39/353,
40/113,
41/76,
42/256,
43/256,
44/128,
45/233,
46/53,
47/353,
48/353,
49/8,
50/248,
51/113,
52/187,
53/307,
54/187,
55/53,
56/67,
57/307,
58/187,
59/325,
60/325,
61/25,
62/145,
63/234,
64/127,
65/7,
66/127,
67/293,
68/127,
69/114,
70/173,
71/353,
72/113,
73/293,
74/173}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
[Ebenfalls Graph ins große Eingabefenster des Streichholzprogramms kopieren, dann Buttons "neu zeichnen", "Ausrichten", "Kanten" und Animationsknopf "Start_blauerWinkel" links neben dem Graph"]
Dieses Ergebnis steht scheinbar im Widerspruch zu den Überlegungen mit der Ableitungsmatrix. Danach dürften es keine zwei Bewegungsmöglichkeiten geben. Wenn der Winkel in P5 vergrößert wird, dann darf der Winkel in P26 sich ebenfalls nur in einer Richtung verändern, entweder größer oder kleiner, und nicht in zwei Varianten. Bei dieser Berechnung eine Bewegungsmöglichkeit wegen Rundungsfehler übersehen geht auch nicht, weil das extra GAP-Programm mit exakter Berechnung bestätigt, dass der Graph (vom Anfang des Beitrages) nur einfach statisch unbestimmt ist.
GAP-LogfileGAP gap> W60:=[[1/2,-1/2*Sqrt(3)],[1/2*Sqrt(3),1/2]];
[ [ 1/2, 1/2*E(12)^7-1/2*E(12)^11 ], [ -1/2*E(12)^7+1/2*E(12)^11, 1/2 ] ]
gap> Wbl:=[[1/4,-1/4*Sqrt(15)],[1/4*Sqrt(15),1/4]]*W60^-1; #acos(1/4)_Graph
[ [ 1/4*E(5)-1/2*E(5)^2-1/2*E(5)^3+1/4*E(5)^4, -1/4*E(60)^7+1/4*E(60)^23-1/4*E(60)^43+1/4*E(60)^47 ], [ 1/4*E(60)^7-1/4*E(60)^23+1/4*E(60)^43-1/4*E(60)^47, 1/4*E(5)-1/2*E(5)^2-1/2*E(5)^3+1/4*E(5)^4 ] ]
gap> P:=[];
[ ]
gap> P[1]:=[0,0];
[ 0, 0 ]
gap> P[2]:=[1,0];
[ 1, 0 ]
gap> P[3]:=P[1]+W60*(P[2]-P[1]);;
gap> P[4]:=P[3]+W60*(P[2]-P[3]);;
gap> P[5]:=P[2]-(P[1]-P[2]);;
gap> P[6]:=P[3]-(P[1]-P[3]);;
gap> P[7]:=P[1]+W60*Wbl^-2*(P[3]-P[1]);;
gap> P[8]:=P[1]+W60*(P[7]-P[1]);;
gap> P[9]:=P[8]+W60*(P[7]-P[8]);;
gap> P[10]:=P[8]-(P[1]-P[8]);;
gap> P[11]:=P[9]-(P[10]-P[9]);;
gap> P[12]:=P[11]+W60*(P[6]-P[11]);;
gap> P[13]:=P[12]+W60*(P[6]-P[12]);;
gap> P[14]:=P[12]-(P[11]-P[12]);;
gap> P[15]:=P[10]+Wbl*(P[9]-P[10]);;
gap> P[16]:=P[10]+W60*(P[15]-P[10]);;
gap> P[17]:=P[16]+W60*(P[15]-P[16]);;
gap> P[18]:=P[16]-(P[10]-P[16]);;
gap> P[19]:=P[15]+W60^3*Wbl^-1*(P[10]-P[15]);;
gap> P[20]:=P[17]+W60^3*Wbl^-1*(P[16]-P[17]);;
gap> P[21]:=P[20]+W60*(P[19]-P[20]);;
gap> P[34]:=P[14]+W60^3*Wbl^-1*(P[13]-P[14]);;
gap> P[36]:=P[18]+W60^3*Wbl^-1*(P[16]-P[18]);;
gap> P[37]:=P[20]-(P[21]-P[20]);;
gap> P[38]:=P[20]+W60^3*Wbl^-1*(P[19]-P[20]);;
gap> P[39]:=P[20]-(P[17]-P[20]);;
gap> P[50]:=P[34]+W60*Wbl*(P[14]-P[34]);;
gap> P[51]:=P[50]+W60*(P[34]-P[50]);;
gap> P[58]:=P[51]+W60^2*(P[13]-P[51]);;
gap> P[69]:=P[51]+W60*(P[13]-P[51]);;
gap> P[74]:=P[51]+Wbl*(P[69]-P[51]);;
gap> P[31]:=P[36]-(P[18]-P[36]);;
gap> P[33]:=P[14]+W60*(P[34]-P[14]);;
gap> P[35]:=P[31]+W60*(P[36]-P[31]);;
gap> P[49]:=P[50]-(P[51]-P[50]);;
gap> P[57]:=P[58]+W60*W60*Wbl*(P[51]-P[58]);;
gap> P[63]:=P[69]+W60*(P[13]-P[69]);;
gap> P[68]:=P[69]-(P[51]-P[69]);;
gap> P[72]:=P[57]-(P[58]-P[57]);;
gap> P[73]:=P[57]+W60*(P[74]-P[57]);;
gap> P[27]:=P[33]+W60*(P[34]-P[33]);;
gap> P[29]:=P[31]+W60*Wbl*(P[35]-P[31]);;
gap> P[30]:=P[29]+W60*(P[31]-P[29]);;
gap> P[32]:=P[30]-(P[31]-P[30]);;
gap> P[44]:=P[50]+W60*(P[49]-P[50]);;
gap> P[47]:=P[49]+W60^3*Wbl^-1*(P[50]-P[49]);;
gap> P[48]:=P[47]-(P[49]-P[47]);;
gap> P[52]:=P[48]+Wbl*(P[47]-P[48]);;
gap> P[53]:=P[48]+W60*(P[52]-P[48]);;
gap> P[54]:=P[57]-(P[74]-P[57]);;
gap> P[55]:=P[53]-(P[48]-P[53]);;
gap> P[56]:=P[58]+W60*(P[57]-P[58]);;
gap> P[64]:=P[68]+W60*Wbl*(P[63]-P[68]);;
gap> P[66]:=P[68]+W60*(P[64]-P[68]);;
gap> P[67]:=P[66]-(P[68]-P[66]);;
gap> P[71]:=P[55]+W60*(P[72]-P[55]);;
gap> P[22]:=P[29]-(P[31]-P[29]);;
gap> P[24]:=P[22]+W60^2*Wbl^-2*(P[29]-P[22]);;
gap> P[25]:=P[24]+W60*(P[27]-P[24]);;
gap> P[28]:=P[22]+W60*(P[29]-P[22]);;
gap> P[42]:=P[44]+W60*Wbl*(P[49]-P[44]);;
gap> P[45]:=P[49]+W60*(P[47]-P[49]);;
gap> P[46]:=P[45]+W60*(P[47]-P[45]);;
gap> P[59]:=P[64]-(P[68]-P[64]);;
gap> P[60]:=P[59]+W60^2*Wbl^-2*(P[64]-P[59]);;
gap> P[61]:=P[60]+W60*(P[59]-P[60]);;
gap> P[62]:=P[5]+W60*(P[60]-P[5]);;
gap> P[65]:=P[64]+W60*(P[59]-P[64]);;
gap> P[70]:=P[67]+W60*(P[71]-P[67]);;
gap> P[23]:=P[22]+W60*(P[24]-P[22]);;
gap> P[26]:=P[23]-(P[22]-P[23]);;
gap> P[40]:=P[42]-(P[44]-P[42]);;
gap> P[41]:=P[42]+W60*(P[40]-P[42]);;
gap> P[43]:=P[41]+W60*(P[26]-P[41]);;
gap> Kante:=[ [1,2],[1,3],[2,5],[2,3], [3,4],[2,4], [4,5],[6,11],[3,6], [7,8],[1,7], [1,8], [8,9], [7,9], [8,10], [9,10], [9,11], [7,11], [11,12], [6,12], [13,69],[12,13], [14,33],[13,14], [14,39],[14,21],[12,14], [15,16],[10,15], [10,16], [16,17], [15,17], [16,18], [17,18], [19,20],[15,19], [20,37],[17,20], [20,21], [19,21], [22,29],[22,28],[22,23], [23,24],[22,24], [23,25], [24,25], [23,26], [25,26], [24,27], [27,32],[28,29],[28,30],[29,31],[29,30],[30,31],[31,36],[31,35],[28,32], [30,32], [27,33], [32,33], [14,34], [34,50],[33,34], [35,36],[35,37],[18,36], [36,37],[18,37], [35,38], [20,38], [38,39], [20,39], [40,41],[40,42],[26,41], [41,43],[41,42], [42,43],[26,43], [44,49],[42,44], [45,46],[40,45], [40,46], [46,47], [45,47], [46,48], [47,48], [47,49], [45,49], [49,50], [44,50], [51,69],[34,51], [51,74],[51,58],[13,51], [50,51], [52,53],[48,52], [48,53], [53,54], [52,54], [53,55], [54,55], [56,57],[52,56], [57,72],[54,57], [57,58], [56,58], [5,60], [59,60], [60,61], [59,61], [5,62], [60,62], [61,62], [61,63], [63,68],[59,64], [64,65],[64,66],[65,67],[59,65], [65,66], [66,67],[67,71],[67,70],[64,68], [66,68], [63,69], [68,69], [70,71],[70,72],[55,71], [71,72],[55,72], [70,73], [57,73], [73,74], [57,74], ];;
gap> Size(Kante);
144
gap> RESTKANTEN:=[[14,39],[14,21],[14,12],[34,33],[51,74],[51,58],[51,13],[51,50],];;
gap>
gap> for K in Kante do Print(" ",(P[K[1]]-P[K[2]])^2); od;
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
gap>
gap> PUNKTEZAHL:=Size(P); KOORDINATENZAHL:=2*PUNKTEZAHL; KANTENZAHL:=Size(Kante);
74
148
144
gap> n:=Maximum(KOORDINATENZAHL,KANTENZAHL); A:=NullMat(n,n);;
148
gap> for i in [1..KANTENZAHL] do
> A[2*Kante[i][1]-1][i]:=P[Kante[i][2]][1]-P[Kante[i][1]][1];
> A[2*Kante[i][1] ][i]:=P[Kante[i][2]][2]-P[Kante[i][1]][2];
> A[2*Kante[i][2]-1][i]:=P[Kante[i][1]][1]-P[Kante[i][2]][1];
> A[2*Kante[i][2] ][i]:=P[Kante[i][1]][2]-P[Kante[i][2]][2];
> od;
gap> Nenner:=Lcm(List(Flat(A),i->DenominatorCyc(i)));
16
gap> A:=Nenner*A;;P:=Nenner*P;;
gap> AlterNenner:=1;
1
gap>
gap> RankA:=Rank(A);
144
gap> Print("gerechnet_mit_Button=\"",gerechnet_mit_Button,"\";");
gerechnet_mit_Button="acos(1/4)";
gap> Print("Beweglichkeit=",KOORDINATENZAHL-RankA-3);
Beweglichkeit=1
gap> Print("Einsetzkanten=",KANTENZAHL-RankA);
Einsetzkanten=0
gap> |
|
Profil
Quote
Link |
Slash
Aktiv
Dabei seit: 23.03.2005
Mitteilungen: 7758
Aus: Cuxhaven-Sahlenburg
| Beitrag No.1903, vom Themenstarter, eingetragen 2020-02-15 11:57
|
Vielen Dank, Stefan, für die Neuerungen im Programm. 
Hast du ein paar alte Graphen im Kopf, die wir auf Beweglichkeit noch mal untersuchen sollten?
-----------------
Bound to be disappointing so why wait?
|
Profil
Quote
Link |
StefanVogel
Senior
Dabei seit: 26.11.2005
Mitteilungen: 3446
Aus: Raun
| Beitrag No.1904, eingetragen 2020-02-15 17:32
|
Graph #755 zum Beispiel.
Weiterhin, wie die Beweglichkeit von Graphen aussieht, wenn man Kanten herausnimmt,
2020-01-20 10:35 - haribo in Beitrag No. 1893 schreibt:
der graph aus #1881 ist also starr, dann kann man ja mal anfangen wieder kreativ zu werden... wenn man 9-19 herausnimmt wie beweglich verhält sich dann die strecke 15-11?, just playing around without target
um sie an einer anderen Stelle wieder einzusetzen. Das sozusagen "with target" ausprobieren.
Im Moment ist das aber alles nur Test von verschiedenen Programmfunktionen, ob dieses Ziel irgendwie erreichbar ist.
|
Profil
Quote
Link |
StefanVogel
Senior
Dabei seit: 26.11.2005
Mitteilungen: 3446
Aus: Raun
| Beitrag No.1905, eingetragen 2020-02-15 18:31
|
2020-02-15 05:55 - StefanVogel in Beitrag No. 1902 schreibt:
Dieses Ergebnis steht scheinbar im Widerspruch zu den Überlegungen mit der Ableitungsmatrix. Danach dürften es keine zwei Bewegungsmöglichkeiten geben. Wenn der Winkel in P5 vergrößert wird, dann darf der Winkel in P26 sich ebenfalls nur in einer Richtung verändern, entweder größer oder kleiner, und nicht in zwei Varianten.
Das ist auch der Fall. Wenn ich in Graph #1902-1+Button neue Eingabe "Rahmen zuerst" den Winkel blauerWinkel bei P1 in kleinsten Schritten von hundertstel, tausendstel, zehntausendstel Grad verringere von anfangs 148.9550° auf 147.4139° und dabei den Graph mit den übrigen Winkeln wieder zurechtziehe (Button "Feinjustieren(8,8)"), dann folgt fuenfterWinkel bei P22 ebenfalls von 88.9550° bis 87.4143°. Im Bild kaum erkennbar diese Veränderung
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1905 = #1902 mit blauerWinkel=147.4139</Bildtext>
%<Ausrichten von="18" nach="55"/>
%<Winkel size="18" color="green" id="gruenerWinkel" value="135.66530615863013"/>
%<Winkel size="18" color="orange" id="orangerWinkel" value="104.33358940119679"/>
%<Winkel size="18" color="violet" id="vierterWinkel" value="75.66530645296255"/>
%<Winkel size="18" color="lime" id="sechsterWinkel" value="109.50712358893763"/>
%<Winkel size="18" color="LightBlue" id="siebenterWinkel" value="147.4143492265599"/>
%<Winkel size="18" color="LightCoral" id="achterWinkel" value="135.66530645296234"/>
%<Winkel size="18" color="LightCyan" id="neunterWinkel" value="104.33358940119686"/>
%<Winkel size="18" color="teal" id="fuenfterWinkel" value="87.41434922655961"/>
%<Winkel size="18" color="blue" id="blauerWinkel" value="147.4139"/>
%<Feinjustieren Anzahl="8,9"/>
%<Rechenweg>
%P[5]=[85.60885137359465,-18.74297846541552]; P[2]=[35.81828675525811,-14.171362231821632]; D=ab(5,2); A(2,5); N(4,2,5); N(3,2,4); N(1,2,3); M(8,1,2,blauerWinkel); N(7,8,1); N(9,8,7); N(10,8,9); M(16,10,8,gruenerWinkel); N(15,16,10); N(17,16,15); N(18,16,17); M(37,18,16,orangerWinkel); N(36,18,37); N(35,36,37); N(31,36,35); M(30,31,36,vierterWinkel); N(29,31,30); N(28,29,30); N(22,29,28); M(24,22,29,fuenfterWinkel); N(23,22,24); N(25,23,24); N(26,23,25); M(43,26,23,sechsterWinkel); N(41,26,43); N(42,41,43); N(40,41,42); M(46,40,41,siebenterWinkel); N(45,46,40); N(47,46,45); N(48,46,47); M(53,48,46,achterWinkel); N(52,53,48); N(54,53,52); N(55,53,54); M(72,55,53,neunterWinkel); N(71,55,72); N(70,71,72); N(67,71,70); Q(59,67,5,2*D,2*D); A(59,67); A(59,5); H(60,5,59,2); A(60,5); L(62,5,60); H(65,67,59,2); A(65,67); L(66,65,67); A(65,59); L(64,59,65); A(64,66); A(60,59); L(61,60,59); A(62,61); N(11,9,7); N(20,37,17); N(32,28,30); N(38,35,20); N(49,47,45); N(57,72,54); N(68,64,66); N(73,70,57); N(6,11,3); N(19,20,15); N(27,24,32); N(44,49,42); N(56,57,52); N(63,61,68); N(12,11,6); N(21,20,19); N(33,27,32); N(39,38,20); N(50,49,44); N(58,57,56); N(69,63,68); N(74,73,57); N(13,69,12); N(14,33,13); N(34,14,50); N(51,69,34);
%A(14,39); R(14,39,"green");
%A(14,21); R(14,21,"green");
%A(14,12); R(14,12,"green");
%A(34,33); R(34,33,"green");
%A(51,74); R(51,74,"green");
%A(51,58); R(51,58,"green");
%A(51,13); R(51,13,"green");
%A(51,50); R(51,50,"green");
%</Rechenweg>
%
%<Knopf id="Stopp_alleWinkel" color="LightGrey"/>
%
%<Knopf id="Start_blauerWinkel" color="blue"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#blauerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_blauerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_gruenerWinkel" color="green"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#gruenerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_gruenerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_orangerWinkel" color="orange"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#orangerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_orangerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_vierterWinkel" color="violet"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#vierterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_vierterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_fuenfterWinkel" color="teal"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#fuenfterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_fuenfterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_sechsterWinkel" color="lime"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#sechsterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_sechsterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_siebenterWinkel" color="LightBlue"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#siebenterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_siebenterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_achterWinkel" color="LightCoral"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#achterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_achterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_neunterWinkel" color="LightCyan"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#neunterWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_neunterWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LightBlue}{rgb}{0.68,0.84,0.90}
\definecolor{LightCoral}{rgb}{0.94,0.50,0.50}
\definecolor{LightCyan}{rgb}{0.88,1.00,1.00}
\definecolor{Lime}{rgb}{0.00,1.00,0.00}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
\definecolor{Teal}{rgb}{0.00,0.50,0.50}
\definecolor{Violet}{rgb}{0.93,0.51,0.93}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.85/0.18,
2/2.85/0.09,
3/2.43/1.00,
4/3.43/0.91,
5/3.84/0.00,
6/3.05/1.78,
7/1.99/1.17,
8/1.06/0.80,
9/1.20/1.79,
10/0.27/1.41,
11/2.12/2.16,
12/2.92/2.78,
13/3.84/2.40,
14/3.70/3.39,
15/1.06/2.02,
16/0.14/2.40,
17/0.93/3.01,
18/0.00/3.39,
19/1.99/2.40,
20/1.85/3.39,
21/2.78/3.01,
22/1.85/6.60,
23/2.85/6.69,
24/2.43/5.78,
25/3.43/5.87,
26/3.84/6.78,
27/3.05/5.00,
28/1.99/5.61,
29/1.06/5.99,
30/1.20/4.99,
31/0.27/5.37,
32/2.12/4.62,
33/2.92/4.01,
34/3.84/4.38,
35/1.06/4.76,
36/0.14/4.38,
37/0.93/3.77,
38/1.99/4.38,
39/2.78/3.77,
40/5.84/6.60,
41/4.84/6.69,
42/5.26/5.78,
43/4.26/5.87,
44/4.64/5.00,
45/5.70/5.61,
46/6.63/5.99,
47/6.49/4.99,
48/7.42/5.37,
49/5.56/4.62,
50/4.77/4.01,
51/3.98/3.39,
52/6.63/4.76,
53/7.55/4.38,
54/6.76/3.77,
55/7.69/3.39,
56/5.70/4.38,
57/5.84/3.39,
58/4.91/3.77,
59/5.84/0.18,
60/4.84/0.09,
61/5.26/1.00,
62/4.26/0.91,
63/4.64/1.78,
64/5.70/1.17,
65/6.63/0.80,
66/6.49/1.79,
67/7.42/1.41,
68/5.56/2.16,
69/4.77/2.78,
70/6.63/2.02,
71/7.55/2.40,
72/6.76/3.01,
73/5.70/2.40,
74/4.91/3.01}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
1/354.75/502.17/0.4/Blue,
10/322.17/457.83/0.4/Green,
18/277.83/382.17/0.4/Orange,
31/262.17/337.83/0.4/Violet,
22/217.83/305.25/0.4/Teal,
26/185.25/294.75/0.4/Lime,
40/174.75/322.17/0.4/LightBlue,
48/142.17/277.83/0.4/LightCoral,
55/97.83/202.17/0.4/LightCyan}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
1/2, 1/3,
2/5,
3/2, 3/4,
4/2, 4/5,
6/11, 6/3,
7/8, 7/1,
8/1,
9/8, 9/7,
10/8, 10/9,
11/9, 11/7,
12/11, 12/6,
13/69, 13/12,
14/33, 14/13, 14/39, 14/21, 14/12,
15/16, 15/10,
16/10,
17/16, 17/15,
18/16, 18/17,
19/20, 19/15,
20/37, 20/17,
21/20, 21/19,
22/29, 22/28,
23/22, 23/24,
24/22,
25/23, 25/24,
26/23, 26/25,
27/24, 27/32,
28/29, 28/30,
29/31, 29/30,
30/31,
31/36, 31/35,
32/28, 32/30,
33/27, 33/32,
34/14, 34/50, 34/33,
35/36, 35/37,
36/18, 36/37,
37/18,
38/35, 38/20,
39/38, 39/20,
40/41, 40/42,
41/26, 41/43,
42/41, 42/43,
43/26,
44/49, 44/42,
45/46, 45/40,
46/40,
47/46, 47/45,
48/46, 48/47,
49/47, 49/45,
50/49, 50/44,
51/69, 51/34, 51/74, 51/58, 51/13, 51/50,
52/53, 52/48,
53/48,
54/53, 54/52,
55/53, 55/54,
56/57, 56/52,
57/72, 57/54,
58/57, 58/56,
60/5, 60/59,
61/60, 61/59,
62/5, 62/60, 62/61,
63/61, 63/68,
64/59, 64/65, 64/66,
65/67, 65/59,
66/65, 66/67,
67/71, 67/70,
68/64, 68/66,
69/63, 69/68,
70/71, 70/72,
71/55, 71/72,
72/55,
73/70, 73/57,
74/73, 74/57}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,74}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[Green,very thick] (p-14) -- (p-39);
\draw[Green,very thick] (p-14) -- (p-21);
\draw[Green,very thick] (p-14) -- (p-12);
\draw[Green,very thick] (p-34) -- (p-33);
\draw[Green,very thick] (p-51) -- (p-74);
\draw[Green,very thick] (p-51) -- (p-58);
\draw[Green,very thick] (p-51) -- (p-13);
\draw[Green,very thick] (p-51) -- (p-50);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
1/354.75/502.17/0.4/Blue,
10/322.17/457.83/0.4/Green,
18/277.83/382.17/0.4/Orange,
31/262.17/337.83/0.4/Violet,
22/217.83/305.25/0.4/Teal,
26/185.25/294.75/0.4/Lime,
40/174.75/322.17/0.4/LightBlue,
48/142.17/277.83/0.4/LightCoral,
55/97.83/202.17/0.4/LightCyan}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/205,
2/265,
3/85,
4/25,
5/215,
6/308,
7/292,
8/172,
9/112,
10/172,
11/188,
12/188,
13/232,
14/68,
15/8,
16/128,
17/8,
18/128,
19/248,
20/128,
21/8,
22/68,
23/95,
24/275,
25/335,
26/145,
27/52,
28/68,
29/68,
30/248,
31/188,
32/172,
33/172,
34/128,
35/352,
36/112,
37/292,
38/112,
39/352,
40/25,
41/25,
42/325,
43/205,
44/128,
45/172,
46/352,
47/232,
48/352,
49/232,
50/248,
51/112,
52/128,
53/8,
54/248,
55/52,
56/68,
57/52,
58/188,
59/335,
60/215,
61/35,
62/155,
63/232,
64/188,
65/308,
66/68,
67/8,
68/128,
69/112,
70/232,
71/52,
72/112,
73/292,
74/172}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/5b75f27345536cf93f3d362b0bb118a4.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#1905 = #1902 mit blauerWinkel=147.4139</Bildtext>
%<Ausrichten von=\"18\" nach=\"55\"/>
%<Winkel size=\"18\" color=\"green\" id=\"gruenerWinkel\" value=\"135.66530615863013\"/>
%<Winkel size=\"18\" color=\"orange\" id=\"orangerWinkel\" value=\"104.33358940119679\"/>
%<Winkel size=\"18\" color=\"violet\" id=\"vierterWinkel\" value=\"75.66530645296255\"/>
%<Winkel size=\"18\" color=\"lime\" id=\"sechsterWinkel\" value=\"109.50712358893763\"/>
%<Winkel size=\"18\" color=\"LightBlue\" id=\"siebenterWinkel\" value=\"147.4143492265599\"/>
%<Winkel size=\"18\" color=\"LightCoral\" id=\"achterWinkel\" value=\"135.66530645296234\"/>
%<Winkel size=\"18\" color=\"LightCyan\" id=\"neunterWinkel\" value=\"104.33358940119686\"/>
%<Winkel size=\"18\" color=\"teal\" id=\"fuenfterWinkel\" value=\"87.41434922655961\"/>
%<Winkel size=\"18\" color=\"blue\" id=\"blauerWinkel\" value=\"147.4139\"/>
%<Feinjustieren Anzahl=\"8,9\"/>
%<Rechenweg>
%P[5]=[85.60885137359465,-18.74297846541552]; P[2]=[35.81828675525811,-14.171362231821632]; D=ab(5,2); A(2,5); N(4,2,5); N(3,2,4); N(1,2,3); M(8,1,2,blauerWinkel); N(7,8,1); N(9,8,7); N(10,8,9); M(16,10,8,gruenerWinkel); N(15,16,10); N(17,16,15); N(18,16,17); M(37,18,16,orangerWinkel); N(36,18,37); N(35,36,37); N(31,36,35); M(30,31,36,vierterWinkel); N(29,31,30); N(28,29,30); N(22,29,28); M(24,22,29,fuenfterWinkel); N(23,22,24); N(25,23,24); N(26,23,25); M(43,26,23,sechsterWinkel); N(41,26,43); N(42,41,43); N(40,41,42); M(46,40,41,siebenterWinkel); N(45,46,40); N(47,46,45); N(48,46,47); M(53,48,46,achterWinkel); N(52,53,48); N(54,53,52); N(55,53,54); M(72,55,53,neunterWinkel); N(71,55,72); N(70,71,72); N(67,71,70); Q(59,67,5,2*D,2*D); A(59,67); A(59,5); H(60,5,59,2); A(60,5); L(62,5,60); H(65,67,59,2); A(65,67); L(66,65,67); A(65,59); L(64,59,65); A(64,66); A(60,59); L(61,60,59); A(62,61); N(11,9,7); N(20,37,17); N(32,28,30); N(38,35,20); N(49,47,45); N(57,72,54); N(68,64,66); N(73,70,57); N(6,11,3); N(19,20,15); N(27,24,32); N(44,49,42); N(56,57,52); N(63,61,68); N(12,11,6); N(21,20,19); N(33,27,32); N(39,38,20); N(50,49,44); N(58,57,56); N(69,63,68); N(74,73,57); N(13,69,12); N(14,33,13); N(34,14,50); N(51,69,34);
%A(14,39); R(14,39,\"green\");
%A(14,21); R(14,21,\"green\");
%A(14,12); R(14,12,\"green\");
%A(34,33); R(34,33,\"green\");
%A(51,74); R(51,74,\"green\");
%A(51,58); R(51,58,\"green\");
%A(51,13); R(51,13,\"green\");
%A(51,50); R(51,50,\"green\");
%</Rechenweg>
%
%<Knopf id=\"Stopp_alleWinkel\" color=\"LightGrey\"/>
%
%<Knopf id=\"Start_blauerWinkel\" color=\"blue\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#blauerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_blauerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_gruenerWinkel\" color=\"green\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#gruenerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_gruenerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_orangerWinkel\" color=\"orange\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#orangerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_orangerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_vierterWinkel\" color=\"violet\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#vierterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_vierterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_fuenfterWinkel\" color=\"teal\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#fuenfterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_fuenfterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_sechsterWinkel\" color=\"lime\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#sechsterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_sechsterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_siebenterWinkel\" color=\"LightBlue\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#siebenterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_siebenterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_achterWinkel\" color=\"LightCoral\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#achterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_achterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_neunterWinkel\" color=\"LightCyan\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#neunterWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_neunterWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{LightBlue}{rgb}{0.68,0.84,0.90}
\definecolor{LightCoral}{rgb}{0.94,0.50,0.50}
\definecolor{LightCyan}{rgb}{0.88,1.00,1.00}
\definecolor{Lime}{rgb}{0.00,1.00,0.00}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
\definecolor{Teal}{rgb}{0.00,0.50,0.50}
\definecolor{Violet}{rgb}{0.93,0.51,0.93}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.85/0.18,
2/2.85/0.09,
3/2.43/1.00,
4/3.43/0.91,
5/3.84/0.00,
6/3.05/1.78,
7/1.99/1.17,
8/1.06/0.80,
9/1.20/1.79,
10/0.27/1.41,
11/2.12/2.16,
12/2.92/2.78,
13/3.84/2.40,
14/3.70/3.39,
15/1.06/2.02,
16/0.14/2.40,
17/0.93/3.01,
18/0.00/3.39,
19/1.99/2.40,
20/1.85/3.39,
21/2.78/3.01,
22/1.85/6.60,
23/2.85/6.69,
24/2.43/5.78,
25/3.43/5.87,
26/3.84/6.78,
27/3.05/5.00,
28/1.99/5.61,
29/1.06/5.99,
30/1.20/4.99,
31/0.27/5.37,
32/2.12/4.62,
33/2.92/4.01,
34/3.84/4.38,
35/1.06/4.76,
36/0.14/4.38,
37/0.93/3.77,
38/1.99/4.38,
39/2.78/3.77,
40/5.84/6.60,
41/4.84/6.69,
42/5.26/5.78,
43/4.26/5.87,
44/4.64/5.00,
45/5.70/5.61,
46/6.63/5.99,
47/6.49/4.99,
48/7.42/5.37,
49/5.56/4.62,
50/4.77/4.01,
51/3.98/3.39,
52/6.63/4.76,
53/7.55/4.38,
54/6.76/3.77,
55/7.69/3.39,
56/5.70/4.38,
57/5.84/3.39,
58/4.91/3.77,
59/5.84/0.18,
60/4.84/0.09,
61/5.26/1.00,
62/4.26/0.91,
63/4.64/1.78,
64/5.70/1.17,
65/6.63/0.80,
66/6.49/1.79,
67/7.42/1.41,
68/5.56/2.16,
69/4.77/2.78,
70/6.63/2.02,
71/7.55/2.40,
72/6.76/3.01,
73/5.70/2.40,
74/4.91/3.01}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
1/354.75/502.17/0.4/Blue,
10/322.17/457.83/0.4/Green,
18/277.83/382.17/0.4/Orange,
31/262.17/337.83/0.4/Violet,
22/217.83/305.25/0.4/Teal,
26/185.25/294.75/0.4/Lime,
40/174.75/322.17/0.4/LightBlue,
48/142.17/277.83/0.4/LightCoral,
55/97.83/202.17/0.4/LightCyan}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
1/2, 1/3,
2/5,
3/2, 3/4,
4/2, 4/5,
6/11, 6/3,
7/8, 7/1,
8/1,
9/8, 9/7,
10/8, 10/9,
11/9, 11/7,
12/11, 12/6,
13/69, 13/12,
14/33, 14/13, 14/39, 14/21, 14/12,
15/16, 15/10,
16/10,
17/16, 17/15,
18/16, 18/17,
19/20, 19/15,
20/37, 20/17,
21/20, 21/19,
22/29, 22/28,
23/22, 23/24,
24/22,
25/23, 25/24,
26/23, 26/25,
27/24, 27/32,
28/29, 28/30,
29/31, 29/30,
30/31,
31/36, 31/35,
32/28, 32/30,
33/27, 33/32,
34/14, 34/50, 34/33,
35/36, 35/37,
36/18, 36/37,
37/18,
38/35, 38/20,
39/38, 39/20,
40/41, 40/42,
41/26, 41/43,
42/41, 42/43,
43/26,
44/49, 44/42,
45/46, 45/40,
46/40,
47/46, 47/45,
48/46, 48/47,
49/47, 49/45,
50/49, 50/44,
51/69, 51/34, 51/74, 51/58, 51/13, 51/50,
52/53, 52/48,
53/48,
54/53, 54/52,
55/53, 55/54,
56/57, 56/52,
57/72, 57/54,
58/57, 58/56,
60/5, 60/59,
61/60, 61/59,
62/5, 62/60, 62/61,
63/61, 63/68,
64/59, 64/65, 64/66,
65/67, 65/59,
66/65, 66/67,
67/71, 67/70,
68/64, 68/66,
69/63, 69/68,
70/71, 70/72,
71/55, 71/72,
72/55,
73/70, 73/57,
74/73, 74/57}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,74}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[Green,very thick] (p-14) -- (p-39);
\draw[Green,very thick] (p-14) -- (p-21);
\draw[Green,very thick] (p-14) -- (p-12);
\draw[Green,very thick] (p-34) -- (p-33);
\draw[Green,very thick] (p-51) -- (p-74);
\draw[Green,very thick] (p-51) -- (p-58);
\draw[Green,very thick] (p-51) -- (p-13);
\draw[Green,very thick] (p-51) -- (p-50);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
1/354.75/502.17/0.4/Blue,
10/322.17/457.83/0.4/Green,
18/277.83/382.17/0.4/Orange,
31/262.17/337.83/0.4/Violet,
22/217.83/305.25/0.4/Teal,
26/185.25/294.75/0.4/Lime,
40/174.75/322.17/0.4/LightBlue,
48/142.17/277.83/0.4/LightCoral,
55/97.83/202.17/0.4/LightCyan}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/205,
2/265,
3/85,
4/25,
5/215,
6/308,
7/292,
8/172,
9/112,
10/172,
11/188,
12/188,
13/232,
14/68,
15/8,
16/128,
17/8,
18/128,
19/248,
20/128,
21/8,
22/68,
23/95,
24/275,
25/335,
26/145,
27/52,
28/68,
29/68,
30/248,
31/188,
32/172,
33/172,
34/128,
35/352,
36/112,
37/292,
38/112,
39/352,
40/25,
41/25,
42/325,
43/205,
44/128,
45/172,
46/352,
47/232,
48/352,
49/232,
50/248,
51/112,
52/128,
53/8,
54/248,
55/52,
56/68,
57/52,
58/188,
59/335,
60/215,
61/35,
62/155,
63/232,
64/188,
65/308,
66/68,
67/8,
68/128,
69/112,
70/232,
71/52,
72/112,
73/292,
74/172}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
Jetzt aber ergänzt Button "beweglich?" im Eingabefenster zwei unabhängige Winkel
gruenerWinkel=135.66530615863013+(-0.033776036047640026)*(fuenfterWinkel-(87.41434922655961))+(-0.0331132232416488)*(blauerWinkel-(147.4139));
orangerWinkel=104.33358940119679+(0.034172632982445765)*(fuenfterWinkel-(87.41434922655961))+(0.034164299479931014)*(blauerWinkel-(147.4139));
vierterWinkel=75.66530645296255+(-0.03312054920773207)*(fuenfterWinkel-(87.41434922655961))+(-0.03376868777536805)*(blauerWinkel-(147.4139));
sechsterWinkel=109.50712358893763+(-1.9137335482983882)*(fuenfterWinkel-(87.41434922655961))+(-0.020829460731078855)*(blauerWinkel-(147.4139));
siebenterWinkel=147.4143492265599+(1.0000094146143543)*(fuenfterWinkel-(87.41434922655961))+(0.0000040969209810061676)*(blauerWinkel-(147.4139));
achterWinkel=135.66530645296234+(-0.03312027244076022)*(fuenfterWinkel-(87.41434922655961))+(-0.03377047835281289)*(blauerWinkel-(147.4139));
neunterWinkel=104.33358940119686+(0.034165760083019706)*(fuenfterWinkel-(87.41434922655961))+(0.03416248513839332)*(blauerWinkel-(147.4139)); |
Das kann ich als Hinweis auffassen, dass in unmittelbarer Nähe ein Kreuzungspunkt zweier verschiedener Bewegungsmöglichkeiten liegt und die Überlegung mit der Ableitungsmatrix ist vorerst gerettet.
|
Profil
Quote
Link |
haribo
Senior
Dabei seit: 25.10.2012
Mitteilungen: 2298
| Beitrag No.1906, eingetragen 2020-02-19 14:15
|
2020-02-01 06:22 - StefanVogel in Beitrag No. 1900 schreibt:
Nach Button neue Eingabe "egal wie"
88 Knoten, 4×Grad 3, 80×Grad 4, 2×Grad 5, 2×Grad 7, 0 Überschneidungen
178 Kanten, minimal 0.99999999999960431651, maximal 1.00000000000029243274
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>Automatisch generierte Eingabe zu: #1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78); nach Button neue Eingabe "egal wie"</Bildtext>
%<Ausrichten von="1" nach="2"/>
%<Winkel size="18" color="blue" id="blauerWinkel" value="-90"/>
%<Winkel size="18" color="green" id="gruenerWinkel" value="-179.9999999999996"/>
%<Winkel size="18" color="orange" id="orangerWinkel" value="-90.00000000000018"/>
%<Feinjustieren Anzahl="8,3"/>
%<Rechenweg>
%P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(2,1); N(3,1,2); N(4,3,2); N(5,4,2); M(38,5,4,blauerWinkel); N(36,5,38); N(8,4,36); N(37,8,36); N(40,37,38); N(43,37,40); N(44,40,38); N(46,43,44); N(72,46,44); N(74,8,43); N(75,8,74); N(7,3,8); N(71,46,72); N(73,7,8); N(76,73,75); N(77,73,76); N(6,1,7); N(9,1,6); N(10,9,6); N(11,9,10); N(69,71,72); M(84,74,8,gruenerWinkel); N(70,84,71); N(83,75,84); N(85,84,70); N(68,70,69); N(67,68,69); N(66,68,67); N(64,66,67); N(65,85,66); N(63,65,64); N(62,63,64); N(61,63,62); N(59,61,62); N(60,65,61); N(58,60,59); N(57,58,59); N(56,58,57); N(54,56,57); N(55,60,56); N(87,85,55); N(53,55,54); N(86,83,87); N(88,86,87); N(52,53,54); N(82,83,86); N(51,53,52); N(79,76,82); N(81,82,86); N(42,81,88); N(49,51,52); N(50,51,42); N(78,77,79); N(80,79,42); N(48,50,49); N(45,42,48); N(47,45,48); N(41,45,47); N(39,42,41); N(34,39,41); N(35,42,39); N(32,80,35); N(33,32,34); N(27,78,32); N(31,33,34); N(30,32,31); N(28,27,30); N(29,28,30); N(26,28,29); N(25,27,26); N(24,25,26); N(23,25,24); N(21,23,24); M(22,23,25,orangerWinkel); N(20,22,21); N(19,20,21); N(18,20,19); N(16,18,19); N(17,22,18); N(12,17,10); N(13,11,12); N(14,11,13); N(15,14,13);
%A(50,88); R(50,88,"green");
%A(80,81); R(80,81,"green");
%A(47,49); R(47,49,"green");
%A(33,35); R(33,35,"green");
%A(29,31); R(29,31,"green");
%A(14,16); R(14,16,"green");
%A(15,16); R(15,16,"green");
%A(15,17); R(15,17,"green");
%</Rechenweg>
%
%<Knopf id="Stopp_alleWinkel" color="LightGrey"/>
%
%<Knopf id="Start_blauerWinkel" color="blue"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#blauerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_blauerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_gruenerWinkel" color="green"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#gruenerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_gruenerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%
%<Knopf id="Start_orangerWinkel" color="orange"/>
%<animate xmlns="http://www.w3.org/2000/svg" href="#orangerWinkel" attributeName="value" values="0;5;0;-5;0" dur="5" additive="sum" repeatCount="indefinite" keyTimes="0;0.25;0.5;0.75;1" calcMode="spline" keySplines=".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1" begin="Start_orangerWinkel.click+0s" end="Stopp_alleWinkel.click+0"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/2.73/0.00,
2/3.73/0.00,
3/3.23/0.87,
4/4.23/0.87,
5/4.73/0.00,
6/2.73/1.00,
7/3.23/1.87,
8/4.23/1.87,
9/1.87/0.50,
10/1.87/1.50,
11/1.00/1.00,
12/2.37/2.37,
13/1.50/1.87,
14/0.50/1.87,
15/1.00/2.73,
16/0.00/2.73,
17/1.87/3.23,
18/0.87/3.23,
19/0.00/3.73,
20/0.87/4.23,
21/0.00/4.73,
22/1.87/4.23,
23/1.00/4.73,
24/0.50/5.60,
25/1.50/5.60,
26/1.00/6.46,
27/2.37/5.10,
28/1.87/5.96,
29/1.87/6.96,
30/2.73/6.46,
31/2.73/7.46,
32/3.23/5.60,
33/3.23/6.60,
34/3.73/7.46,
35/4.10/6.10,
36/4.73/1.00,
37/5.23/1.87,
38/5.60/0.50,
39/4.60/6.96,
40/6.10/1.37,
41/4.60/7.96,
42/5.10/6.10,
43/6.10/2.37,
44/6.60/0.50,
45/5.10/7.10,
46/6.60/1.50,
47/5.60/7.96,
48/6.10/7.10,
49/6.60/7.96,
50/6.10/6.10,
51/6.60/6.96,
52/7.46/7.46,
53/7.46/6.46,
54/8.33/6.96,
55/6.96/5.60,
56/7.83/6.10,
57/8.83/6.10,
58/8.33/5.23,
59/9.33/5.23,
60/7.46/4.73,
61/8.46/4.73,
62/9.33/4.23,
63/8.46/3.73,
64/9.33/3.23,
65/7.46/3.73,
66/8.33/3.23,
67/8.83/2.37,
68/7.83/2.37,
69/8.33/1.50,
70/6.96/2.87,
71/7.46/2.00,
72/7.46/1.00,
73/3.73/2.73,
74/5.10/2.37,
75/4.23/2.87,
76/3.73/3.73,
77/2.87/3.23,
78/2.87/4.23,
79/3.73/4.73,
80/4.23/5.60,
81/5.10/5.10,
82/4.60/4.23,
83/5.10/3.37,
84/5.96/2.87,
85/6.46/3.73,
86/5.60/4.23,
87/6.46/4.73,
88/5.60/5.23}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
5/120.00/390.00/0.4/Blue,
74/210.00/390.00/0.4/Green,
23/60.00/330.00/0.4/Orange}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
2/1,
3/1, 3/2,
4/3, 4/2,
5/4, 5/2,
6/1, 6/7,
7/3, 7/8,
8/4, 8/36,
9/1, 9/6,
10/9, 10/6,
11/9, 11/10,
12/17, 12/10,
13/11, 13/12,
14/11, 14/13, 14/16,
15/14, 15/13, 15/16, 15/17,
16/18, 16/19,
17/22, 17/18,
18/20, 18/19,
19/20, 19/21,
20/22, 20/21,
21/23, 21/24,
22/23,
23/25, 23/24,
24/25, 24/26,
25/27, 25/26,
26/28, 26/29,
27/78, 27/32,
28/27, 28/30,
29/28, 29/30, 29/31,
30/32, 30/31,
31/33, 31/34,
32/80, 32/35,
33/32, 33/34, 33/35,
34/39, 34/41,
35/42, 35/39,
36/5, 36/38,
37/8, 37/36,
38/5,
39/42, 39/41,
40/37, 40/38,
41/45, 41/47,
42/81, 42/88,
43/37, 43/40,
44/40, 44/38,
45/42, 45/48,
46/43, 46/44,
47/45, 47/48, 47/49,
48/50, 48/49,
49/51, 49/52,
50/51, 50/42, 50/88,
51/53, 51/52,
52/53, 52/54,
53/55, 53/54,
54/56, 54/57,
55/60, 55/56,
56/58, 56/57,
57/58, 57/59,
58/60, 58/59,
59/61, 59/62,
60/65, 60/61,
61/63, 61/62,
62/63, 62/64,
63/65, 63/64,
64/66, 64/67,
65/85, 65/66,
66/68, 66/67,
67/68, 67/69,
68/70, 68/69,
69/71, 69/72,
70/84, 70/71,
71/46, 71/72,
72/46, 72/44,
73/7, 73/8,
74/8, 74/43,
75/8, 75/74,
76/73, 76/75,
77/73, 77/76,
78/77, 78/79,
79/76, 79/82,
80/79, 80/42, 80/81,
81/82, 81/86,
82/83, 82/86,
83/75, 83/84,
84/74,
85/84, 85/70,
86/83, 86/87,
87/85, 87/55,
88/86, 88/87}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,88}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[Green,very thick] (p-50) -- (p-88);
\draw[Green,very thick] (p-80) -- (p-81);
\draw[Green,very thick] (p-47) -- (p-49);
\draw[Green,very thick] (p-33) -- (p-35);
\draw[Green,very thick] (p-29) -- (p-31);
\draw[Green,very thick] (p-14) -- (p-16);
\draw[Green,very thick] (p-15) -- (p-16);
\draw[Green,very thick] (p-15) -- (p-17);
\draw[red,very thick] (p-34) -- (p-38);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
5/120.00/390.00/0.4/Blue,
74/210.00/390.00/0.4/Green,
23/60.00/330.00/0.4/Orange}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/210,
2/330,
3/150,
4/30,
5/330,
6/360,
7/210,
8/330,
9/180,
10/60,
11/180,
12/347,
13/30,
14/270,
15/30,
16/240,
17/77,
18/300,
19/120,
20/60,
21/120,
22/48,
23/330,
24/210,
25/30,
26/90,
27/167,
28/240,
29/180,
30/360,
31/60,
32/240,
33/270,
34/30,
35/210,
36/120,
37/30,
38/360,
39/300,
40/90,
41/60,
42/60,
43/60,
44/240,
45/270,
46/180,
47/30,
48/270,
49/120,
50/30,
51/240,
52/60,
53/240,
54/360,
55/93,
56/210,
57/330,
58/210,
59/60,
60/137,
61/120,
62/360,
63/180,
64/300,
65/227,
66/90,
67/270,
68/150,
69/360,
70/330,
71/60,
72/360,
73/300,
74/360,
75/120,
76/60,
77/180,
78/257,
79/62,
80/180,
81/90,
82/150,
83/270,
84/210,
85/90,
86/240,
87/360,
88/270}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/c81f4418cc0caebc8716cb4f2e205ac5.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>Automatisch generierte Eingabe zu: #1892 = #467-2 mit Entfernen der Kanten Z(23,79); Z(13,78); nach Button neue Eingabe \"egal wie\"</Bildtext>
%<Ausrichten von=\"1\" nach=\"2\"/>
%<Winkel size=\"18\" color=\"blue\" id=\"blauerWinkel\" value=\"-90\"/>
%<Winkel size=\"18\" color=\"green\" id=\"gruenerWinkel\" value=\"-179.9999999999996\"/>
%<Winkel size=\"18\" color=\"orange\" id=\"orangerWinkel\" value=\"-90.00000000000018\"/>
%<Feinjustieren Anzahl=\"8,3\"/>
%<Rechenweg>
%P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(2,1); N(3,1,2); N(4,3,2); N(5,4,2); M(38,5,4,blauerWinkel); N(36,5,38); N(8,4,36); N(37,8,36); N(40,37,38); N(43,37,40); N(44,40,38); N(46,43,44); N(72,46,44); N(74,8,43); N(75,8,74); N(7,3,8); N(71,46,72); N(73,7,8); N(76,73,75); N(77,73,76); N(6,1,7); N(9,1,6); N(10,9,6); N(11,9,10); N(69,71,72); M(84,74,8,gruenerWinkel); N(70,84,71); N(83,75,84); N(85,84,70); N(68,70,69); N(67,68,69); N(66,68,67); N(64,66,67); N(65,85,66); N(63,65,64); N(62,63,64); N(61,63,62); N(59,61,62); N(60,65,61); N(58,60,59); N(57,58,59); N(56,58,57); N(54,56,57); N(55,60,56); N(87,85,55); N(53,55,54); N(86,83,87); N(88,86,87); N(52,53,54); N(82,83,86); N(51,53,52); N(79,76,82); N(81,82,86); N(42,81,88); N(49,51,52); N(50,51,42); N(78,77,79); N(80,79,42); N(48,50,49); N(45,42,48); N(47,45,48); N(41,45,47); N(39,42,41); N(34,39,41); N(35,42,39); N(32,80,35); N(33,32,34); N(27,78,32); N(31,33,34); N(30,32,31); N(28,27,30); N(29,28,30); N(26,28,29); N(25,27,26); N(24,25,26); N(23,25,24); N(21,23,24); M(22,23,25,orangerWinkel); N(20,22,21); N(19,20,21); N(18,20,19); N(16,18,19); N(17,22,18); N(12,17,10); N(13,11,12); N(14,11,13); N(15,14,13);
%A(50,88); R(50,88,\"green\");
%A(80,81); R(80,81,\"green\");
%A(47,49); R(47,49,\"green\");
%A(33,35); R(33,35,\"green\");
%A(29,31); R(29,31,\"green\");
%A(14,16); R(14,16,\"green\");
%A(15,16); R(15,16,\"green\");
%A(15,17); R(15,17,\"green\");
%</Rechenweg>
%
%<Knopf id=\"Stopp_alleWinkel\" color=\"LightGrey\"/>
%
%<Knopf id=\"Start_blauerWinkel\" color=\"blue\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#blauerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_blauerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_gruenerWinkel\" color=\"green\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#gruenerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_gruenerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%
%<Knopf id=\"Start_orangerWinkel\" color=\"orange\"/>
%<animate xmlns=\"http://www.w3.org/2000/svg\" href=\"#orangerWinkel\" attributeName=\"value\" values=\"0;5;0;-5;0\" dur=\"5\" additive=\"sum\" repeatCount=\"indefinite\" keyTimes=\"0;0.25;0.5;0.75;1\" calcMode=\"spline\" keySplines=\".3 0 .7 1;.3 0 .7 1;.3 0 .7 1;.3 0 .7 1\" begin=\"Start_orangerWinkel.click+0s\" end=\"Stopp_alleWinkel.click+0\"/>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Green}{rgb}{0.00,0.50,0.00}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/2.73/0.00,
2/3.73/0.00,
3/3.23/0.87,
4/4.23/0.87,
5/4.73/0.00,
6/2.73/1.00,
7/3.23/1.87,
8/4.23/1.87,
9/1.87/0.50,
10/1.87/1.50,
11/1.00/1.00,
12/2.37/2.37,
13/1.50/1.87,
14/0.50/1.87,
15/1.00/2.73,
16/0.00/2.73,
17/1.87/3.23,
18/0.87/3.23,
19/0.00/3.73,
20/0.87/4.23,
21/0.00/4.73,
22/1.87/4.23,
23/1.00/4.73,
24/0.50/5.60,
25/1.50/5.60,
26/1.00/6.46,
27/2.37/5.10,
28/1.87/5.96,
29/1.87/6.96,
30/2.73/6.46,
31/2.73/7.46,
32/3.23/5.60,
33/3.23/6.60,
34/3.73/7.46,
35/4.10/6.10,
36/4.73/1.00,
37/5.23/1.87,
38/5.60/0.50,
39/4.60/6.96,
40/6.10/1.37,
41/4.60/7.96,
42/5.10/6.10,
43/6.10/2.37,
44/6.60/0.50,
45/5.10/7.10,
46/6.60/1.50,
47/5.60/7.96,
48/6.10/7.10,
49/6.60/7.96,
50/6.10/6.10,
51/6.60/6.96,
52/7.46/7.46,
53/7.46/6.46,
54/8.33/6.96,
55/6.96/5.60,
56/7.83/6.10,
57/8.83/6.10,
58/8.33/5.23,
59/9.33/5.23,
60/7.46/4.73,
61/8.46/4.73,
62/9.33/4.23,
63/8.46/3.73,
64/9.33/3.23,
65/7.46/3.73,
66/8.33/3.23,
67/8.83/2.37,
68/7.83/2.37,
69/8.33/1.50,
70/6.96/2.87,
71/7.46/2.00,
72/7.46/1.00,
73/3.73/2.73,
74/5.10/2.37,
75/4.23/2.87,
76/3.73/3.73,
77/2.87/3.23,
78/2.87/4.23,
79/3.73/4.73,
80/4.23/5.60,
81/5.10/5.10,
82/4.60/4.23,
83/5.10/3.37,
84/5.96/2.87,
85/6.46/3.73,
86/5.60/4.23,
87/6.46/4.73,
88/5.60/5.23}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- cycle;
%gefüllte Winkel als \fill[red!20] (p-1) -- +(0:0.3 cm) arc (0:60:0.3 cm) -- cycle;
\foreach \i/\a/\b/\r/\c in {
5/120.00/390.00/0.4/Blue,
74/210.00/390.00/0.4/Green,
23/60.00/330.00/0.4/Orange}
\fill[\c!20] (p-\i) -- +(\a:\r cm) arc (\a:\b:\r cm) -- cycle;
%Kanten als \draw[gray,thick] (p-1) -- (p-2);
\foreach \i/\j in {
2/1,
3/1, 3/2,
4/3, 4/2,
5/4, 5/2,
6/1, 6/7,
7/3, 7/8,
8/4, 8/36,
9/1, 9/6,
10/9, 10/6,
11/9, 11/10,
12/17, 12/10,
13/11, 13/12,
14/11, 14/13, 14/16,
15/14, 15/13, 15/16, 15/17,
16/18, 16/19,
17/22, 17/18,
18/20, 18/19,
19/20, 19/21,
20/22, 20/21,
21/23, 21/24,
22/23,
23/25, 23/24,
24/25, 24/26,
25/27, 25/26,
26/28, 26/29,
27/78, 27/32,
28/27, 28/30,
29/28, 29/30, 29/31,
30/32, 30/31,
31/33, 31/34,
32/80, 32/35,
33/32, 33/34, 33/35,
34/39, 34/41,
35/42, 35/39,
36/5, 36/38,
37/8, 37/36,
38/5,
39/42, 39/41,
40/37, 40/38,
41/45, 41/47,
42/81, 42/88,
43/37, 43/40,
44/40, 44/38,
45/42, 45/48,
46/43, 46/44,
47/45, 47/48, 47/49,
48/50, 48/49,
49/51, 49/52,
50/51, 50/42, 50/88,
51/53, 51/52,
52/53, 52/54,
53/55, 53/54,
54/56, 54/57,
55/60, 55/56,
56/58, 56/57,
57/58, 57/59,
58/60, 58/59,
59/61, 59/62,
60/65, 60/61,
61/63, 61/62,
62/63, 62/64,
63/65, 63/64,
64/66, 64/67,
65/85, 65/66,
66/68, 66/67,
67/68, 67/69,
68/70, 68/69,
69/71, 69/72,
70/84, 70/71,
71/46, 71/72,
72/46, 72/44,
73/7, 73/8,
74/8, 74/43,
75/8, 75/74,
76/73, 76/75,
77/73, 77/76,
78/77, 78/79,
79/76, 79/82,
80/79, 80/42, 80/81,
81/82, 81/86,
82/83, 82/86,
83/75, 83/84,
84/74,
85/84, 85/70,
86/83, 86/87,
87/85, 87/55,
88/86, 88/87}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,88}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[Green,very thick] (p-50) -- (p-88);
\draw[Green,very thick] (p-80) -- (p-81);
\draw[Green,very thick] (p-47) -- (p-49);
\draw[Green,very thick] (p-33) -- (p-35);
\draw[Green,very thick] (p-29) -- (p-31);
\draw[Green,very thick] (p-14) -- (p-16);
\draw[Green,very thick] (p-15) -- (p-16);
\draw[Green,very thick] (p-15) -- (p-17);
\draw[red,very thick] (p-34) -- (p-38);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
5/120.00/390.00/0.4/Blue,
74/210.00/390.00/0.4/Green,
23/60.00/330.00/0.4/Orange}
{
\draw[\c,thick] (p-\i) +(\a:\r cm) arc (\a:\b-4:\r cm);
\fill[\c!90!black] (p-\i) -- +(\b:\r cm) coordinate (pfeilspitze-\i) -- ([turn]-24.84:0.08cm) -- ([turn]-31.04:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]15.522:0.04cm) -- ([turn]-39.275:0.04cm) -- ([turn]15.522:0.08cm) -- ([turn]-120.00:0.08cm) -- ([turn]-31.04:0.08cm) -- (pfeilspitze-\i);
}
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/210,
2/330,
3/150,
4/30,
5/330,
6/360,
7/210,
8/330,
9/180,
10/60,
11/180,
12/347,
13/30,
14/270,
15/30,
16/240,
17/77,
18/300,
19/120,
20/60,
21/120,
22/48,
23/330,
24/210,
25/30,
26/90,
27/167,
28/240,
29/180,
30/360,
31/60,
32/240,
33/270,
34/30,
35/210,
36/120,
37/30,
38/360,
39/300,
40/90,
41/60,
42/60,
43/60,
44/240,
45/270,
46/180,
47/30,
48/270,
49/120,
50/30,
51/240,
52/60,
53/240,
54/360,
55/93,
56/210,
57/330,
58/210,
59/60,
60/137,
61/120,
62/360,
63/180,
64/300,
65/227,
66/90,
67/270,
68/150,
69/360,
70/330,
71/60,
72/360,
73/300,
74/360,
75/120,
76/60,
77/180,
78/257,
79/62,
80/180,
81/90,
82/150,
83/270,
84/210,
85/90,
86/240,
87/360,
88/270}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
hallo stefan,
mir ist es gelungen in deine zeichnung die rote linie von 34-38 einzufügen, darauf bin ich schonmal stolz
ich hab mal wieder versucht mit deinem komplexen streichholzprogram herumzuspielen
und obige zeichnung, bzw #1892-1 als grundlage genommen... und deinen oben beschriebenen weg bis zur eingabe "egal wie" nachzuvollziehen, erfolg diesmal gar nicht so schlecht, d.h. es zerknüllt meist erst nach mehreren minuten... ansich wollte ich dann folgende eingaben machen: [Z(82,86);A(34,38)]
und irgendwie herausbekommen ob die beweglichkeit der rechten hälfte ausreicht um einen daraus gespiegelten 4/7er herzustellen...
also ungefähr so wie hier im png händisch hergestellt, müsste man in der mitte auseinanderdrücken bis noch ein holz dazwischen passt...
nun das bedeutet wohl das man neu eingeben muss??? oder hat man irgendwie eine chance mit "Z" sehr viel, also weitgehend all die inneren linken linien, herauszulöschen und wieder neue dazuzufügen?
die zweite wichtige frage ist, was muss ich machen um irgendwie, also derzeit meist nur zufällig, hergestellte zwischenlösungen abzuspeichern, damit ich sie danach gesichert wieder aufrufen/herstellen kann
reicht es wenn ich zum speichern alles zwischen
<Streichholzgraph>....</Streichholzgraph>
als text in ein word dokument schreibe, oder brauch ich dann dazu weitere winkeleinstellungen oder ähnliches?
lg haribo
|
Profil
Quote
Link |
haribo
Senior
Dabei seit: 25.10.2012
Mitteilungen: 2298
| Beitrag No.1907, eingetragen 2020-02-19 14:39
|
händisch geht es wohl immer einfacher für mich, ist wohl auch noch ein falscher fünfer drin
aber es ging mir diesmal wirklich drum es mit dem program zu versuchen...
zu nem etwas erstaunlich unsymetrischen 4/7er mit 177 hölzern konnte ich es noch retten, sofern ich nichts übersehen habe
das dürfte immerhin mein persönlicher 4/7 rekord sein
|
Profil
Quote
Link |
Slash
Aktiv
Dabei seit: 23.03.2005
Mitteilungen: 7758
Aus: Cuxhaven-Sahlenburg
| Beitrag No.1908, vom Themenstarter, eingetragen 2020-02-19 20:11
|
2020-02-19 14:15 - haribo in Beitrag No. 1906 schreibt:
reicht es wenn ich zum speichern alles zwischen
<Streichholzgraph>....</Streichholzgraph>
als text in ein word dokument schreibe, oder brauch ich dann dazu weitere winkeleinstellungen oder ähnliches?
lg haribo
Ja, das reicht. Texteditor reicht auch.
-----------------
Bound to be disappointing so why wait?
|
Profil
Quote
Link |
haribo
Senior
Dabei seit: 25.10.2012
Mitteilungen: 2298
| Beitrag No.1909, eingetragen 2020-02-19 21:57
|
bei den beweglichen klappt es bei mir eher nicht, scheints sind die eingestellten winkel nicht in dem angegebenen bereich abgespeichert?
haribo
|
Profil
Quote
Link |
|
Home
2020-02-21 23:42 U ?
Wie unterstütze ich den Matheplaneten mit Geld?
[Neues Thema]