Das neue Paper für GEOM mit vier 51er Näherungen ist fast fertig. Ich schicke es euch dann zur Ansicht/Kontrolle bevor ich es an GEOM schicke. Wie immer mit uns dreien als Autoren.
----------------- Bound to be disappointing so why wait?
In Graph #2034 ist P51 mit P45, P48, P46, P47 verbunden, in Fig.7 (#1946-2) mit P48, P46, P47, P50, in Fig.5 (#1925) mit P46, P47, P50, P42, (dort sind Bezeichnungen P50 und P51 vertauscht), da bleibt noch übrig, P51 mit P47, P50, P42, P44 zu verbinden. Dafür erhalte ich mit Button "besser annähern multi" und Checkbox "nur faire Graphen" komplett durchgelaufen folgendes Ergebnis
Slash
Aktiv Dabei seit: 23.03.2005 Mitteilungen: 7971
Aus: Cuxhaven-Sahlenburg
Beitrag No.2044, vom Themenstarter, eingetragen 2020-06-13 13:10
Mir kam gerade eine (neue) Idee für einen Ansatz um automatisiert minimale Graphen zu finden, und zwar mit Dreiecken. Sehr vereinfacht ausgedrückt: Wir geben einen Rahmen (lila, beige) vor und platzieren dann drei oder vier Dreiecke (rosa) im Inneren. Das Programm soll dann Kanten finden bzw. einen weiteren Knoten in großen freien Gebieten setzen um einen 4-regulären Graphen zu erzeugen. Indem man zuvor 2er-Elemente (beige) im Rahmen um ein Dreieck erweitert (blau) wird der Platz im Innern zusätzlich eingeschränkt.
Ich gehe auch so vor, dass ich erst den Rahmen konstruiere und dann das Innere fülle, aber "immer" von außen nach innen. Das zuvor Dreiecke im Inneren plaziert werden, wäre also der große Unterschied zur händischen Methode. Das zu programmieren wäre wahrscheinlich äußerst schwierig, aber wir könnten ja mal eine Art Anleitung dafür erstellen und schauen, ob es sich umsetzen lässt.
Was auch noch auffällt bei den minimalen 51er Approximationen (auch beim Harborth-Graphen und den anderen) ist: Die Abstände im Inneren zu den Knoten sind oft so, dass sich weitere Dreiecke (grün) einzeichnen lassen, wenn auch nicht ganz exakt. Dass also jeder minimale 4er auch immer weitere 4/5er und auch 4/6er Approximationen beinhaltet. Der 114er macht das sogar ganz exakt. Das wäre ein weiterer Ansatz um den Innenraum zu füllen.
Letztendlich brauchen wir ja nur noch ein ungefähres 4er Netz, das Stefans Programm dann zurechtziehen kann.
----------------- Bound to be disappointing so why wait?
Slash
Aktiv Dabei seit: 23.03.2005 Mitteilungen: 7971
Aus: Cuxhaven-Sahlenburg
Beitrag No.2045, vom Themenstarter, eingetragen 2020-06-13 19:51
Hier mein kompletter Durchlauf des neuen Graphen mit Multi aber ohne Fair-Kästchen.
51 Knoten, 51×Grad 4, 0 Überschneidungen,
102 Kanten, minimal 0.98966433195655578725, maximal 1.01466952729600978778, Einsetzkanten=Beweglichkeit+3,
nicht passende Kanten:
|P45-P3|=0.98966433195655578725
|P45-P6|=1.00651870039999224993
|P51-P50|=1.01466952729600978778
----------------- Bound to be disappointing so why wait?
Slash
Aktiv Dabei seit: 23.03.2005 Mitteilungen: 7971
Aus: Cuxhaven-Sahlenburg
Beitrag No.2046, vom Themenstarter, eingetragen 2020-06-13 20:03
Hier mein Versuch einen 53er in den 51er-Rahmen zu quetschen.
53 Knoten, 53×Grad 4, 0 Überschneidungen,
106 Kanten, minimal 0.86343129311781541269, maximal 1.08093348831732716242, Einsetzkanten=Beweglichkeit+3,
nicht passende Kanten:
|P40-P44|=0.99765546647059899499
|P42-P53|=1.08093348831732716242
|P45-P47|=1.01543221611957501516
|P46-P53|=0.98799321857638855438
|P50-P51|=0.99064435842485010220
|P50-P52|=0.89738336104251514858
|P51-P46|=0.92901588053062056360
|P52-P44|=0.86343129311781541269
|P40-P44|=0.99765546647059899499
und mehr
----------------- Bound to be disappointing so why wait?
haribo
Senior Dabei seit: 25.10.2012 Mitteilungen: 2441
Beitrag No.2048, eingetragen 2020-06-13 20:28
Bau noch kleine Zufälle ein dann kann ein Rechner ewig rechnen... aber irgendwie muss man eine maximale abweichungsgrenze definieren ... 0,8x macht irgendwie ja keinen Spaß mehr
liebe Grüße haribo
StefanVogel
Senior Dabei seit: 26.11.2005 Mitteilungen: 3599
Aus: Raun
Beitrag No.2049, eingetragen 2020-06-14 00:54
Für das Streichholzgraph-Programm ist nicht so sehr die Abweichung von Kantenlänge 1 von Bedeutung sondern die Anzahl der nicht passenden Kanten. Bei 3 oder weniger unpassenden Kanten kann das Programm sofort mit der Suche von besseren Lösungen loslegen. Die Kantenlängen dürfen dabei auch fast Null oder 2 oder mehr sein.
haribo
Senior Dabei seit: 25.10.2012 Mitteilungen: 2441
Beitrag No.2050, eingetragen 2020-06-14 05:11
Ok Stefan, die Suche nach unsymmetrischen ist ja sowieso klasse und der best-erscheinende Ansatz um Harborth zu unterbieten
Was müssen wir denn liefern um die bestehenden Lücken zwischen 104 und 126 (war das die Grenze?) mit unsymmetrischen zu schließen? Welche Lücken haben wir genau?
@slash, ansich muss man nicht Dreiecke und Einzellinien in den Ring werfen, sondern nur eine Handvoll Punkte mit je vier 1/2 tentakeln welche eben nur linear-geradeaus andocken dürfen
Noch fehlt die Theorie welche Menge eine Handvoll sinnigerweise ist...
StefanVogel
Senior Dabei seit: 26.11.2005 Mitteilungen: 3599
Aus: Raun
Beitrag No.2051, eingetragen 2020-06-14 09:39
Eine Handvoll Punkte in den Ring werfen, besseres weiß ich auch nicht. Diese dann irgendwie so ausrichten, dass nur noch 3 unpassende Kanten übrigbleiben. Graph #2046 beispielsweise, gleich Button "Feinjustieren" führt zu Überschneidung, da habe ich dann P52, P53 wieder entfernt und weitere nicht passende Kanten, dann einzeln nach und nach wieder eingesetzt und mit "Feinjustieren" zurechtgezogen, so dass dabei keine Überschneidungen entstehen. Ein allgemein verwendbares Rezept wird das nicht. Hat auch nicht gleich beim ersten Versuch funktioniert.
Slash
Aktiv Dabei seit: 23.03.2005 Mitteilungen: 7971
Aus: Cuxhaven-Sahlenburg
Beitrag No.2052, vom Themenstarter, eingetragen 2020-06-14 15:25
Hier ein "echter" falscher Fuffziger. Es ist sogar ein fairer Graph, allerdings keine besonders gute Approximation. Vielleicht geht er noch besser, da nicht ganz durchgerechnet. Winkel bei P11 ist 0.80793343341222234599. Besonderheit hier: Nur ein 2er-Element im Rahmen bildet ein großes gleichseitiges Dreieck.
50 Knoten, 50×Grad 4, 0 Überschneidungen,
100 Kanten, minimal 0.99999999999999622524, maximal 1.27213542994280137677, Einsetzkanten=Beweglichkeit+3,
nicht passende Kanten:
|P46-P16|=1.07975495922223752032
|P48-P50|=1.27213542994280137677
|P49-P50|=1.24406482547251262538
----------------- Bound to be disappointing so why wait?
abkürzen. Oder geht das sogar schon so ähnlich? P1 liegt dann immer unten am Fensterrahmen und die Winkel werden so abgeglichen, dass es keine sehr schmalen/weiten gibt.
Gruß, Slash
----------------- Bound to be disappointing so why wait?
also vor Rahmen(...) die ersten zwei Punkte P[1] und P[2] und den Einheitsabstand D festlegen und die erste Kante A(2,1) einsetzen. Ergebnis ist
38 Knoten, 16×Grad 3, 22×Grad 4, 0 Überschneidungen,
68 Kanten, minimal 0.99999999999999911182, maximal 1.00000000000000088818, Einsetzkanten=Beweglichkeit-5,
oder mit Eingabe Rahmen(2,3,4,3,3,4,3);
44 Knoten, 14×Grad 3, 30×Grad 4, 0 Überschneidungen,
81 Kanten, minimal 0.99999999999999855671, maximal 1.00000000000000111022, Einsetzkanten=Beweglichkeit-4,
Doch es passiert auch, dass der Rahmen zerknüllt wird, obwohl es eine Lösung gibt. Das ist alles wieder nur so, das wenigstens irgendwas geht. Zuerst wird der Rahmen so angeordnet, dass die Eckpunkte auf einem gemeinsamen Umkreis liegen. Dann wird versucht, die Winkel so auszugleichen, dass die Summe Außenwinkel64 minimiert wird, stümperhaft durch hin- und herprobieren. So richtig allgemein scheint das noch nicht zu funktionieren. Besonders wenn lange Rahmenbereiche am Ende der Eingabe liegen wie in Rahmen(2,3,4,3,3,4,4).
EDIT: Anschließend noch Button neue Eingabe "Rahmen zuerst" damit der Rahmen beweglich wird.
StefanVogel
Senior Dabei seit: 26.11.2005 Mitteilungen: 3599
Aus: Raun
Beitrag No.2056, eingetragen 2020-06-21 12:23
Wenn ich Graph #2051 ins Streichholzprogramm kopiere und dann Button neue Eingabe "Rahmen zuerst", anschließend Button "Feinjustieren", so wird nicht wieder der gleiche Graph erzeugt, obwohl der Ausgangsgraph bereits nicht mehr als drei unpassende Kanten hat. Bei Button neue Eingabe "wenig Winkel" und "Feinjustieren" wird der Graph zerknüllt und nach Button neue Eingabe "egal wie" findet "Feinjustieren" gar keine Lösung. Grund dafür ist, bei neuer Eingabe werden teilweise die nicht passenden Kanten zum Festlegen neuer Knotenpunkte verwendet und nicht erst am Schluss als verbleibende Restkanten eingesetzt. In der automatisch erzeugten Eingabe sieht das dann etwa so aus
mit der Bedeutung, Q(...)="platziere Punkt P53 im Abstand 1 zu Punkt P50 und im Abstand 1.277241... zu Punkt P48, so dass der Weg P53 über P50 nach P48 eine Linkskurve ergibt" sowie M(...)="plaziere Punkt P40 im Abstand 1.152888... zu Punkt P53 im Winkel ∠(P48,P53,P40)=23.3516...°". Über die Funktion jam(1.2772412333614098) (war Abkürzung für "justiere auch mit") hat anschließender Button Feinjustieren die Möglichkeit, diesen Abstand auf 1 zu setzen. Dadurch entsteht garantiert ein anderer Graph als der Ausgangsgraph. Diese Funktion ersetze ich jetzt durch eine namens jum() (keine Ahnung wofür das eine Abkürzung sein soll)
da werden jetzt zusätzliche bewegliche Winkel orangerWinkel, vierterWinkel erzeugt und die Funktion jum() wandelt diese mit Arkustangens in eine Länge um. orangerWinkel=45, vierterWinkel=45 bedeutet Länge 1. Grafisch werden diese Winkel (noch?) nicht mit dargestellt. Auẞerdem werden am Ende der Eingabe die betreffenden Kanten als einzustellende Abstände R(53,48); R(40,53) angefügt. So können jetzt diese Kanten genau wie die anderen Kanten eingestellt werden oder auch als übrigbleibende unpassende Kanten ausgewählt werden. Das habe ich in Streichholzgraph-1898.htm geändert (auch Funktion Rahmen(...) aus dem vorhergehenden Beitrag mit). Das sind wieder jede Menge zu erwartende Folgefehler und dass vieles nicht mehr den gleichen Verlauf nimmt wie bisher. Graph #2051-1 ist als Startbild eingestellt und der Versuch vom Anfang des Beitrages ergibt für jeden Button neue Eingabe und anschließendes Feinjustieren den unveränderten Ausgangsgraph, genau das, was mit dieser Veränderung beabsichtigt war.
StefanVogel
Senior Dabei seit: 26.11.2005 Mitteilungen: 3599
Aus: Raun
Beitrag No.2057, eingetragen 2020-06-27 08:17
Neuer Button neue Eingabe "viele Winkel", damit wird jede Kante verstellbar gemacht über einen beweglichen Winkel, außer der ersten Kante zur Festlegung des Einheitsabstandes. Bei einem Graph wie Fig.5=#1925-1 in der besser angenäherten Variante #1972 mit 102 Kanten ergibt das 101 verstellbare Kanten mit 98 beweglichen Winkeln (die erste Kante ist nicht verstellbar, die letzten drei Kanten nur mit den bisherigen 98 Winkeln wegen Einsetzkanten=Beweglichkeit+3).
51 Knoten, 51×Grad 4, 0 Überschneidungen,
102 Kanten, minimal 0.99469016650450881034, maximal 1.00451152082520267506, Einsetzkanten=Beweglichkeit+3,
Auf eine graphische Darstellung aller 98 Winkel habe ich verzichtet. Der Unterschied zu beispielsweise Button "egal wie" ist nur in der Eingabe erkennbar
bedeutet, dass P7 mit P1 und P6 verbunden wird durch Kanten, die mit Winkel95 und Winkel96 eingestellt werden können, und P38 wird mit P5 durch eine Kante verbunden, die mit P5-P4 einen Winkel der Größe Winkel97 einschließt und selbst in der Länge mit Winkel Winkel98 verstellt werden kann. Normale Eingabe wäre gewesen L(7,1,6); M(38,5,4,Winkel98). Vollkommen übergeschnappt jetzt mit diesen vielen Winkeln? Das muss ich schnell vertuschen mit gleichnamigem Button "Vertuschen" (rechts neben Button "Feinjustieren"). Dieser Button blockiert dann auch längere Zeit die Browserseite, eine Minute oder zwei, mit dem Ergebnis
51 Knoten, 51×Grad 4, 0 Überschneidungen,
102 Kanten, minimal 0.99873086449989634250, maximal 1.00124096540961193824, Einsetzkanten=Beweglichkeit+3,
bringt aber nochmal eine Verbesserung um eine "halbe" Kommastelle. ebenso lassen sich auch Fig.6=#1946-1 und Fig.7=#1946-2 noch verbessern. Die Abweichungen von Kantenlänge 1 werden mit der Methode der kleinsten Quadrate minimiert. Mit Minimierung der absoluten Abweichung wäre vielleicht noch eine weitere Verbesserung möglich, doch da weiß ich nicht, ob es ein schnelles Verfahren dafür gibt, außer reihum probieren, welche Winkeländerung die maximale absolute Abweichung verbessert.
Wie zu erwarten, war ein grober Fehler drin, die Berechnung des Außenwinkels, beispielsweise rechts im Eckpunkt P39, erfolgt mit 60°-∠(P38,P39,P40). Wenn sich die Ecken P38 und P40 um 1° überlappen, wird nicht ein Winkel von -1° gemessen, sondern um das negative Vorzeichen zu vermeiden ein Winkel von 359°. So kommt für den Außenwinkel ein Wert -299° heraus. Den betragsmäßig minimieren führt nur zu weiterer Überlappung. Das ist jetzt geändert, bei Außenwinkel kleiner 0 wird wieder 360° addiert, so dass in dem Beispiel der benötigte Wert 61° herauskommt. Auch die schrittweise Minimierung ist nochmal neu, die war nur so auf die Schnelle wie sie sich nach verschiedenen Versuchen gerade so ergeben hat mit paar brauchbaren Ergebnissen. Als beste Lösung bei Rahmen(2,2,2,2,4,3,4,4) müsste etwas wie
46 Knoten, 16×Grad 3, 30×Grad 4, 0 Überschneidungen,
84 Kanten, minimal 0.99999999999999844569, maximal 1.00000000000000088818, Einsetzkanten=Beweglichkeit-5,
einzustellende Kanten, Abstände und Winkel:
herauskommen, also links unten in P9 ein Außenwinkel 0°. Mit feinerer schrittweiser Annäherung lässt sich das auch in dieser Richtung verbessern, doch dauert dann bedeutend länger. So richtig ausrechnen wie sich das gehört zum Beispiel mit Lagrange-Multiplikatoren, da habe ich die Gleichungen, kann sie aber bis jetzt noch nicht lösen.
Home / Home ohne Frame
Wie unterstütze ich den Matheplaneten mit Geld?
Beitrag No.2040, eingetragen 2020-06-10 22:24
Notiz
Profil
Quote
Link
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>[16,49,69]</Bildtext>
%<Ausrichten von="27" nach="25"/>
%<Winkel size="18" color="blue" id="blauerWinkel" value="135.44901656790375"/>
%<Winkel size="18" color="green" id="gruenerWinkel" value="75.33493053611132"/>
%<Winkel size="18" color="orange" id="orangerWinkel" value="130.23499299381191"/>
%<Winkel size="18" color="violet" id="vierterWinkel" value="134.5007311543001"/>
%<Winkel size="18" color="teal" id="fuenfterWinkel" value="135.464831429482"/>
%<Winkel size="18" color="lime" id="sechsterWinkel" value="90.20693533594131"/>
%<Winkel size="18" color="LightBlue" id="siebenterWinkel" value="290.19084700457114"/>
%<Winkel size="18" color="LightCoral" id="achterWinkel" value="11.59319829041266"/>
%<Winkel size="18" color="LightCyan" id="neunterWinkel" value="267.7949432261417"/>
%<Winkel size="18" color="LightGoldenrodYellow" id="zehnterWinkel" value="171.91295496742487"/>
%<Feinjustieren Anzahl="10,10"/>
%<Rechenweg>
%P[29]=[23.05850825935677,-122.49949422496942]; P[31]=[-29.772377571448096,-51.07533974761151]; D=ab(29,31); A(31,29); L(30,31,29); L(32,31,30); L(33,31,32); M(35,33,31,blauerWinkel); L(34,35,33); L(36,35,34); L(37,35,36); L(38,37,36); L(5,37,38); M(4,5,37,gruenerWinkel); L(2,5,4); L(3,2,4); L(1,2,3); M(7,1,2,orangerWinkel); L(6,7,1); L(8,7,6); L(9,7,8); L(10,9,8); L(11,9,10); M(13,11,9,vierterWinkel); L(12,13,11); L(14,13,12); L(15,13,14); M(17,15,13,fuenfterWinkel); L(16,17,15); L(18,17,16); L(19,17,18); Q(23,19,29,2*D,3*D); A(23,29); H(27,29,23,3); A(27,29); L(28,29,27); A(23,19); H(21,19,23,2); A(21,19); L(20,21,19); A(21,23); L(22,23,21); A(22,20); H(25,29,23,3/2); A(27,25); L(26,27,25); A(28,26); A(25,23); L(24,25,23); A(26,24); L(39,32,30); N(43,4,38); N(45,6,3); L(46,14,12); L(47,18,16); L(50,22,20); M(48,10,9,sechsterWinkel); M(42,24,26,siebenterWinkel); M(41,28,26,achterWinkel); M(40,34,35,neunterWinkel); L(49,46,48); M(51,42,24,zehnterWinkel); L(44,42,51);
%A(50,47); R(50,47,"green");
%A(48,46); R(48,46,"green");
%A(41,39); R(41,39,"green");
%A(41,42); R(41,42,"green");
%A(40,39); R(40,39,"green");
%A(40,43); R(40,43,"green");
%A(49,43); R(49,43,"green");
%A(51,47); R(51,47,"green");
%A(44,40); R(44,40,"green");
%A(51,50); R(51,50,"brown");
%A(44,41); R(44,41,"grey");
%A(49,45); R(49,45,"grey");
%A(48,45); R(48,45,"grey");
%</Rechenweg>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Brown}{rgb}{0.64,0.16,0.16}
\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{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}
\definecolor{Grey}{rgb}{0.50,0.50,0.50}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/2.01/5.79,
2/1.22/5.18,
3/2.14/4.80,
4/1.34/4.19,
5/0.42/4.58,
6/2.31/4.84,
7/2.99/5.57,
8/3.29/4.62,
9/3.96/5.36,
10/4.27/4.40,
11/4.94/5.14,
12/4.47/4.26,
13/5.47/4.29,
14/5.00/3.41,
15/6.00/3.44,
16/5.05/3.14,
17/5.78/2.47,
18/4.83/2.17,
19/5.57/1.49,
20/4.60/1.73,
21/4.88/0.77,
22/3.91/1.00,
23/4.19/0.04,
24/3.68/0.90,
25/3.19/0.03,
26/2.68/0.89,
27/2.19/0.01,
28/1.677/0.873,
29/1.19/0.00,
30/1.588/0.917,
31/0.59/0.80,
32/0.99/1.72,
33/0.00/1.61,
34/0.93/1.98,
35/0.14/2.60,
36/1.07/2.97,
37/0.28/3.59,
38/1.21/3.96,
39/1.99/1.83,
40/1.57/2.74,
41/2.65/1.09,
42/3.32/1.84,
43/2.13/3.58,
44/2.36/2.13,
45/2.44/3.84,
46/4.00/3.37,
47/4.09/2.84,
48/3.31/4.10,
49/3.03/3.14,
50/3.62/1.96,
51/3.09/2.81}
\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 {
33/306.49/441.94/0.4/Blue,
5/261.94/337.27/0.4/Green,
1/217.27/347.51/0.4/Orange,
11/167.51/302.01/0.4/Violet,
15/122.01/257.47/0.4/Teal,
10/107.51/197.72/0.4/Lime,
24/180.83/471.02/0.4/LightBlue,
28/0.83/12.42/0.4/LightCoral,
34/141.94/409.73/0.4/LightCyan,
42/291.02/462.93/0.4/LightGoldenrodYellow}
\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, 2/4,
3/2, 3/4,
4/5,
5/37, 5/38,
6/7, 6/1,
7/1,
8/7, 8/6,
9/7, 9/8,
10/9, 10/8,
11/9, 11/10,
12/13, 12/11,
13/11,
14/13, 14/12,
15/13, 15/14,
16/17, 16/15,
17/15,
18/17, 18/16,
19/17, 19/18,
20/21, 20/19,
21/19, 21/23,
22/23, 22/21, 22/20,
24/25, 24/23,
25/23,
26/27, 26/25, 26/24,
27/29, 27/25,
28/29, 28/27, 28/26,
30/31, 30/29,
31/29,
32/31, 32/30,
33/31, 33/32,
34/35, 34/33,
35/33,
36/35, 36/34,
37/35, 37/36,
38/37, 38/36,
39/32, 39/30,
40/34, 40/39, 40/43,
41/28, 41/39, 41/42,
42/24,
43/4, 43/38,
44/42, 44/51, 44/40, 44/41,
45/6, 45/3,
46/14, 46/12,
47/18, 47/16,
48/10, 48/46, 48/45,
49/46, 49/48, 49/43, 49/45,
50/22, 50/20, 50/47,
51/42, 51/47, 51/50}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,51}
\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);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-44) -- (p-41);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-48) -- (p-45);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-49) -- (p-45);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
33/306.49/441.94/0.4/Blue,
5/261.94/337.27/0.4/Green,
1/217.27/347.51/0.4/Orange,
11/167.51/302.01/0.4/Violet,
15/122.01/257.47/0.4/Teal,
10/107.51/197.72/0.4/Lime,
24/180.83/471.02/0.4/LightBlue,
28/0.83/12.42/0.4/LightCoral,
34/141.94/409.73/0.4/LightCyan,
42/291.02/462.93/0.4/LightGoldenrodYellow}
{
\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 {
1/67,
2/187,
3/7,
4/307,
5/187,
6/198,
7/78,
8/318,
9/18,
10/258,
11/92,
12/92,
13/332,
14/212,
15/47,
16/47,
17/287,
18/287,
19/287,
20/16,
21/316,
22/136,
23/331,
24/31,
25/211,
26/31,
27/211,
28/151,
29/276,
30/336,
31/276,
32/96,
33/156,
34/292,
35/232,
36/52,
37/172,
38/52,
39/36,
40/85,
41/345,
42/313,
43/19,
44/193,
45/163,
46/344,
47/32,
48/104,
49/224,
50/272,
51/73}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/85ae6d743bf125639991150443a33996.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>[16,49,69]</Bildtext>
%<Ausrichten von=\"27\" nach=\"25\"/>
%<Winkel size=\"18\" color=\"blue\" id=\"blauerWinkel\" value=\"135.44901656790375\"/>
%<Winkel size=\"18\" color=\"green\" id=\"gruenerWinkel\" value=\"75.33493053611132\"/>
%<Winkel size=\"18\" color=\"orange\" id=\"orangerWinkel\" value=\"130.23499299381191\"/>
%<Winkel size=\"18\" color=\"violet\" id=\"vierterWinkel\" value=\"134.5007311543001\"/>
%<Winkel size=\"18\" color=\"teal\" id=\"fuenfterWinkel\" value=\"135.464831429482\"/>
%<Winkel size=\"18\" color=\"lime\" id=\"sechsterWinkel\" value=\"90.20693533594131\"/>
%<Winkel size=\"18\" color=\"LightBlue\" id=\"siebenterWinkel\" value=\"290.19084700457114\"/>
%<Winkel size=\"18\" color=\"LightCoral\" id=\"achterWinkel\" value=\"11.59319829041266\"/>
%<Winkel size=\"18\" color=\"LightCyan\" id=\"neunterWinkel\" value=\"267.7949432261417\"/>
%<Winkel size=\"18\" color=\"LightGoldenrodYellow\" id=\"zehnterWinkel\" value=\"171.91295496742487\"/>
%<Feinjustieren Anzahl=\"10,10\"/>
%<Rechenweg>
%P[29]=[23.05850825935677,-122.49949422496942]; P[31]=[-29.772377571448096,-51.07533974761151]; D=ab(29,31); A(31,29); L(30,31,29); L(32,31,30); L(33,31,32); M(35,33,31,blauerWinkel); L(34,35,33); L(36,35,34); L(37,35,36); L(38,37,36); L(5,37,38); M(4,5,37,gruenerWinkel); L(2,5,4); L(3,2,4); L(1,2,3); M(7,1,2,orangerWinkel); L(6,7,1); L(8,7,6); L(9,7,8); L(10,9,8); L(11,9,10); M(13,11,9,vierterWinkel); L(12,13,11); L(14,13,12); L(15,13,14); M(17,15,13,fuenfterWinkel); L(16,17,15); L(18,17,16); L(19,17,18); Q(23,19,29,2*D,3*D); A(23,29); H(27,29,23,3); A(27,29); L(28,29,27); A(23,19); H(21,19,23,2); A(21,19); L(20,21,19); A(21,23); L(22,23,21); A(22,20); H(25,29,23,3/2); A(27,25); L(26,27,25); A(28,26); A(25,23); L(24,25,23); A(26,24); L(39,32,30); N(43,4,38); N(45,6,3); L(46,14,12); L(47,18,16); L(50,22,20); M(48,10,9,sechsterWinkel); M(42,24,26,siebenterWinkel); M(41,28,26,achterWinkel); M(40,34,35,neunterWinkel); L(49,46,48); M(51,42,24,zehnterWinkel); L(44,42,51);
%A(50,47); R(50,47,\"green\");
%A(48,46); R(48,46,\"green\");
%A(41,39); R(41,39,\"green\");
%A(41,42); R(41,42,\"green\");
%A(40,39); R(40,39,\"green\");
%A(40,43); R(40,43,\"green\");
%A(49,43); R(49,43,\"green\");
%A(51,47); R(51,47,\"green\");
%A(44,40); R(44,40,\"green\");
%A(51,50); R(51,50,\"brown\");
%A(44,41); R(44,41,\"grey\");
%A(49,45); R(49,45,\"grey\");
%A(48,45); R(48,45,\"grey\");
%</Rechenweg>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Brown}{rgb}{0.64,0.16,0.16}
\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{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}
\definecolor{Grey}{rgb}{0.50,0.50,0.50}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/2.01/5.79,
2/1.22/5.18,
3/2.14/4.80,
4/1.34/4.19,
5/0.42/4.58,
6/2.31/4.84,
7/2.99/5.57,
8/3.29/4.62,
9/3.96/5.36,
10/4.27/4.40,
11/4.94/5.14,
12/4.47/4.26,
13/5.47/4.29,
14/5.00/3.41,
15/6.00/3.44,
16/5.05/3.14,
17/5.78/2.47,
18/4.83/2.17,
19/5.57/1.49,
20/4.60/1.73,
21/4.88/0.77,
22/3.91/1.00,
23/4.19/0.04,
24/3.68/0.90,
25/3.19/0.03,
26/2.68/0.89,
27/2.19/0.01,
28/1.677/0.873,
29/1.19/0.00,
30/1.588/0.917,
31/0.59/0.80,
32/0.99/1.72,
33/0.00/1.61,
34/0.93/1.98,
35/0.14/2.60,
36/1.07/2.97,
37/0.28/3.59,
38/1.21/3.96,
39/1.99/1.83,
40/1.57/2.74,
41/2.65/1.09,
42/3.32/1.84,
43/2.13/3.58,
44/2.36/2.13,
45/2.44/3.84,
46/4.00/3.37,
47/4.09/2.84,
48/3.31/4.10,
49/3.03/3.14,
50/3.62/1.96,
51/3.09/2.81}
\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 {
33/306.49/441.94/0.4/Blue,
5/261.94/337.27/0.4/Green,
1/217.27/347.51/0.4/Orange,
11/167.51/302.01/0.4/Violet,
15/122.01/257.47/0.4/Teal,
10/107.51/197.72/0.4/Lime,
24/180.83/471.02/0.4/LightBlue,
28/0.83/12.42/0.4/LightCoral,
34/141.94/409.73/0.4/LightCyan,
42/291.02/462.93/0.4/LightGoldenrodYellow}
\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, 2/4,
3/2, 3/4,
4/5,
5/37, 5/38,
6/7, 6/1,
7/1,
8/7, 8/6,
9/7, 9/8,
10/9, 10/8,
11/9, 11/10,
12/13, 12/11,
13/11,
14/13, 14/12,
15/13, 15/14,
16/17, 16/15,
17/15,
18/17, 18/16,
19/17, 19/18,
20/21, 20/19,
21/19, 21/23,
22/23, 22/21, 22/20,
24/25, 24/23,
25/23,
26/27, 26/25, 26/24,
27/29, 27/25,
28/29, 28/27, 28/26,
30/31, 30/29,
31/29,
32/31, 32/30,
33/31, 33/32,
34/35, 34/33,
35/33,
36/35, 36/34,
37/35, 37/36,
38/37, 38/36,
39/32, 39/30,
40/34, 40/39, 40/43,
41/28, 41/39, 41/42,
42/24,
43/4, 43/38,
44/42, 44/51, 44/40, 44/41,
45/6, 45/3,
46/14, 46/12,
47/18, 47/16,
48/10, 48/46, 48/45,
49/46, 49/48, 49/43, 49/45,
50/22, 50/20, 50/47,
51/42, 51/47, 51/50}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,51}
\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);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-44) -- (p-41);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-48) -- (p-45);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-49) -- (p-45);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
33/306.49/441.94/0.4/Blue,
5/261.94/337.27/0.4/Green,
1/217.27/347.51/0.4/Orange,
11/167.51/302.01/0.4/Violet,
15/122.01/257.47/0.4/Teal,
10/107.51/197.72/0.4/Lime,
24/180.83/471.02/0.4/LightBlue,
28/0.83/12.42/0.4/LightCoral,
34/141.94/409.73/0.4/LightCyan,
42/291.02/462.93/0.4/LightGoldenrodYellow}
{
\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 {
1/67,
2/187,
3/7,
4/307,
5/187,
6/198,
7/78,
8/318,
9/18,
10/258,
11/92,
12/92,
13/332,
14/212,
15/47,
16/47,
17/287,
18/287,
19/287,
20/16,
21/316,
22/136,
23/331,
24/31,
25/211,
26/31,
27/211,
28/151,
29/276,
30/336,
31/276,
32/96,
33/156,
34/292,
35/232,
36/52,
37/172,
38/52,
39/36,
40/85,
41/345,
42/313,
43/19,
44/193,
45/163,
46/344,
47/32,
48/104,
49/224,
50/272,
51/73}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>[36,116,166,254]</Bildtext>
%<Ausrichten von="27" nach="25"/>
%<Winkel size="18" color="blue" id="blauerWinkel" value="141.18996051134036"/>
%<Winkel size="18" color="green" id="gruenerWinkel" value="71.62128800864492"/>
%<Winkel size="18" color="orange" id="orangerWinkel" value="129.58165709631936"/>
%<Winkel size="18" color="violet" id="vierterWinkel" value="135.058931012254"/>
%<Winkel size="18" color="teal" id="fuenfterWinkel" value="137.99849046899104"/>
%<Winkel size="18" color="lime" id="sechsterWinkel" value="300"/>
%<Winkel size="18" color="LightBlue" id="siebenterWinkel" value="91.38351227960801"/>
%<Winkel size="18" color="LightCoral" id="achterWinkel" value="291.8384633727108"/>
%<Winkel size="18" color="LightCyan" id="neunterWinkel" value="9.247539177719297"/>
%<Winkel size="18" color="LightGoldenrodYellow" id="zehnterWinkel" value="255.8023511778959"/>
%<Feinjustieren Anzahl="10,10"/>
%<Rechenweg>
%P[29]=[50.81387382481367,-122.49950644299267]; P[31]=[2.8654999305428532,-52.82418521770546]; D=ab(29,31); A(31,29); L(30,31,29); L(32,31,30); L(33,31,32); M(35,33,31,blauerWinkel); L(34,35,33); L(36,35,34); L(37,35,36); L(38,37,36); L(5,37,38); M(4,5,37,gruenerWinkel); L(2,5,4); L(3,2,4); L(1,2,3); M(7,1,2,orangerWinkel); L(6,7,1); L(8,7,6); L(9,7,8); L(10,9,8); L(11,9,10); M(13,11,9,vierterWinkel); L(12,13,11); L(14,13,12); L(15,13,14); M(17,15,13,fuenfterWinkel); L(16,17,15); L(18,17,16); L(19,17,18); Q(23,19,29,2*D,3*D); A(23,29); H(27,29,23,3); A(27,29); L(28,29,27); A(23,19); H(21,19,23,2); A(21,19); L(20,21,19); A(21,23); L(22,23,21); A(22,20); H(25,29,23,3/2); A(27,25); L(26,27,25); A(28,26); A(25,23); L(24,25,23); A(26,24); L(39,32,30); N(43,4,38); L(46,14,12); L(47,18,16); M(50,20,22,sechsterWinkel); M(48,10,9,siebenterWinkel); M(42,24,26,achterWinkel); M(41,28,26,neunterWinkel); M(40,34,35,zehnterWinkel); L(44,41,42); L(49,46,48); L(51,44,42); L(45,49,48);
%A(50,47); R(50,47,"green");
%A(48,46); R(48,46,"green");
%A(41,39); R(41,39,"green");
%A(41,42); R(41,42,"green");
%A(40,39); R(40,39,"green");
%A(40,43); R(40,43,"green");
%A(44,40); R(44,40,"green");
%A(49,43); R(49,43,"green");
%A(51,47); R(51,47,"green");
%A(50,22); R(50,22,"brown");
%A(51,50); R(51,50,"grey");
%A(45,3); R(45,3,"grey");
%A(45,6); R(45,6,"grey");
%</Rechenweg>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Brown}{rgb}{0.64,0.16,0.16}
\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{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}
\definecolor{Grey}{rgb}{0.50,0.50,0.50}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.81363548911171879041/5.85246821647402537536,
2/1.01864644722481578754/5.24584442590878285984,
3/1.94149258133777813384/4.86067561518709467805,
4/1.14650353945087513097/4.25405182462185216252,
5/0.22365740533791236833/4.63922063534354034431,
6/2.10479582581471191816/4.89579394676097390260,
7/2.78771987818164346251/5.62628332977672229731,
8/3.07888021488463659026/4.66960906006367171273,
9/3.76180426725156902279/5.40009844307942010744,
10/4.05296460395456126236/4.44342417336636863467,
11/4.73588865632149236262/5.17391355638211702939,
12/4.26620702489235625876/4.29107769106055858543,
13/5.26560612734741173568/4.32573939921278594056,
14/4.79592449591827563182/3.44290353389122705252,
15/5.79532359837332933239/3.47756524204345529583,
16/4.85554062173343048414/3.13579345149038868357,
17/5.62141516296922993945/2.49280341495261081874,
18/4.68163218632932931484/2.15103162439954509466,
19/5.44750672756512877015/1.50804158786176700779,
20/4.46608029107279147496/1.69988045189601066909,
21/4.79065617963215562014/0.75402079393088872195,
22/3.80922974313981788086/0.94585965796513293835,
23/4.13380563169918247013/0.00000000000001024908,
24/3.63380563169917980559/0.86602540378444725633,
25/3.13380563169918202604/0.00000000000000688872,
26/2.63380563169917936150/0.86602540378444370361,
27/2.13380563169918202604/0.00000000000000336035,
28/1.63380563169917891742/0.86602540378444037295,
29/1.13380563169918180400/0.00000000000000000000,
30/1.56377268305081540412/0.90284457951077157212,
31/0.56690281584959090200/0.82378467901618868119,
32/0.99686986720122450212/1.72662925852696025331,
33/0.00000000000000000000/1.64756935803237736238,
34/0.90089156936152925415/2.08161357266185609305,
35/0.07455246844597068767/2.64478645046943139363,
36/0.97544403780749977528/3.07883066509891012430,
37/0.14910493689194137534/3.64200354290648631306,
38/1.04999650625347062949/4.07604775753596459964,
39/1.99373973440244900424/1.80568915902154314423,
40/1.64953677672807552668/2.74458442683804149098,
41/2.62080890115403564167/1.02672557828783950207,
42/3.26181457573893096580/1.79426171759983477116,
43/1.97284264036643319784/3.69087894681427597376,
44/2.27660594347966327433/1.96562084610433740473,
45/2.13272436914352025994/3.88966279689907867834,
46/3.79652539346322015490/3.40824182573900014148,
47/3.91575764509353030363/2.79402166093732295948,
48/3.10359914494977218169/4.12925029595351666956,
49/2.82565061765696912133/3.16865432668456215026,
50/3.48465385458045195932/1.89171931593025521856,
51/2.91761161806455859846/2.73315698541633311791}
\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 {
33/304.53/445.72/0.4/Blue,
5/265.72/337.35/0.4/Green,
1/217.35/346.93/0.4/Orange,
11/166.93/301.99/0.4/Violet,
15/121.99/259.98/0.4/Teal,
20/228.94/528.94/0.4/Lime,
10/106.93/198.31/0.4/LightBlue,
24/180.00/471.84/0.4/LightCoral,
28/0.00/9.25/0.4/LightCyan,
34/145.72/401.53/0.4/LightGoldenrodYellow}
\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, 2/4,
3/2, 3/4,
4/5,
5/37, 5/38,
6/7, 6/1,
7/1,
8/7, 8/6,
9/7, 9/8,
10/9, 10/8,
11/9, 11/10,
12/13, 12/11,
13/11,
14/13, 14/12,
15/13, 15/14,
16/17, 16/15,
17/15,
18/17, 18/16,
19/17, 19/18,
20/21, 20/19,
21/19, 21/23,
22/23, 22/21, 22/20,
24/25, 24/23,
25/23,
26/27, 26/25, 26/24,
27/29, 27/25,
28/29, 28/27, 28/26,
30/31, 30/29,
31/29,
32/31, 32/30,
33/31, 33/32,
34/35, 34/33,
35/33,
36/35, 36/34,
37/35, 37/36,
38/37, 38/36,
39/32, 39/30,
40/34, 40/39, 40/43,
41/28, 41/39, 41/42,
42/24,
43/4, 43/38,
44/41, 44/42, 44/40,
45/49, 45/48, 45/3, 45/6,
46/14, 46/12,
47/18, 47/16,
48/10, 48/46,
49/46, 49/48, 49/43,
50/20, 50/47, 50/22,
51/44, 51/42, 51/47, 51/50}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,51}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[Green,very thick] (p-50) -- (p-47);
\draw[Green,very thick] (p-48) -- (p-46);
\draw[Green,very thick] (p-41) -- (p-39);
\draw[Green,very thick] (p-41) -- (p-42);
\draw[Green,very thick] (p-40) -- (p-39);
\draw[Green,very thick] (p-40) -- (p-43);
\draw[Green,very thick] (p-44) -- (p-40);
\draw[Green,very thick] (p-49) -- (p-43);
\draw[Green,very thick] (p-51) -- (p-47);
\draw[Brown,very thick] (p-50) -- (p-22);
\draw[Grey,very thick] (p-51) -- (p-50);
\draw[Grey,very thick] (p-45) -- (p-3);
\draw[Grey,very thick] (p-45) -- (p-6);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-45) -- (p-3);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-45) -- (p-6);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-51) -- (p-50);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
33/304.53/445.72/0.4/Blue,
5/265.72/337.35/0.4/Green,
1/217.35/346.93/0.4/Orange,
11/166.93/301.99/0.4/Violet,
15/121.99/259.98/0.4/Teal,
20/228.94/528.94/0.4/Lime,
10/106.93/198.31/0.4/LightBlue,
24/180.00/471.84/0.4/LightCoral,
28/0.00/9.25/0.4/LightCyan,
34/145.72/401.53/0.4/LightGoldenrodYellow}
{
\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 {
1/67,
2/127,
3/307,
4/307,
5/187,
6/197,
7/17,
8/317,
9/17,
10/257,
11/92,
12/92,
13/332,
14/272,
15/50,
16/110,
17/290,
18/170,
19/19,
20/19,
21/319,
22/139,
23/330,
24/30,
25/330,
26/90,
27/330,
28/150,
29/210,
30/35,
31/155,
32/35,
33/236,
34/296,
35/176,
36/56,
37/116,
38/356,
39/35,
40/78,
41/260,
42/20,
43/112,
44/200,
45/164,
46/344,
47/170,
48/104,
49/284,
50/274,
51/154}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/d88203633ab1c6dc4258481a8cdc0924.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>[36,116,166,254]</Bildtext>
%<Ausrichten von=\"27\" nach=\"25\"/>
%<Winkel size=\"18\" color=\"blue\" id=\"blauerWinkel\" value=\"141.18996051134036\"/>
%<Winkel size=\"18\" color=\"green\" id=\"gruenerWinkel\" value=\"71.62128800864492\"/>
%<Winkel size=\"18\" color=\"orange\" id=\"orangerWinkel\" value=\"129.58165709631936\"/>
%<Winkel size=\"18\" color=\"violet\" id=\"vierterWinkel\" value=\"135.058931012254\"/>
%<Winkel size=\"18\" color=\"teal\" id=\"fuenfterWinkel\" value=\"137.99849046899104\"/>
%<Winkel size=\"18\" color=\"lime\" id=\"sechsterWinkel\" value=\"300\"/>
%<Winkel size=\"18\" color=\"LightBlue\" id=\"siebenterWinkel\" value=\"91.38351227960801\"/>
%<Winkel size=\"18\" color=\"LightCoral\" id=\"achterWinkel\" value=\"291.8384633727108\"/>
%<Winkel size=\"18\" color=\"LightCyan\" id=\"neunterWinkel\" value=\"9.247539177719297\"/>
%<Winkel size=\"18\" color=\"LightGoldenrodYellow\" id=\"zehnterWinkel\" value=\"255.8023511778959\"/>
%<Feinjustieren Anzahl=\"10,10\"/>
%<Rechenweg>
%P[29]=[50.81387382481367,-122.49950644299267]; P[31]=[2.8654999305428532,-52.82418521770546]; D=ab(29,31); A(31,29); L(30,31,29); L(32,31,30); L(33,31,32); M(35,33,31,blauerWinkel); L(34,35,33); L(36,35,34); L(37,35,36); L(38,37,36); L(5,37,38); M(4,5,37,gruenerWinkel); L(2,5,4); L(3,2,4); L(1,2,3); M(7,1,2,orangerWinkel); L(6,7,1); L(8,7,6); L(9,7,8); L(10,9,8); L(11,9,10); M(13,11,9,vierterWinkel); L(12,13,11); L(14,13,12); L(15,13,14); M(17,15,13,fuenfterWinkel); L(16,17,15); L(18,17,16); L(19,17,18); Q(23,19,29,2*D,3*D); A(23,29); H(27,29,23,3); A(27,29); L(28,29,27); A(23,19); H(21,19,23,2); A(21,19); L(20,21,19); A(21,23); L(22,23,21); A(22,20); H(25,29,23,3/2); A(27,25); L(26,27,25); A(28,26); A(25,23); L(24,25,23); A(26,24); L(39,32,30); N(43,4,38); L(46,14,12); L(47,18,16); M(50,20,22,sechsterWinkel); M(48,10,9,siebenterWinkel); M(42,24,26,achterWinkel); M(41,28,26,neunterWinkel); M(40,34,35,zehnterWinkel); L(44,41,42); L(49,46,48); L(51,44,42); L(45,49,48);
%A(50,47); R(50,47,\"green\");
%A(48,46); R(48,46,\"green\");
%A(41,39); R(41,39,\"green\");
%A(41,42); R(41,42,\"green\");
%A(40,39); R(40,39,\"green\");
%A(40,43); R(40,43,\"green\");
%A(44,40); R(44,40,\"green\");
%A(49,43); R(49,43,\"green\");
%A(51,47); R(51,47,\"green\");
%A(50,22); R(50,22,\"brown\");
%A(51,50); R(51,50,\"grey\");
%A(45,3); R(45,3,\"grey\");
%A(45,6); R(45,6,\"grey\");
%</Rechenweg>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Blue}{rgb}{0.00,0.00,1.00}
\definecolor{Brown}{rgb}{0.64,0.16,0.16}
\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{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}
\definecolor{Grey}{rgb}{0.50,0.50,0.50}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.81363548911171879041/5.85246821647402537536,
2/1.01864644722481578754/5.24584442590878285984,
3/1.94149258133777813384/4.86067561518709467805,
4/1.14650353945087513097/4.25405182462185216252,
5/0.22365740533791236833/4.63922063534354034431,
6/2.10479582581471191816/4.89579394676097390260,
7/2.78771987818164346251/5.62628332977672229731,
8/3.07888021488463659026/4.66960906006367171273,
9/3.76180426725156902279/5.40009844307942010744,
10/4.05296460395456126236/4.44342417336636863467,
11/4.73588865632149236262/5.17391355638211702939,
12/4.26620702489235625876/4.29107769106055858543,
13/5.26560612734741173568/4.32573939921278594056,
14/4.79592449591827563182/3.44290353389122705252,
15/5.79532359837332933239/3.47756524204345529583,
16/4.85554062173343048414/3.13579345149038868357,
17/5.62141516296922993945/2.49280341495261081874,
18/4.68163218632932931484/2.15103162439954509466,
19/5.44750672756512877015/1.50804158786176700779,
20/4.46608029107279147496/1.69988045189601066909,
21/4.79065617963215562014/0.75402079393088872195,
22/3.80922974313981788086/0.94585965796513293835,
23/4.13380563169918247013/0.00000000000001024908,
24/3.63380563169917980559/0.86602540378444725633,
25/3.13380563169918202604/0.00000000000000688872,
26/2.63380563169917936150/0.86602540378444370361,
27/2.13380563169918202604/0.00000000000000336035,
28/1.63380563169917891742/0.86602540378444037295,
29/1.13380563169918180400/0.00000000000000000000,
30/1.56377268305081540412/0.90284457951077157212,
31/0.56690281584959090200/0.82378467901618868119,
32/0.99686986720122450212/1.72662925852696025331,
33/0.00000000000000000000/1.64756935803237736238,
34/0.90089156936152925415/2.08161357266185609305,
35/0.07455246844597068767/2.64478645046943139363,
36/0.97544403780749977528/3.07883066509891012430,
37/0.14910493689194137534/3.64200354290648631306,
38/1.04999650625347062949/4.07604775753596459964,
39/1.99373973440244900424/1.80568915902154314423,
40/1.64953677672807552668/2.74458442683804149098,
41/2.62080890115403564167/1.02672557828783950207,
42/3.26181457573893096580/1.79426171759983477116,
43/1.97284264036643319784/3.69087894681427597376,
44/2.27660594347966327433/1.96562084610433740473,
45/2.13272436914352025994/3.88966279689907867834,
46/3.79652539346322015490/3.40824182573900014148,
47/3.91575764509353030363/2.79402166093732295948,
48/3.10359914494977218169/4.12925029595351666956,
49/2.82565061765696912133/3.16865432668456215026,
50/3.48465385458045195932/1.89171931593025521856,
51/2.91761161806455859846/2.73315698541633311791}
\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 {
33/304.53/445.72/0.4/Blue,
5/265.72/337.35/0.4/Green,
1/217.35/346.93/0.4/Orange,
11/166.93/301.99/0.4/Violet,
15/121.99/259.98/0.4/Teal,
20/228.94/528.94/0.4/Lime,
10/106.93/198.31/0.4/LightBlue,
24/180.00/471.84/0.4/LightCoral,
28/0.00/9.25/0.4/LightCyan,
34/145.72/401.53/0.4/LightGoldenrodYellow}
\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, 2/4,
3/2, 3/4,
4/5,
5/37, 5/38,
6/7, 6/1,
7/1,
8/7, 8/6,
9/7, 9/8,
10/9, 10/8,
11/9, 11/10,
12/13, 12/11,
13/11,
14/13, 14/12,
15/13, 15/14,
16/17, 16/15,
17/15,
18/17, 18/16,
19/17, 19/18,
20/21, 20/19,
21/19, 21/23,
22/23, 22/21, 22/20,
24/25, 24/23,
25/23,
26/27, 26/25, 26/24,
27/29, 27/25,
28/29, 28/27, 28/26,
30/31, 30/29,
31/29,
32/31, 32/30,
33/31, 33/32,
34/35, 34/33,
35/33,
36/35, 36/34,
37/35, 37/36,
38/37, 38/36,
39/32, 39/30,
40/34, 40/39, 40/43,
41/28, 41/39, 41/42,
42/24,
43/4, 43/38,
44/41, 44/42, 44/40,
45/49, 45/48, 45/3, 45/6,
46/14, 46/12,
47/18, 47/16,
48/10, 48/46,
49/46, 49/48, 49/43,
50/20, 50/47, 50/22,
51/44, 51/42, 51/47, 51/50}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,51}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[Green,very thick] (p-50) -- (p-47);
\draw[Green,very thick] (p-48) -- (p-46);
\draw[Green,very thick] (p-41) -- (p-39);
\draw[Green,very thick] (p-41) -- (p-42);
\draw[Green,very thick] (p-40) -- (p-39);
\draw[Green,very thick] (p-40) -- (p-43);
\draw[Green,very thick] (p-44) -- (p-40);
\draw[Green,very thick] (p-49) -- (p-43);
\draw[Green,very thick] (p-51) -- (p-47);
\draw[Brown,very thick] (p-50) -- (p-22);
\draw[Grey,very thick] (p-51) -- (p-50);
\draw[Grey,very thick] (p-45) -- (p-3);
\draw[Grey,very thick] (p-45) -- (p-6);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-45) -- (p-3);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-45) -- (p-6);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-51) -- (p-50);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
33/304.53/445.72/0.4/Blue,
5/265.72/337.35/0.4/Green,
1/217.35/346.93/0.4/Orange,
11/166.93/301.99/0.4/Violet,
15/121.99/259.98/0.4/Teal,
20/228.94/528.94/0.4/Lime,
10/106.93/198.31/0.4/LightBlue,
24/180.00/471.84/0.4/LightCoral,
28/0.00/9.25/0.4/LightCyan,
34/145.72/401.53/0.4/LightGoldenrodYellow}
{
\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 {
1/67,
2/127,
3/307,
4/307,
5/187,
6/197,
7/17,
8/317,
9/17,
10/257,
11/92,
12/92,
13/332,
14/272,
15/50,
16/110,
17/290,
18/170,
19/19,
20/19,
21/319,
22/139,
23/330,
24/30,
25/330,
26/90,
27/330,
28/150,
29/210,
30/35,
31/155,
32/35,
33/236,
34/296,
35/176,
36/56,
37/116,
38/356,
39/35,
40/78,
41/260,
42/20,
43/112,
44/200,
45/164,
46/344,
47/170,
48/104,
49/284,
50/274,
51/154}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>Fig.5 4-regular planar graph with 51 vertices. This graph is rigid and asymmetric.</Bildtext>
%<Ausrichten von="27" nach="25"/>
%<Winkel size="18" color="blue" id="blauerWinkel" value="123.75071666127874"/>
%<Winkel size="18" color="green" id="gruenerWinkel" value="135.94731612268453"/>
%<Winkel size="18" color="orange" id="orangerWinkel" value="76.17124492132862"/>
%<Winkel size="18" color="violet" id="vierterWinkel" value="123.7498457562082"/>
%<Winkel size="18" color="teal" id="fuenfterWinkel" value="150.34000000000006"/>
%<Winkel size="18" color="lime" id="sechsterWinkel" value="126.911362456572"/>
%<Winkel size="18" color="LightBlue" id="siebenterWinkel" value="292.3748450219602"/>
%<Winkel size="18" color="LightCoral" id="achterWinkel" value="93.72441895274778"/>
%<Winkel size="18" color="LightCyan" id="neunterWinkel" value="233.0872054331202"/>
%<Winkel size="18" color="LightGoldenrodYellow" id="zehnterWinkel" value="67.62695128385326"/>
%<Winkel size="18" color="LightGreen" id="elfterWinkel" value="266.7464121925173"/>
%<Winkel size="18" color="LightGray" id="zwoelfterWinkel" value="194.78224973087902"/>
%<Winkel size="18" color="LightPink" id="dreizehnterWinkel" value="131.62940423506836"/>
%<Winkel size="18" color="LightSalmon" id="vierzehnterWinkel" value="278.8543964247019"/>
%<Feinjustieren Anzahl="9,14"/>
%<Rechenweg>
%P[23]=[277.49906148857485,-124.97112069855191]; P[25]=[191.77855418836458,-124.22686989907095]; D=ab(23,25); A(25,23); L(24,25,23); L(26,25,24); L(27,25,26); L(28,27,26); L(29,27,28); M(31,29,27,blauerWinkel); L(30,31,29); L(32,31,30); L(33,31,32); M(35,33,31,gruenerWinkel); L(34,35,33); L(36,35,34); L(37,35,36); L(38,37,36); L(5,37,38); M(4,5,37,orangerWinkel); L(2,5,4); L(3,2,4); L(1,2,3); M(7,1,2,vierterWinkel); L(6,7,1); L(8,7,6); L(9,7,8); L(10,9,8); L(11,9,10); M(13,11,9,fuenfterWinkel); L(12,13,11); L(14,13,12); L(15,13,14); Q(19,15,23,2*D,2*D); A(19,23); H(21,23,19,2); A(21,23); L(22,23,21); A(19,15); H(17,15,19,2); A(17,15); L(16,17,15); A(17,19); L(18,19,17); A(18,16); A(21,19); L(20,21,19); A(22,20); L(39,32,30); L(43,3,4); L(45,22,20); L(46,14,12); L(47,18,16); M(51,10,9,sechsterWinkel); M(49,6,7,siebenterWinkel); M(48,38,37,achterWinkel); M(42,24,25,neunterWinkel); M(41,28,27,zehnterWinkel); M(40,34,35,elfterWinkel); L(44,41,42); M(53,45,22,zwoelfterWinkel); M(52,40,34,dreizehnterWinkel); M(50,48,38,vierzehnterWinkel);
%A(49,43); R(49,43,"green");
%A(49,51); R(49,51,"green");
%A(48,43); R(48,43,"green");
%A(41,39); R(41,39,"green");
%A(41,42); R(41,42,"green");
%A(40,39); R(40,39,"green");
%A(53,47); R(53,47,"green");
%A(52,48); R(52,48,"green");
%A(50,49); R(50,49,"green");
%RA(40,44,"blue"); RA(42,53,"blue"); RA(45,47,"blue"); RA(46,53,"blue"); RA(50,51,"blue"); RA(50,52,"blue"); RA(51,46,"blue"); RA(52,44,"blue");
%</Rechenweg>
%</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 {
1/2.19293877090076039238/5.80318384166551659575,
2/1.37752627788550729981/5.22430348594885352043,
3/2.28655761819553582370/4.80757573029277462950,
4/1.47114512518028339727/4.22869537457611333053,
5/0.56211378487025442929/4.64542313023219222146,
6/2.35147040101049942251/4.81582994247093232332,
7/3.12727814518375923925/5.44679931104661640973,
8/3.28580977529349871347/4.45944541185203213729,
9/4.06161751946675764202/5.09041478042771711188,
10/4.22014914957649711624/4.10306088123313372762,
11/4.99595689374975648889/4.73403024980881692585,
12/4.64512308685442931733/3.79759251031978362079,
13/5.63151886176207039370/3.96198039078654273837,
14/5.28068505486674322214/3.02554265129750943331,
15/6.26708082977438341032/3.18993053176426855089,
16/5.28565961475255896573/2.99806495719424015434,
17/5.94253068395281403014/2.24406204045736457076,
18/4.96110946893098958554/2.05219646588733528603,
19/5.61798053813124464995/1.29819354915046081267,
20/4.67549332110302007237/1.63243574537707925032,
21/4.85727469666817768257/0.64909677457523040633,
22/3.91478747963995354908/0.98333897080184951012,
23/4.09656885520511071519/0.00000000000000000000,
24/3.60410650503342999684/0.87033374843411959176,
25/3.09660654420438774537/0.00868196856099679760,
26/2.60414419403270747111/0.87901571699511649172,
27/2.09664423320366521963/0.01736393712199376174,
28/1.60418188303198494538/0.88769768555611328065,
29/1.09668192220294269390/0.02604590568299072761,
30/1.54672939419393751237/0.91905053778436718304,
31/0.54834096110147134695/0.86230076538684596876,
32/0.99838843309246605440/1.75530539748822222990,
33/0.00000000000000000000/1.69855562509070123767,
34/0.94437300449150940462/2.02743193677592925539,
35/0.18737126162341827262/2.68084479347119808423,
36/1.13174426611492795480/3.00972110515642654605,
37/0.37474252324683654525/3.66313396185169537489,
38/1.31911552773834572783/3.99201027353692339261,
39/1.99677686618493166471/1.81205516988574366621,
40/1.63969650252746790287/2.74612883608678481906,
41/2.59645003986789379979/1.01181015442797428427,
42/3.21997620189864441897/1.79361263924316283180,
43/2.38017646549031169911/3.81196761892003443961,
44/2.23115230829151744985/1.94270089307841109516,
45/3.73300610407479638297/1.96667794160369835410,
46/4.29428927995910214577/2.86115477083074987164,
47/4.30423839973073452114/2.80619938262421042552,
48/1.70864146947500872287/3.07099477925131436606,
49/3.23025854794563738182/4.33861783783997712050,
50/2.55872355193033262921/3.59764499817125305015,
51/3.52590570064209840595/3.38332062696658786294,
52/2.63880200145651411248/2.70384169844729083110,
53/3.30634601681590911681/2.87108999920810603612}
\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 {
29/359.50/483.25/0.4/Blue,
33/303.25/439.20/0.4/Green,
5/259.20/335.37/0.4/Orange,
1/215.37/339.12/0.4/Violet,
11/159.12/309.46/0.4/Teal,
10/99.12/226.03/0.4/Lime,
6/39.12/331.50/0.4/LightBlue,
38/199.20/292.93/0.4/LightCoral,
24/239.50/472.59/0.4/LightCyan,
28/299.50/367.13/0.4/LightGoldenrodYellow,
34/139.20/405.95/0.4/LightGreen,
45/280.47/475.26/0.4/LightGray,
40/225.95/357.58/0.4/LightPink,
48/112.93/391.78/0.4/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 {
1/2, 1/3,
2/5, 2/4,
3/2, 3/4,
4/5,
5/37, 5/38,
6/7, 6/1,
7/1,
8/7, 8/6,
9/7, 9/8,
10/9, 10/8,
11/9, 11/10,
12/13, 12/11,
13/11,
14/13, 14/12,
15/13, 15/14,
16/17, 16/15,
17/15, 17/19,
18/19, 18/17, 18/16,
20/21, 20/19,
21/23, 21/19,
22/23, 22/21, 22/20,
24/25, 24/23,
25/23,
26/25, 26/24,
27/25, 27/26,
28/27, 28/26,
29/27, 29/28,
30/31, 30/29,
31/29,
32/31, 32/30,
33/31, 33/32,
34/35, 34/33,
35/33,
36/35, 36/34,
37/35, 37/36,
38/37, 38/36,
39/32, 39/30,
40/34, 40/39, 40/44,
41/28, 41/39, 41/42,
42/24, 42/53,
43/3, 43/4,
44/41, 44/42,
45/22, 45/20, 45/47,
46/14, 46/12, 46/53,
47/18, 47/16,
48/38, 48/43,
49/6, 49/43, 49/51,
50/48, 50/49, 50/51, 50/52,
51/10, 51/46,
52/40, 52/48, 52/44,
53/45, 53/47}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,53}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[Green,very thick] (p-49) -- (p-43);
\draw[Green,very thick] (p-49) -- (p-51);
\draw[Green,very thick] (p-48) -- (p-43);
\draw[Green,very thick] (p-41) -- (p-39);
\draw[Green,very thick] (p-41) -- (p-42);
\draw[Green,very thick] (p-40) -- (p-39);
\draw[Green,very thick] (p-53) -- (p-47);
\draw[Green,very thick] (p-52) -- (p-48);
\draw[Green,very thick] (p-50) -- (p-49);
\draw[Blue,very thick] (p-40) -- (p-44);
\draw[Blue,very thick] (p-42) -- (p-53);
\draw[Blue,very thick] (p-45) -- (p-47);
\draw[Blue,very thick] (p-46) -- (p-53);
\draw[Blue,very thick] (p-50) -- (p-51);
\draw[Blue,very thick] (p-50) -- (p-52);
\draw[Blue,very thick] (p-51) -- (p-46);
\draw[Blue,very thick] (p-52) -- (p-44);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-40) -- (p-44);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-42) -- (p-53);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-45) -- (p-47);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-46) -- (p-53);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-50) -- (p-51);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-50) -- (p-52);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-51) -- (p-46);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-52) -- (p-44);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
29/359.50/483.25/0.4/Blue,
33/303.25/439.20/0.4/Green,
5/259.20/335.37/0.4/Orange,
1/215.37/339.12/0.4/Violet,
11/159.12/309.46/0.4/Teal,
10/99.12/226.03/0.4/Lime,
6/39.12/331.50/0.4/LightBlue,
38/199.20/292.93/0.4/LightCoral,
24/239.50/472.59/0.4/LightCyan,
28/299.50/367.13/0.4/LightGoldenrodYellow,
34/139.20/405.95/0.4/LightGreen,
45/280.47/475.26/0.4/LightGray,
40/225.95/357.58/0.4/LightPink,
48/112.93/391.78/0.4/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 {
1/65,
2/125,
3/65,
4/305,
5/185,
6/189,
7/9,
8/189,
9/129,
10/249,
11/9,
12/159,
13/39,
14/279,
15/41,
16/41,
17/281,
18/161,
19/10,
20/10,
21/310,
22/190,
23/330,
24/30,
25/270,
26/150,
27/270,
28/90,
29/273,
30/333,
31/273,
32/153,
33/153,
34/289,
35/229,
36/349,
37/169,
38/349,
39/33,
40/81,
41/261,
42/21,
43/305,
44/141,
45/266,
46/219,
47/26,
48/263,
49/78,
50/198,
51/317,
52/307,
53/146}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/9425ab41c83adb2ff4ef8935340e6fe2.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>Fig.5 4-regular planar graph with 51 vertices. This graph is rigid and asymmetric.</Bildtext>
%<Ausrichten von=\"27\" nach=\"25\"/>
%<Winkel size=\"18\" color=\"blue\" id=\"blauerWinkel\" value=\"123.75071666127874\"/>
%<Winkel size=\"18\" color=\"green\" id=\"gruenerWinkel\" value=\"135.94731612268453\"/>
%<Winkel size=\"18\" color=\"orange\" id=\"orangerWinkel\" value=\"76.17124492132862\"/>
%<Winkel size=\"18\" color=\"violet\" id=\"vierterWinkel\" value=\"123.7498457562082\"/>
%<Winkel size=\"18\" color=\"teal\" id=\"fuenfterWinkel\" value=\"150.34000000000006\"/>
%<Winkel size=\"18\" color=\"lime\" id=\"sechsterWinkel\" value=\"126.911362456572\"/>
%<Winkel size=\"18\" color=\"LightBlue\" id=\"siebenterWinkel\" value=\"292.3748450219602\"/>
%<Winkel size=\"18\" color=\"LightCoral\" id=\"achterWinkel\" value=\"93.72441895274778\"/>
%<Winkel size=\"18\" color=\"LightCyan\" id=\"neunterWinkel\" value=\"233.0872054331202\"/>
%<Winkel size=\"18\" color=\"LightGoldenrodYellow\" id=\"zehnterWinkel\" value=\"67.62695128385326\"/>
%<Winkel size=\"18\" color=\"LightGreen\" id=\"elfterWinkel\" value=\"266.7464121925173\"/>
%<Winkel size=\"18\" color=\"LightGray\" id=\"zwoelfterWinkel\" value=\"194.78224973087902\"/>
%<Winkel size=\"18\" color=\"LightPink\" id=\"dreizehnterWinkel\" value=\"131.62940423506836\"/>
%<Winkel size=\"18\" color=\"LightSalmon\" id=\"vierzehnterWinkel\" value=\"278.8543964247019\"/>
%<Feinjustieren Anzahl=\"9,14\"/>
%<Rechenweg>
%P[23]=[277.49906148857485,-124.97112069855191]; P[25]=[191.77855418836458,-124.22686989907095]; D=ab(23,25); A(25,23); L(24,25,23); L(26,25,24); L(27,25,26); L(28,27,26); L(29,27,28); M(31,29,27,blauerWinkel); L(30,31,29); L(32,31,30); L(33,31,32); M(35,33,31,gruenerWinkel); L(34,35,33); L(36,35,34); L(37,35,36); L(38,37,36); L(5,37,38); M(4,5,37,orangerWinkel); L(2,5,4); L(3,2,4); L(1,2,3); M(7,1,2,vierterWinkel); L(6,7,1); L(8,7,6); L(9,7,8); L(10,9,8); L(11,9,10); M(13,11,9,fuenfterWinkel); L(12,13,11); L(14,13,12); L(15,13,14); Q(19,15,23,2*D,2*D); A(19,23); H(21,23,19,2); A(21,23); L(22,23,21); A(19,15); H(17,15,19,2); A(17,15); L(16,17,15); A(17,19); L(18,19,17); A(18,16); A(21,19); L(20,21,19); A(22,20); L(39,32,30); L(43,3,4); L(45,22,20); L(46,14,12); L(47,18,16); M(51,10,9,sechsterWinkel); M(49,6,7,siebenterWinkel); M(48,38,37,achterWinkel); M(42,24,25,neunterWinkel); M(41,28,27,zehnterWinkel); M(40,34,35,elfterWinkel); L(44,41,42); M(53,45,22,zwoelfterWinkel); M(52,40,34,dreizehnterWinkel); M(50,48,38,vierzehnterWinkel);
%A(49,43); R(49,43,\"green\");
%A(49,51); R(49,51,\"green\");
%A(48,43); R(48,43,\"green\");
%A(41,39); R(41,39,\"green\");
%A(41,42); R(41,42,\"green\");
%A(40,39); R(40,39,\"green\");
%A(53,47); R(53,47,\"green\");
%A(52,48); R(52,48,\"green\");
%A(50,49); R(50,49,\"green\");
%RA(40,44,\"blue\"); RA(42,53,\"blue\"); RA(45,47,\"blue\"); RA(46,53,\"blue\"); RA(50,51,\"blue\"); RA(50,52,\"blue\"); RA(51,46,\"blue\"); RA(52,44,\"blue\");
%</Rechenweg>
%</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 {
1/2.19293877090076039238/5.80318384166551659575,
2/1.37752627788550729981/5.22430348594885352043,
3/2.28655761819553582370/4.80757573029277462950,
4/1.47114512518028339727/4.22869537457611333053,
5/0.56211378487025442929/4.64542313023219222146,
6/2.35147040101049942251/4.81582994247093232332,
7/3.12727814518375923925/5.44679931104661640973,
8/3.28580977529349871347/4.45944541185203213729,
9/4.06161751946675764202/5.09041478042771711188,
10/4.22014914957649711624/4.10306088123313372762,
11/4.99595689374975648889/4.73403024980881692585,
12/4.64512308685442931733/3.79759251031978362079,
13/5.63151886176207039370/3.96198039078654273837,
14/5.28068505486674322214/3.02554265129750943331,
15/6.26708082977438341032/3.18993053176426855089,
16/5.28565961475255896573/2.99806495719424015434,
17/5.94253068395281403014/2.24406204045736457076,
18/4.96110946893098958554/2.05219646588733528603,
19/5.61798053813124464995/1.29819354915046081267,
20/4.67549332110302007237/1.63243574537707925032,
21/4.85727469666817768257/0.64909677457523040633,
22/3.91478747963995354908/0.98333897080184951012,
23/4.09656885520511071519/0.00000000000000000000,
24/3.60410650503342999684/0.87033374843411959176,
25/3.09660654420438774537/0.00868196856099679760,
26/2.60414419403270747111/0.87901571699511649172,
27/2.09664423320366521963/0.01736393712199376174,
28/1.60418188303198494538/0.88769768555611328065,
29/1.09668192220294269390/0.02604590568299072761,
30/1.54672939419393751237/0.91905053778436718304,
31/0.54834096110147134695/0.86230076538684596876,
32/0.99838843309246605440/1.75530539748822222990,
33/0.00000000000000000000/1.69855562509070123767,
34/0.94437300449150940462/2.02743193677592925539,
35/0.18737126162341827262/2.68084479347119808423,
36/1.13174426611492795480/3.00972110515642654605,
37/0.37474252324683654525/3.66313396185169537489,
38/1.31911552773834572783/3.99201027353692339261,
39/1.99677686618493166471/1.81205516988574366621,
40/1.63969650252746790287/2.74612883608678481906,
41/2.59645003986789379979/1.01181015442797428427,
42/3.21997620189864441897/1.79361263924316283180,
43/2.38017646549031169911/3.81196761892003443961,
44/2.23115230829151744985/1.94270089307841109516,
45/3.73300610407479638297/1.96667794160369835410,
46/4.29428927995910214577/2.86115477083074987164,
47/4.30423839973073452114/2.80619938262421042552,
48/1.70864146947500872287/3.07099477925131436606,
49/3.23025854794563738182/4.33861783783997712050,
50/2.55872355193033262921/3.59764499817125305015,
51/3.52590570064209840595/3.38332062696658786294,
52/2.63880200145651411248/2.70384169844729083110,
53/3.30634601681590911681/2.87108999920810603612}
\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 {
29/359.50/483.25/0.4/Blue,
33/303.25/439.20/0.4/Green,
5/259.20/335.37/0.4/Orange,
1/215.37/339.12/0.4/Violet,
11/159.12/309.46/0.4/Teal,
10/99.12/226.03/0.4/Lime,
6/39.12/331.50/0.4/LightBlue,
38/199.20/292.93/0.4/LightCoral,
24/239.50/472.59/0.4/LightCyan,
28/299.50/367.13/0.4/LightGoldenrodYellow,
34/139.20/405.95/0.4/LightGreen,
45/280.47/475.26/0.4/LightGray,
40/225.95/357.58/0.4/LightPink,
48/112.93/391.78/0.4/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 {
1/2, 1/3,
2/5, 2/4,
3/2, 3/4,
4/5,
5/37, 5/38,
6/7, 6/1,
7/1,
8/7, 8/6,
9/7, 9/8,
10/9, 10/8,
11/9, 11/10,
12/13, 12/11,
13/11,
14/13, 14/12,
15/13, 15/14,
16/17, 16/15,
17/15, 17/19,
18/19, 18/17, 18/16,
20/21, 20/19,
21/23, 21/19,
22/23, 22/21, 22/20,
24/25, 24/23,
25/23,
26/25, 26/24,
27/25, 27/26,
28/27, 28/26,
29/27, 29/28,
30/31, 30/29,
31/29,
32/31, 32/30,
33/31, 33/32,
34/35, 34/33,
35/33,
36/35, 36/34,
37/35, 37/36,
38/37, 38/36,
39/32, 39/30,
40/34, 40/39, 40/44,
41/28, 41/39, 41/42,
42/24, 42/53,
43/3, 43/4,
44/41, 44/42,
45/22, 45/20, 45/47,
46/14, 46/12, 46/53,
47/18, 47/16,
48/38, 48/43,
49/6, 49/43, 49/51,
50/48, 50/49, 50/51, 50/52,
51/10, 51/46,
52/40, 52/48, 52/44,
53/45, 53/47}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,53}
\fill[red] (p-\i) circle (1.125pt);
%einzustellende Kanten als \draw[green] (p-1) -- (p-2);
\draw[Green,very thick] (p-49) -- (p-43);
\draw[Green,very thick] (p-49) -- (p-51);
\draw[Green,very thick] (p-48) -- (p-43);
\draw[Green,very thick] (p-41) -- (p-39);
\draw[Green,very thick] (p-41) -- (p-42);
\draw[Green,very thick] (p-40) -- (p-39);
\draw[Green,very thick] (p-53) -- (p-47);
\draw[Green,very thick] (p-52) -- (p-48);
\draw[Green,very thick] (p-50) -- (p-49);
\draw[Blue,very thick] (p-40) -- (p-44);
\draw[Blue,very thick] (p-42) -- (p-53);
\draw[Blue,very thick] (p-45) -- (p-47);
\draw[Blue,very thick] (p-46) -- (p-53);
\draw[Blue,very thick] (p-50) -- (p-51);
\draw[Blue,very thick] (p-50) -- (p-52);
\draw[Blue,very thick] (p-51) -- (p-46);
\draw[Blue,very thick] (p-52) -- (p-44);
%nicht passende Kanten als \draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-1) -- (p-2);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-40) -- (p-44);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-42) -- (p-53);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-45) -- (p-47);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-46) -- (p-53);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-50) -- (p-51);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-50) -- (p-52);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-51) -- (p-46);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-52) -- (p-44);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
29/359.50/483.25/0.4/Blue,
33/303.25/439.20/0.4/Green,
5/259.20/335.37/0.4/Orange,
1/215.37/339.12/0.4/Violet,
11/159.12/309.46/0.4/Teal,
10/99.12/226.03/0.4/Lime,
6/39.12/331.50/0.4/LightBlue,
38/199.20/292.93/0.4/LightCoral,
24/239.50/472.59/0.4/LightCyan,
28/299.50/367.13/0.4/LightGoldenrodYellow,
34/139.20/405.95/0.4/LightGreen,
45/280.47/475.26/0.4/LightGray,
40/225.95/357.58/0.4/LightPink,
48/112.93/391.78/0.4/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 {
1/65,
2/125,
3/65,
4/305,
5/185,
6/189,
7/9,
8/189,
9/129,
10/249,
11/9,
12/159,
13/39,
14/279,
15/41,
16/41,
17/281,
18/161,
19/10,
20/10,
21/310,
22/190,
23/330,
24/30,
25/270,
26/150,
27/270,
28/90,
29/273,
30/333,
31/273,
32/153,
33/153,
34/289,
35/229,
36/349,
37/169,
38/349,
39/33,
40/81,
41/261,
42/21,
43/305,
44/141,
45/266,
46/219,
47/26,
48/263,
49/78,
50/198,
51/317,
52/307,
53/146}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#2046 mit nur 3 nicht passenden Kanten</Bildtext>
%<Ausrichten von="27" nach="25"/>
%<Winkel size="18" color="blue" id="blauerWinkel" value="124.35426112574547"/>
%<Winkel size="18" color="green" id="gruenerWinkel" value="139.3780917083093"/>
%<Winkel size="18" color="orange" id="orangerWinkel" value="75.1377828746346"/>
%<Winkel size="18" color="violet" id="vierterWinkel" value="123.77830302258792"/>
%<Winkel size="18" color="teal" id="fuenfterWinkel" value="144.331517535816"/>
%<Winkel size="18" color="lime" id="sechsterWinkel" value="126.95810758120652"/>
%<Winkel size="18" color="LightBlue" id="siebenterWinkel" value="292.3161446383474"/>
%<Winkel size="18" color="LightCoral" id="achterWinkel" value="91.54962695475666"/>
%<Winkel size="18" color="LightCyan" id="neunterWinkel" value="232.11840160729716"/>
%<Winkel size="18" color="LightGoldenrodYellow" id="zehnterWinkel" value="68.87414739830785"/>
%<Winkel size="18" color="LightGreen" id="elfterWinkel" value="259.5636510706451"/>
%<Winkel size="18" color="LightGray" id="zwoelfterWinkel" value="194.78224973087902"/>
%<Winkel size="18" color="LightPink" id="dreizehnterWinkel" value="131.62940423506836"/>
%<Winkel size="18" color="LightSalmon" id="vierzehnterWinkel" value="279.969785308762"/>
%<Feinjustieren Anzahl="12,14"/>
%<Rechenweg>P[23]=[277.49906148857485,-124.97112069855191]; P[25]=[191.77855418836458,-124.22686989907095]; D=ab(23,25); A(25,23); L(24,25,23); L(26,25,24); L(27,25,26); L(28,27,26); L(29,27,28); M(31,29,27,blauerWinkel); L(30,31,29); L(32,31,30); L(33,31,32); M(35,33,31,gruenerWinkel); L(34,35,33); L(36,35,34); L(37,35,36); L(38,37,36); L(5,37,38); M(4,5,37,orangerWinkel); L(2,5,4); L(3,2,4); L(1,2,3); M(7,1,2,vierterWinkel); L(6,7,1); L(8,7,6); L(9,7,8); L(10,9,8); L(11,9,10); M(13,11,9,fuenfterWinkel); L(12,13,11); L(14,13,12); L(15,13,14); Q(19,15,23,2*D,2*D); A(19,23); H(21,23,19,2); A(21,23); L(22,23,21); A(19,15); H(17,15,19,2); A(17,15); L(16,17,15); A(17,19); L(18,19,17); A(18,16); A(21,19); L(20,21,19); A(22,20); L(39,32,30); L(43,3,4); L(45,22,20); L(46,14,12); L(47,18,16); M(51,10,9,sechsterWinkel); M(49,6,7,siebenterWinkel); M(48,38,37,achterWinkel); M(42,24,25,neunterWinkel); M(41,28,27,zehnterWinkel); M(40,34,35,elfterWinkel); L(44,41,42); M(53,45,22,zwoelfterWinkel); M(52,40,34,dreizehnterWinkel); M(50,48,38,vierzehnterWinkel);
%A(49,43); R(49,43,"green");
%A(49,51); R(49,51,"green");
%A(48,43); R(48,43,"green");
%A(41,39); R(41,39,"green");
%A(41,42); R(41,42,"green");
%A(40,39); R(40,39,"green");
%A(53,47); R(53,47,"green");
%A(52,48); R(52,48,"green");
%A(50,49); R(50,49,"green");
%RA(40,44,"blue"); RA(42,53,"blue"); RA(45,47,"blue"); RA(46,53,"blue"); RA(50,51,"blue"); RA(50,52,"blue"); RA(51,46,"blue"); RA(52,44,"blue"); Z(53); Z(52); Z(51,46); N(52,47,46); RA(42,52); RA(45,52); N(53,50,44); A(51,46); A(48,53); A(40,53);
%</Rechenweg>
%</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 {
1/1.92/5.91,
2/1.14/5.29,
3/2.067/4.918,
4/1.28/4.30,
5/0.35/4.67,
6/2.132/4.930,
7/2.87/5.60,
8/3.08/4.62,
9/3.83/5.29,
10/4.04/4.32,
11/4.78/4.99,
12/4.38/4.07,
13/5.37/4.18,
14/4.97/3.27,
15/5.97/3.38,
16/5.01/3.09,
17/5.74/2.41,
18/4.78/2.12,
19/5.51/1.43,
20/4.54/1.68,
21/4.81/0.72,
22/3.84/0.96,
23/4.11/0.00,
24/3.62/0.87,
25/3.11/0.01,
26/2.62/0.88,
27/2.11/0.02,
28/1.622/0.888,
29/1.11/0.03,
30/1.555/0.924,
31/0.56/0.86,
32/1.00/1.75,
33/0.00/1.69,
34/0.92/2.08,
35/0.12/2.68,
36/1.04/3.07,
37/0.24/3.67,
38/1.15/4.07,
39/2.00/1.82,
40/1.65/2.76,
41/2.61/1.03,
42/3.25/1.80,
43/2.21/3.93,
44/2.27/1.97,
45/3.57/1.92,
46/3.98/3.15,
47/4.05/2.80,
48/1.57/3.16,
49/3.03/4.50,
50/2.40/3.73,
51/3.38/3.56,
52/3.05/2.78,
53/2.80/2.82}
\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 {
29/359.50/483.86/0.4/Blue,
33/303.86/443.23/0.4/Green,
5/263.23/338.37/0.4/Orange,
1/218.37/342.15/0.4/Violet,
11/162.15/306.48/0.4/Teal,
10/102.15/229.11/0.4/Lime,
6/42.15/334.47/0.4/LightBlue,
38/203.23/294.78/0.4/LightCoral,
24/239.50/471.62/0.4/LightCyan,
28/299.50/368.38/0.4/LightGoldenrodYellow,
34/143.23/402.80/0.4/LightGreen,
45/285.76/490.68/0.4/LightGray,
40/222.80/360.76/0.4/LightPink,
48/114.78/394.75/0.4/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 {
1/2, 1/3,
2/5, 2/4,
3/2, 3/4,
4/5,
5/37, 5/38,
6/7, 6/1,
7/1,
8/7, 8/6,
9/7, 9/8,
10/9, 10/8,
11/9, 11/10,
12/13, 12/11,
13/11,
14/13, 14/12,
15/13, 15/14,
16/17, 16/15,
17/15, 17/19,
18/19, 18/17, 18/16,
20/21, 20/19,
21/23, 21/19,
22/23, 22/21, 22/20,
24/25, 24/23,
25/23,
26/25, 26/24,
27/25, 27/26,
28/27, 28/26,
29/27, 29/28,
30/31, 30/29,
31/29,
32/31, 32/30,
33/31, 33/32,
34/35, 34/33,
35/33,
36/35, 36/34,
37/35, 37/36,
38/37, 38/36,
39/32, 39/30,
40/34, 40/39, 40/44, 40/53,
41/28, 41/39, 41/42,
42/24, 42/52,
43/3, 43/4,
44/41, 44/42,
45/22, 45/20, 45/47, 45/52,
46/14, 46/12,
47/18, 47/16,
48/38, 48/43, 48/53,
49/6, 49/43, 49/51,
50/48, 50/49, 50/51,
51/10, 51/46,
52/47, 52/46,
53/50, 53/44}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,53}
\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);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-40) -- (p-53);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-48) -- (p-53);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-51) -- (p-46);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
29/359.50/483.86/0.4/Blue,
33/303.86/443.23/0.4/Green,
5/263.23/338.37/0.4/Orange,
1/218.37/342.15/0.4/Violet,
11/162.15/306.48/0.4/Teal,
10/102.15/229.11/0.4/Lime,
6/42.15/334.47/0.4/LightBlue,
38/203.23/294.78/0.4/LightCoral,
24/239.50/471.62/0.4/LightCyan,
28/299.50/368.38/0.4/LightGoldenrodYellow,
34/143.23/402.80/0.4/LightGreen,
45/285.76/490.68/0.4/LightGray,
40/222.80/360.76/0.4/LightPink,
48/114.78/394.75/0.4/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 {
1/68,
2/68,
3/8,
4/308,
5/113,
6/252,
7/72,
8/252,
9/72,
10/252,
11/12,
12/96,
13/36,
14/336,
15/336,
16/107,
17/47,
18/287,
19/287,
20/136,
21/316,
22/136,
23/256,
24/30,
25/270,
26/150,
27/270,
28/90,
29/274,
30/334,
31/154,
32/34,
33/154,
34/293,
35/233,
36/353,
37/173,
38/353,
39/34,
40/79,
41/260,
42/20,
43/308,
44/140,
45/271,
46/216,
47/31,
48/265,
49/80,
50/200,
51/320,
52/151,
53/178}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/caab81ec627a12328aa3e684bb1e9cb4.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>#2046 mit nur 3 nicht passenden Kanten</Bildtext>
%<Ausrichten von=\"27\" nach=\"25\"/>
%<Winkel size=\"18\" color=\"blue\" id=\"blauerWinkel\" value=\"124.35426112574547\"/>
%<Winkel size=\"18\" color=\"green\" id=\"gruenerWinkel\" value=\"139.3780917083093\"/>
%<Winkel size=\"18\" color=\"orange\" id=\"orangerWinkel\" value=\"75.1377828746346\"/>
%<Winkel size=\"18\" color=\"violet\" id=\"vierterWinkel\" value=\"123.77830302258792\"/>
%<Winkel size=\"18\" color=\"teal\" id=\"fuenfterWinkel\" value=\"144.331517535816\"/>
%<Winkel size=\"18\" color=\"lime\" id=\"sechsterWinkel\" value=\"126.95810758120652\"/>
%<Winkel size=\"18\" color=\"LightBlue\" id=\"siebenterWinkel\" value=\"292.3161446383474\"/>
%<Winkel size=\"18\" color=\"LightCoral\" id=\"achterWinkel\" value=\"91.54962695475666\"/>
%<Winkel size=\"18\" color=\"LightCyan\" id=\"neunterWinkel\" value=\"232.11840160729716\"/>
%<Winkel size=\"18\" color=\"LightGoldenrodYellow\" id=\"zehnterWinkel\" value=\"68.87414739830785\"/>
%<Winkel size=\"18\" color=\"LightGreen\" id=\"elfterWinkel\" value=\"259.5636510706451\"/>
%<Winkel size=\"18\" color=\"LightGray\" id=\"zwoelfterWinkel\" value=\"194.78224973087902\"/>
%<Winkel size=\"18\" color=\"LightPink\" id=\"dreizehnterWinkel\" value=\"131.62940423506836\"/>
%<Winkel size=\"18\" color=\"LightSalmon\" id=\"vierzehnterWinkel\" value=\"279.969785308762\"/>
%<Feinjustieren Anzahl=\"12,14\"/>
%<Rechenweg>P[23]=[277.49906148857485,-124.97112069855191]; P[25]=[191.77855418836458,-124.22686989907095]; D=ab(23,25); A(25,23); L(24,25,23); L(26,25,24); L(27,25,26); L(28,27,26); L(29,27,28); M(31,29,27,blauerWinkel); L(30,31,29); L(32,31,30); L(33,31,32); M(35,33,31,gruenerWinkel); L(34,35,33); L(36,35,34); L(37,35,36); L(38,37,36); L(5,37,38); M(4,5,37,orangerWinkel); L(2,5,4); L(3,2,4); L(1,2,3); M(7,1,2,vierterWinkel); L(6,7,1); L(8,7,6); L(9,7,8); L(10,9,8); L(11,9,10); M(13,11,9,fuenfterWinkel); L(12,13,11); L(14,13,12); L(15,13,14); Q(19,15,23,2*D,2*D); A(19,23); H(21,23,19,2); A(21,23); L(22,23,21); A(19,15); H(17,15,19,2); A(17,15); L(16,17,15); A(17,19); L(18,19,17); A(18,16); A(21,19); L(20,21,19); A(22,20); L(39,32,30); L(43,3,4); L(45,22,20); L(46,14,12); L(47,18,16); M(51,10,9,sechsterWinkel); M(49,6,7,siebenterWinkel); M(48,38,37,achterWinkel); M(42,24,25,neunterWinkel); M(41,28,27,zehnterWinkel); M(40,34,35,elfterWinkel); L(44,41,42); M(53,45,22,zwoelfterWinkel); M(52,40,34,dreizehnterWinkel); M(50,48,38,vierzehnterWinkel);
%A(49,43); R(49,43,\"green\");
%A(49,51); R(49,51,\"green\");
%A(48,43); R(48,43,\"green\");
%A(41,39); R(41,39,\"green\");
%A(41,42); R(41,42,\"green\");
%A(40,39); R(40,39,\"green\");
%A(53,47); R(53,47,\"green\");
%A(52,48); R(52,48,\"green\");
%A(50,49); R(50,49,\"green\");
%RA(40,44,\"blue\"); RA(42,53,\"blue\"); RA(45,47,\"blue\"); RA(46,53,\"blue\"); RA(50,51,\"blue\"); RA(50,52,\"blue\"); RA(51,46,\"blue\"); RA(52,44,\"blue\"); Z(53); Z(52); Z(51,46); N(52,47,46); RA(42,52); RA(45,52); N(53,50,44); A(51,46); A(48,53); A(40,53);
%</Rechenweg>
%</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 {
1/1.92/5.91,
2/1.14/5.29,
3/2.067/4.918,
4/1.28/4.30,
5/0.35/4.67,
6/2.132/4.930,
7/2.87/5.60,
8/3.08/4.62,
9/3.83/5.29,
10/4.04/4.32,
11/4.78/4.99,
12/4.38/4.07,
13/5.37/4.18,
14/4.97/3.27,
15/5.97/3.38,
16/5.01/3.09,
17/5.74/2.41,
18/4.78/2.12,
19/5.51/1.43,
20/4.54/1.68,
21/4.81/0.72,
22/3.84/0.96,
23/4.11/0.00,
24/3.62/0.87,
25/3.11/0.01,
26/2.62/0.88,
27/2.11/0.02,
28/1.622/0.888,
29/1.11/0.03,
30/1.555/0.924,
31/0.56/0.86,
32/1.00/1.75,
33/0.00/1.69,
34/0.92/2.08,
35/0.12/2.68,
36/1.04/3.07,
37/0.24/3.67,
38/1.15/4.07,
39/2.00/1.82,
40/1.65/2.76,
41/2.61/1.03,
42/3.25/1.80,
43/2.21/3.93,
44/2.27/1.97,
45/3.57/1.92,
46/3.98/3.15,
47/4.05/2.80,
48/1.57/3.16,
49/3.03/4.50,
50/2.40/3.73,
51/3.38/3.56,
52/3.05/2.78,
53/2.80/2.82}
\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 {
29/359.50/483.86/0.4/Blue,
33/303.86/443.23/0.4/Green,
5/263.23/338.37/0.4/Orange,
1/218.37/342.15/0.4/Violet,
11/162.15/306.48/0.4/Teal,
10/102.15/229.11/0.4/Lime,
6/42.15/334.47/0.4/LightBlue,
38/203.23/294.78/0.4/LightCoral,
24/239.50/471.62/0.4/LightCyan,
28/299.50/368.38/0.4/LightGoldenrodYellow,
34/143.23/402.80/0.4/LightGreen,
45/285.76/490.68/0.4/LightGray,
40/222.80/360.76/0.4/LightPink,
48/114.78/394.75/0.4/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 {
1/2, 1/3,
2/5, 2/4,
3/2, 3/4,
4/5,
5/37, 5/38,
6/7, 6/1,
7/1,
8/7, 8/6,
9/7, 9/8,
10/9, 10/8,
11/9, 11/10,
12/13, 12/11,
13/11,
14/13, 14/12,
15/13, 15/14,
16/17, 16/15,
17/15, 17/19,
18/19, 18/17, 18/16,
20/21, 20/19,
21/23, 21/19,
22/23, 22/21, 22/20,
24/25, 24/23,
25/23,
26/25, 26/24,
27/25, 27/26,
28/27, 28/26,
29/27, 29/28,
30/31, 30/29,
31/29,
32/31, 32/30,
33/31, 33/32,
34/35, 34/33,
35/33,
36/35, 36/34,
37/35, 37/36,
38/37, 38/36,
39/32, 39/30,
40/34, 40/39, 40/44, 40/53,
41/28, 41/39, 41/42,
42/24, 42/52,
43/3, 43/4,
44/41, 44/42,
45/22, 45/20, 45/47, 45/52,
46/14, 46/12,
47/18, 47/16,
48/38, 48/43, 48/53,
49/6, 49/43, 49/51,
50/48, 50/49, 50/51,
51/10, 51/46,
52/47, 52/46,
53/50, 53/44}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,53}
\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);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-40) -- (p-53);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-48) -- (p-53);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-51) -- (p-46);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
29/359.50/483.86/0.4/Blue,
33/303.86/443.23/0.4/Green,
5/263.23/338.37/0.4/Orange,
1/218.37/342.15/0.4/Violet,
11/162.15/306.48/0.4/Teal,
10/102.15/229.11/0.4/Lime,
6/42.15/334.47/0.4/LightBlue,
38/203.23/294.78/0.4/LightCoral,
24/239.50/471.62/0.4/LightCyan,
28/299.50/368.38/0.4/LightGoldenrodYellow,
34/143.23/402.80/0.4/LightGreen,
45/285.76/490.68/0.4/LightGray,
40/222.80/360.76/0.4/LightPink,
48/114.78/394.75/0.4/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 {
1/68,
2/68,
3/8,
4/308,
5/113,
6/252,
7/72,
8/252,
9/72,
10/252,
11/12,
12/96,
13/36,
14/336,
15/336,
16/107,
17/47,
18/287,
19/287,
20/136,
21/316,
22/136,
23/256,
24/30,
25/270,
26/150,
27/270,
28/90,
29/274,
30/334,
31/154,
32/34,
33/154,
34/293,
35/233,
36/353,
37/173,
38/353,
39/34,
40/79,
41/260,
42/20,
43/308,
44/140,
45/271,
46/216,
47/31,
48/265,
49/80,
50/200,
51/320,
52/151,
53/178}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>[26,67,100,110]</Bildtext>
%<Ausrichten von="27" nach="25"/>
%<Winkel size="18" color="blue" id="blauerWinkel" value="124.15871460997224"/>
%<Winkel size="18" color="green" id="gruenerWinkel" value="137.7497907719929"/>
%<Winkel size="18" color="orange" id="orangerWinkel" value="76.57571481907588"/>
%<Winkel size="18" color="violet" id="vierterWinkel" value="121.51907378772847"/>
%<Winkel size="18" color="teal" id="fuenfterWinkel" value="150.02614989113974"/>
%<Winkel size="18" color="lime" id="sechsterWinkel" value="122.13710861241822"/>
%<Winkel size="18" color="LightBlue" id="siebenterWinkel" value="297.81146954112745"/>
%<Winkel size="18" color="LightCoral" id="achterWinkel" value="94.57423951208949"/>
%<Winkel size="18" color="LightCyan" id="neunterWinkel" value="232.4270373750075"/>
%<Winkel size="18" color="LightGoldenrodYellow" id="zehnterWinkel" value="68.46955771374815"/>
%<Winkel size="18" color="LightGreen" id="elfterWinkel" value="262.9638976232083"/>
%<Winkel size="18" color="LightGray" id="zwoelfterWinkel" value="163.39634317893064"/>
%<Feinjustieren Anzahl="12,12"/>
%<Rechenweg>
%P[23]=[277.49906148857485,-124.97112069855191]; P[25]=[191.77855418836458,-124.22686989907095]; D=ab(23,25); A(25,23); L(24,25,23); L(26,25,24); L(27,25,26); L(28,27,26); L(29,27,28); M(31,29,27,blauerWinkel); L(30,31,29); L(32,31,30); L(33,31,32); M(35,33,31,gruenerWinkel); L(34,35,33); L(36,35,34); L(37,35,36); L(38,37,36); L(5,37,38); M(4,5,37,orangerWinkel); L(2,5,4); L(3,2,4); L(1,2,3); M(7,1,2,vierterWinkel); L(6,7,1); L(8,7,6); L(9,7,8); L(10,9,8); L(11,9,10); M(13,11,9,fuenfterWinkel); L(12,13,11); L(14,13,12); L(15,13,14); Q(19,15,23,2*D,2*D); A(19,23); H(21,23,19,2); A(21,23); L(22,23,21); A(19,15); H(17,15,19,2); A(17,15); L(16,17,15); A(17,19); L(18,19,17); A(18,16); A(21,19); L(20,21,19); A(22,20); L(39,32,30); L(43,3,4); L(45,22,20); L(46,14,12); L(47,18,16); M(51,10,9,sechsterWinkel); M(49,6,7,siebenterWinkel); M(48,38,37,achterWinkel); M(42,24,25,neunterWinkel); M(41,28,27,zehnterWinkel); M(40,34,35,elfterWinkel); L(44,41,42); L(50,51,49); L(53,50,48); M(52,42,24,zwoelfterWinkel);
%A(47,45); R(47,45,"green");
%A(51,46); R(51,46,"green");
%A(49,51); R(49,51,"green");
%A(41,39); R(41,39,"green");
%A(41,42); R(41,42,"green");
%A(40,39); R(40,39,"green");
%A(44,40); R(44,40,"green");
%A(50,48); R(50,48,"green");
%A(53,40); R(53,40,"green");
%A(53,44); R(53,44,"green");
%A(52,46); R(52,46,"green");
%A(48,43); R(48,43,"brown");
%A(49,43); R(49,43,"grey");
%A(52,45); R(52,45,"grey");
%A(52,47); R(52,47,"grey");
%</Rechenweg>
%</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{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 {
1/2.02/5.89,
2/1.24/5.27,
3/2.163/4.898,
4/1.38/4.28,
5/0.45/4.66,
6/2.189/4.902,
7/2.96/5.54,
8/3.126/4.552,
9/3.90/5.19,
10/4.06/4.20,
11/4.83/4.84,
12/4.48/3.90,
13/5.47/4.07,
14/5.121/3.130,
15/6.11/3.30,
16/5.138/3.049,
17/5.84/2.33,
18/4.87/2.09,
19/5.57/1.37,
20/4.61/1.66,
21/4.84/0.68,
22/3.88/0.97,
23/4.11/0.00,
24/3.62/0.87,
25/3.11/0.01,
26/2.62/0.88,
27/2.11/0.02,
28/1.616/0.888,
29/1.11/0.03,
30/1.552/0.922,
31/0.55/0.86,
32/1.00/1.75,
33/0.00/1.69,
34/0.93/2.06,
35/0.15/2.68,
36/1.08/3.04,
37/0.30/3.67,
38/1.23/4.03,
39/2.00/1.82,
40/1.65/2.76,
41/2.61/1.03,
42/3.24/1.80,
43/2.302/3.907,
44/2.26/1.96,
45/3.65/1.95,
46/4.14/2.96,
47/4.17/2.80,
48/1.67/3.13,
49/3.112/4.516,
50/2.366/3.850,
51/3.32/3.54,
52/3.15/2.79,
53/2.64/2.89}
\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 {
29/359.50/483.66/0.4/Blue,
33/303.66/441.41/0.4/Green,
5/261.41/337.99/0.4/Orange,
1/217.99/339.51/0.4/Violet,
11/159.51/309.53/0.4/Teal,
10/99.51/221.64/0.4/Lime,
6/39.51/337.32/0.4/LightBlue,
38/201.41/295.99/0.4/LightCoral,
24/239.50/471.93/0.4/LightCyan,
28/299.50/367.97/0.4/LightGoldenrodYellow,
34/141.41/404.37/0.4/LightGreen,
42/291.93/455.33/0.4/LightGray}
\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, 2/4,
3/2, 3/4,
4/5,
5/37, 5/38,
6/7, 6/1,
7/1,
8/7, 8/6,
9/7, 9/8,
10/9, 10/8,
11/9, 11/10,
12/13, 12/11,
13/11,
14/13, 14/12,
15/13, 15/14,
16/17, 16/15,
17/15, 17/19,
18/19, 18/17, 18/16,
20/21, 20/19,
21/23, 21/19,
22/23, 22/21, 22/20,
24/25, 24/23,
25/23,
26/25, 26/24,
27/25, 27/26,
28/27, 28/26,
29/27, 29/28,
30/31, 30/29,
31/29,
32/31, 32/30,
33/31, 33/32,
34/35, 34/33,
35/33,
36/35, 36/34,
37/35, 37/36,
38/37, 38/36,
39/32, 39/30,
40/34, 40/39,
41/28, 41/39, 41/42,
42/24,
43/3, 43/4,
44/41, 44/42, 44/40,
45/22, 45/20,
46/14, 46/12,
47/18, 47/16, 47/45,
48/38, 48/43,
49/6, 49/51, 49/43,
50/51, 50/49, 50/48,
51/10, 51/46,
52/42, 52/46, 52/45, 52/47,
53/50, 53/48, 53/40, 53/44}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,53}
\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);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-49) -- (p-43);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-52) -- (p-45);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-52) -- (p-47);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
29/359.50/483.66/0.4/Blue,
33/303.66/441.41/0.4/Green,
5/261.41/337.99/0.4/Orange,
1/217.99/339.51/0.4/Violet,
11/159.51/309.53/0.4/Teal,
10/99.51/221.64/0.4/Lime,
6/39.51/337.32/0.4/LightBlue,
38/201.41/295.99/0.4/LightCoral,
24/239.50/471.93/0.4/LightCyan,
28/299.50/367.97/0.4/LightGoldenrodYellow,
34/141.41/404.37/0.4/LightGreen,
42/291.93/455.33/0.4/LightGray}
{
\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 {
1/130,
2/128,
3/68,
4/188,
5/111,
6/190,
7/10,
8/250,
9/10,
10/310,
11/10,
12/220,
13/40,
14/220,
15/44,
16/44,
17/344,
18/224,
19/284,
20/73,
21/253,
22/193,
23/330,
24/30,
25/270,
26/150,
27/270,
28/90,
29/274,
30/334,
31/274,
32/94,
33/154,
34/291,
35/111,
36/51,
37/111,
38/51,
39/34,
40/158,
41/260,
42/20,
43/308,
44/278,
45/133,
46/220,
47/164,
48/196,
49/72,
50/76,
51/312,
52/151,
53/38}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/7b8ca7d186f522adbc599e13fa4c9fd1.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>[26,67,100,110]</Bildtext>
%<Ausrichten von=\"27\" nach=\"25\"/>
%<Winkel size=\"18\" color=\"blue\" id=\"blauerWinkel\" value=\"124.15871460997224\"/>
%<Winkel size=\"18\" color=\"green\" id=\"gruenerWinkel\" value=\"137.7497907719929\"/>
%<Winkel size=\"18\" color=\"orange\" id=\"orangerWinkel\" value=\"76.57571481907588\"/>
%<Winkel size=\"18\" color=\"violet\" id=\"vierterWinkel\" value=\"121.51907378772847\"/>
%<Winkel size=\"18\" color=\"teal\" id=\"fuenfterWinkel\" value=\"150.02614989113974\"/>
%<Winkel size=\"18\" color=\"lime\" id=\"sechsterWinkel\" value=\"122.13710861241822\"/>
%<Winkel size=\"18\" color=\"LightBlue\" id=\"siebenterWinkel\" value=\"297.81146954112745\"/>
%<Winkel size=\"18\" color=\"LightCoral\" id=\"achterWinkel\" value=\"94.57423951208949\"/>
%<Winkel size=\"18\" color=\"LightCyan\" id=\"neunterWinkel\" value=\"232.4270373750075\"/>
%<Winkel size=\"18\" color=\"LightGoldenrodYellow\" id=\"zehnterWinkel\" value=\"68.46955771374815\"/>
%<Winkel size=\"18\" color=\"LightGreen\" id=\"elfterWinkel\" value=\"262.9638976232083\"/>
%<Winkel size=\"18\" color=\"LightGray\" id=\"zwoelfterWinkel\" value=\"163.39634317893064\"/>
%<Feinjustieren Anzahl=\"12,12\"/>
%<Rechenweg>
%P[23]=[277.49906148857485,-124.97112069855191]; P[25]=[191.77855418836458,-124.22686989907095]; D=ab(23,25); A(25,23); L(24,25,23); L(26,25,24); L(27,25,26); L(28,27,26); L(29,27,28); M(31,29,27,blauerWinkel); L(30,31,29); L(32,31,30); L(33,31,32); M(35,33,31,gruenerWinkel); L(34,35,33); L(36,35,34); L(37,35,36); L(38,37,36); L(5,37,38); M(4,5,37,orangerWinkel); L(2,5,4); L(3,2,4); L(1,2,3); M(7,1,2,vierterWinkel); L(6,7,1); L(8,7,6); L(9,7,8); L(10,9,8); L(11,9,10); M(13,11,9,fuenfterWinkel); L(12,13,11); L(14,13,12); L(15,13,14); Q(19,15,23,2*D,2*D); A(19,23); H(21,23,19,2); A(21,23); L(22,23,21); A(19,15); H(17,15,19,2); A(17,15); L(16,17,15); A(17,19); L(18,19,17); A(18,16); A(21,19); L(20,21,19); A(22,20); L(39,32,30); L(43,3,4); L(45,22,20); L(46,14,12); L(47,18,16); M(51,10,9,sechsterWinkel); M(49,6,7,siebenterWinkel); M(48,38,37,achterWinkel); M(42,24,25,neunterWinkel); M(41,28,27,zehnterWinkel); M(40,34,35,elfterWinkel); L(44,41,42); L(50,51,49); L(53,50,48); M(52,42,24,zwoelfterWinkel);
%A(47,45); R(47,45,\"green\");
%A(51,46); R(51,46,\"green\");
%A(49,51); R(49,51,\"green\");
%A(41,39); R(41,39,\"green\");
%A(41,42); R(41,42,\"green\");
%A(40,39); R(40,39,\"green\");
%A(44,40); R(44,40,\"green\");
%A(50,48); R(50,48,\"green\");
%A(53,40); R(53,40,\"green\");
%A(53,44); R(53,44,\"green\");
%A(52,46); R(52,46,\"green\");
%A(48,43); R(48,43,\"brown\");
%A(49,43); R(49,43,\"grey\");
%A(52,45); R(52,45,\"grey\");
%A(52,47); R(52,47,\"grey\");
%</Rechenweg>
%</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{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 {
1/2.02/5.89,
2/1.24/5.27,
3/2.163/4.898,
4/1.38/4.28,
5/0.45/4.66,
6/2.189/4.902,
7/2.96/5.54,
8/3.126/4.552,
9/3.90/5.19,
10/4.06/4.20,
11/4.83/4.84,
12/4.48/3.90,
13/5.47/4.07,
14/5.121/3.130,
15/6.11/3.30,
16/5.138/3.049,
17/5.84/2.33,
18/4.87/2.09,
19/5.57/1.37,
20/4.61/1.66,
21/4.84/0.68,
22/3.88/0.97,
23/4.11/0.00,
24/3.62/0.87,
25/3.11/0.01,
26/2.62/0.88,
27/2.11/0.02,
28/1.616/0.888,
29/1.11/0.03,
30/1.552/0.922,
31/0.55/0.86,
32/1.00/1.75,
33/0.00/1.69,
34/0.93/2.06,
35/0.15/2.68,
36/1.08/3.04,
37/0.30/3.67,
38/1.23/4.03,
39/2.00/1.82,
40/1.65/2.76,
41/2.61/1.03,
42/3.24/1.80,
43/2.302/3.907,
44/2.26/1.96,
45/3.65/1.95,
46/4.14/2.96,
47/4.17/2.80,
48/1.67/3.13,
49/3.112/4.516,
50/2.366/3.850,
51/3.32/3.54,
52/3.15/2.79,
53/2.64/2.89}
\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 {
29/359.50/483.66/0.4/Blue,
33/303.66/441.41/0.4/Green,
5/261.41/337.99/0.4/Orange,
1/217.99/339.51/0.4/Violet,
11/159.51/309.53/0.4/Teal,
10/99.51/221.64/0.4/Lime,
6/39.51/337.32/0.4/LightBlue,
38/201.41/295.99/0.4/LightCoral,
24/239.50/471.93/0.4/LightCyan,
28/299.50/367.97/0.4/LightGoldenrodYellow,
34/141.41/404.37/0.4/LightGreen,
42/291.93/455.33/0.4/LightGray}
\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, 2/4,
3/2, 3/4,
4/5,
5/37, 5/38,
6/7, 6/1,
7/1,
8/7, 8/6,
9/7, 9/8,
10/9, 10/8,
11/9, 11/10,
12/13, 12/11,
13/11,
14/13, 14/12,
15/13, 15/14,
16/17, 16/15,
17/15, 17/19,
18/19, 18/17, 18/16,
20/21, 20/19,
21/23, 21/19,
22/23, 22/21, 22/20,
24/25, 24/23,
25/23,
26/25, 26/24,
27/25, 27/26,
28/27, 28/26,
29/27, 29/28,
30/31, 30/29,
31/29,
32/31, 32/30,
33/31, 33/32,
34/35, 34/33,
35/33,
36/35, 36/34,
37/35, 37/36,
38/37, 38/36,
39/32, 39/30,
40/34, 40/39,
41/28, 41/39, 41/42,
42/24,
43/3, 43/4,
44/41, 44/42, 44/40,
45/22, 45/20,
46/14, 46/12,
47/18, 47/16, 47/45,
48/38, 48/43,
49/6, 49/51, 49/43,
50/51, 50/49, 50/48,
51/10, 51/46,
52/42, 52/46, 52/45, 52/47,
53/50, 53/48, 53/40, 53/44}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,53}
\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);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-49) -- (p-43);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-52) -- (p-45);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-52) -- (p-47);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
29/359.50/483.66/0.4/Blue,
33/303.66/441.41/0.4/Green,
5/261.41/337.99/0.4/Orange,
1/217.99/339.51/0.4/Violet,
11/159.51/309.53/0.4/Teal,
10/99.51/221.64/0.4/Lime,
6/39.51/337.32/0.4/LightBlue,
38/201.41/295.99/0.4/LightCoral,
24/239.50/471.93/0.4/LightCyan,
28/299.50/367.97/0.4/LightGoldenrodYellow,
34/141.41/404.37/0.4/LightGreen,
42/291.93/455.33/0.4/LightGray}
{
\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 {
1/130,
2/128,
3/68,
4/188,
5/111,
6/190,
7/10,
8/250,
9/10,
10/310,
11/10,
12/220,
13/40,
14/220,
15/44,
16/44,
17/344,
18/224,
19/284,
20/73,
21/253,
22/193,
23/330,
24/30,
25/270,
26/150,
27/270,
28/90,
29/274,
30/334,
31/274,
32/94,
33/154,
34/291,
35/111,
36/51,
37/111,
38/51,
39/34,
40/158,
41/260,
42/20,
43/308,
44/278,
45/133,
46/220,
47/164,
48/196,
49/72,
50/76,
51/312,
52/151,
53/38}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>[21]</Bildtext>
%<Ausrichten von="27" nach="25"/>
%<Winkel size="18" color="blue" id="blauerWinkel" value="130.75313159021968"/>
%<Winkel size="18" color="green" id="gruenerWinkel" value="130.82544101311456"/>
%<Winkel size="18" color="orange" id="orangerWinkel" value="74.73786277076553"/>
%<Winkel size="18" color="violet" id="vierterWinkel" value="135.88810050470713"/>
%<Winkel size="18" color="teal" id="fuenfterWinkel" value="120.80793343341226"/>
%<Winkel size="18" color="lime" id="sechsterWinkel" value="146.06343282760773"/>
%<Winkel size="18" color="LightBlue" id="siebenterWinkel" value="82.29211582561682"/>
%<Winkel size="18" color="LightCoral" id="achterWinkel" value="277.55514194184656"/>
%<Feinjustieren Anzahl="8,8"/>
%<Rechenweg>
%P[23]=[321.77586716807025,-122.4995025376255]; P[25]=[234.40736183467087,-122.4995025376254]; D=ab(23,25); A(25,23); L(24,25,23); L(26,25,24); L(27,25,26); L(28,27,26); L(29,27,28); M(31,29,27,blauerWinkel); L(30,31,29); L(32,31,30); L(33,31,32); M(35,33,31,gruenerWinkel); L(34,35,33); L(36,35,34); L(37,35,36); L(38,37,36); L(5,37,38); M(4,5,37,orangerWinkel); L(2,5,4); L(3,2,4); L(1,2,3); M(7,1,2,vierterWinkel); L(6,7,1); L(8,7,6); L(9,7,8); L(10,9,8); L(11,9,10); M(13,11,9,fuenfterWinkel); L(12,13,11); L(14,13,12); L(15,13,14); Q(19,15,23,2*D,2*D); A(19,23); H(21,23,19,2); A(21,23); L(22,23,21); A(19,15); H(17,15,19,2); A(17,15); L(16,17,15); A(17,19); L(18,19,17); A(18,16); A(21,19); L(20,21,19); A(22,20); L(39,32,30); N(42,24,22); N(43,4,38); N(45,20,18); N(48,6,3); N(50,12,10); M(46,14,13,sechsterWinkel); M(41,28,27,siebenterWinkel); M(40,34,35,achterWinkel); N(44,40,41); N(47,44,42); N(49,43,44);
%A(41,39); R(41,39,"green");
%A(41,42); R(41,42,"green");
%A(40,39); R(40,39,"green");
%A(40,43); R(40,43,"green");
%A(47,46); R(47,46,"green");
%A(47,45); R(47,45,"green");
%A(49,48); R(49,48,"green");
%A(45,46); R(45,46,"brown");
%A(46,16); R(46,16,"grey");
%A(48,50); R(48,50,"grey");
%A(49,50); R(49,50,"grey");
%</Rechenweg>
%</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{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 {
1/2.05087581370431060179/5.66720017904189354851,
2/1.24511738441517860743/5.07495584295288448828,
3/2.16089523936027516626/4.67327074191955293969,
4/1.35513681007114361599/4.08102640583054387946,
5/0.43935895512604661306/4.48271150686387542805,
6/2.42878989682759893753/4.74135950928435612184,
7/3.04163439513278044402/5.53156304059579628785,
8/3.41954847825606966794/4.60572237083825974935,
9/4.03239297656125028624/5.39592590214969991536,
10/4.41030705968453951016/4.47008523239216337686,
11/5.02315155798972146073/5.26028876370360443104,
12/4.42151035657644264631/4.46152229923355125862,
13/5.41408300720522728255/4.33986896708128888633,
14/4.81244180579194935632/3.54110250261123615800,
15/5.80501445642073399256/3.41944917045897378571,
16/4.91676351460175542485/2.96009063471842903681,
17/5.75870514690777923761/2.42052202203801236635,
18/4.87045420508880066990/1.96116348629746739540,
19/5.71239583739482359448/1.42159487361705116903,
20/4.74512881951698783922/1.67535561945004540796,
21/5.00899907608124639324/0.71079743680852558452,
22/4.04173205820341063799/0.96455818264151982344,
23/4.30560231476766919201/0.00000000000000000000,
24/3.80560231476767052428/0.86602540378443915170,
25/3.30560231476766919201/0.00000000000000113858,
26/2.80560231476767096837/0.86602540378444048397,
27/2.30560231476766919201/0.00000000000000276512,
28/1.80560231476767096837/0.86602540378444226032,
29/1.30560231476766941405/0.00000000000000439166,
30/1.63524135887969834791/0.94410703873920764906,
31/0.65280115738383459600/0.75752930564984244377,
32/0.98244020149586386292/1.70163634438904587398,
33/0.00000000000000000000/1.51505861129968066869,
34/0.92991409157868787361/1.88283542172059825681,
35/0.14645298504201562095/2.50427624315441210712,
36/1.07636707662070341129/2.87205305357532969524,
37/0.29290597008403107537/3.49349387500914332350,
38/1.22282006166271894898/3.86127068543006179979,
39/1.96488040299172750380/1.88821407747841085722,
40/1.44295034378190778490/2.74120236186057963934,
41/2.73086423938344768914/1.24535424642142000806,
42/3.54173205820341152616/1.83058358642595919719,
43/2.13859791660781572986/3.45958558439673069529,
44/2.20893418017362686001/2.09834253080358745791,
45/3.90318718721096358237/2.21492423213046008001,
46/3.86735535362073701293/3.21428206579243758156,
47/3.01980199899359336158/2.68357187080812797930,
48/2.53880932248356305792/3.74743007216201595710,
49/2.90458175299953413884/2.81672575333973762568,
50/3.80866585827123227403/3.67131876792213329708}
\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 {
29/360.00/490.75/0.4/Blue,
33/310.75/441.58/0.4/Green,
5/261.58/336.32/0.4/Orange,
1/216.32/352.20/0.4/Violet,
11/172.20/293.01/0.4/Teal,
14/53.01/199.08/0.4/Lime,
28/300.00/382.29/0.4/LightBlue,
34/141.58/419.13/0.4/LightCoral}
\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, 2/4,
3/2, 3/4,
4/5,
5/37, 5/38,
6/7, 6/1,
7/1,
8/7, 8/6,
9/7, 9/8,
10/9, 10/8,
11/9, 11/10,
12/13, 12/11,
13/11,
14/13, 14/12,
15/13, 15/14,
16/17, 16/15,
17/15, 17/19,
18/19, 18/17, 18/16,
20/21, 20/19,
21/23, 21/19,
22/23, 22/21, 22/20,
24/25, 24/23,
25/23,
26/25, 26/24,
27/25, 27/26,
28/27, 28/26,
29/27, 29/28,
30/31, 30/29,
31/29,
32/31, 32/30,
33/31, 33/32,
34/35, 34/33,
35/33,
36/35, 36/34,
37/35, 37/36,
38/37, 38/36,
39/32, 39/30,
40/34, 40/39, 40/43,
41/28, 41/39, 41/42,
42/24, 42/22,
43/4, 43/38,
44/40, 44/41,
45/20, 45/18, 45/46,
46/14, 46/16,
47/44, 47/42, 47/46, 47/45,
48/6, 48/3, 48/50,
49/43, 49/44, 49/48, 49/50,
50/12, 50/10}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,50}
\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);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-46) -- (p-16);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-48) -- (p-50);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-49) -- (p-50);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
29/360.00/490.75/0.4/Blue,
33/310.75/441.58/0.4/Green,
5/261.58/336.32/0.4/Orange,
1/216.32/352.20/0.4/Violet,
11/172.20/293.01/0.4/Teal,
14/53.01/199.08/0.4/Lime,
28/300.00/382.29/0.4/LightBlue,
34/141.58/419.13/0.4/LightCoral}
{
\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 {
1/66,
2/126,
3/306,
4/306,
5/186,
6/262,
7/142,
8/262,
9/82,
10/322,
11/22,
12/203,
13/83,
14/203,
15/57,
16/117,
17/357,
18/177,
19/15,
20/135,
21/15,
22/195,
23/330,
24/90,
25/270,
26/30,
27/210,
28/150,
29/210,
30/41,
31/161,
32/101,
33/161,
34/292,
35/232,
36/352,
37/232,
38/352,
39/41,
40/93,
41/354,
42/73,
43/14,
44/275,
45/302,
46/62,
47/182,
48/144,
49/257,
50/297}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/005b7dc0b05c123037aa3971ea7c2fe1.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>[21]</Bildtext>
%<Ausrichten von=\"27\" nach=\"25\"/>
%<Winkel size=\"18\" color=\"blue\" id=\"blauerWinkel\" value=\"130.75313159021968\"/>
%<Winkel size=\"18\" color=\"green\" id=\"gruenerWinkel\" value=\"130.82544101311456\"/>
%<Winkel size=\"18\" color=\"orange\" id=\"orangerWinkel\" value=\"74.73786277076553\"/>
%<Winkel size=\"18\" color=\"violet\" id=\"vierterWinkel\" value=\"135.88810050470713\"/>
%<Winkel size=\"18\" color=\"teal\" id=\"fuenfterWinkel\" value=\"120.80793343341226\"/>
%<Winkel size=\"18\" color=\"lime\" id=\"sechsterWinkel\" value=\"146.06343282760773\"/>
%<Winkel size=\"18\" color=\"LightBlue\" id=\"siebenterWinkel\" value=\"82.29211582561682\"/>
%<Winkel size=\"18\" color=\"LightCoral\" id=\"achterWinkel\" value=\"277.55514194184656\"/>
%<Feinjustieren Anzahl=\"8,8\"/>
%<Rechenweg>
%P[23]=[321.77586716807025,-122.4995025376255]; P[25]=[234.40736183467087,-122.4995025376254]; D=ab(23,25); A(25,23); L(24,25,23); L(26,25,24); L(27,25,26); L(28,27,26); L(29,27,28); M(31,29,27,blauerWinkel); L(30,31,29); L(32,31,30); L(33,31,32); M(35,33,31,gruenerWinkel); L(34,35,33); L(36,35,34); L(37,35,36); L(38,37,36); L(5,37,38); M(4,5,37,orangerWinkel); L(2,5,4); L(3,2,4); L(1,2,3); M(7,1,2,vierterWinkel); L(6,7,1); L(8,7,6); L(9,7,8); L(10,9,8); L(11,9,10); M(13,11,9,fuenfterWinkel); L(12,13,11); L(14,13,12); L(15,13,14); Q(19,15,23,2*D,2*D); A(19,23); H(21,23,19,2); A(21,23); L(22,23,21); A(19,15); H(17,15,19,2); A(17,15); L(16,17,15); A(17,19); L(18,19,17); A(18,16); A(21,19); L(20,21,19); A(22,20); L(39,32,30); N(42,24,22); N(43,4,38); N(45,20,18); N(48,6,3); N(50,12,10); M(46,14,13,sechsterWinkel); M(41,28,27,siebenterWinkel); M(40,34,35,achterWinkel); N(44,40,41); N(47,44,42); N(49,43,44);
%A(41,39); R(41,39,\"green\");
%A(41,42); R(41,42,\"green\");
%A(40,39); R(40,39,\"green\");
%A(40,43); R(40,43,\"green\");
%A(47,46); R(47,46,\"green\");
%A(47,45); R(47,45,\"green\");
%A(49,48); R(49,48,\"green\");
%A(45,46); R(45,46,\"brown\");
%A(46,16); R(46,16,\"grey\");
%A(48,50); R(48,50,\"grey\");
%A(49,50); R(49,50,\"grey\");
%</Rechenweg>
%</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{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 {
1/2.05087581370431060179/5.66720017904189354851,
2/1.24511738441517860743/5.07495584295288448828,
3/2.16089523936027516626/4.67327074191955293969,
4/1.35513681007114361599/4.08102640583054387946,
5/0.43935895512604661306/4.48271150686387542805,
6/2.42878989682759893753/4.74135950928435612184,
7/3.04163439513278044402/5.53156304059579628785,
8/3.41954847825606966794/4.60572237083825974935,
9/4.03239297656125028624/5.39592590214969991536,
10/4.41030705968453951016/4.47008523239216337686,
11/5.02315155798972146073/5.26028876370360443104,
12/4.42151035657644264631/4.46152229923355125862,
13/5.41408300720522728255/4.33986896708128888633,
14/4.81244180579194935632/3.54110250261123615800,
15/5.80501445642073399256/3.41944917045897378571,
16/4.91676351460175542485/2.96009063471842903681,
17/5.75870514690777923761/2.42052202203801236635,
18/4.87045420508880066990/1.96116348629746739540,
19/5.71239583739482359448/1.42159487361705116903,
20/4.74512881951698783922/1.67535561945004540796,
21/5.00899907608124639324/0.71079743680852558452,
22/4.04173205820341063799/0.96455818264151982344,
23/4.30560231476766919201/0.00000000000000000000,
24/3.80560231476767052428/0.86602540378443915170,
25/3.30560231476766919201/0.00000000000000113858,
26/2.80560231476767096837/0.86602540378444048397,
27/2.30560231476766919201/0.00000000000000276512,
28/1.80560231476767096837/0.86602540378444226032,
29/1.30560231476766941405/0.00000000000000439166,
30/1.63524135887969834791/0.94410703873920764906,
31/0.65280115738383459600/0.75752930564984244377,
32/0.98244020149586386292/1.70163634438904587398,
33/0.00000000000000000000/1.51505861129968066869,
34/0.92991409157868787361/1.88283542172059825681,
35/0.14645298504201562095/2.50427624315441210712,
36/1.07636707662070341129/2.87205305357532969524,
37/0.29290597008403107537/3.49349387500914332350,
38/1.22282006166271894898/3.86127068543006179979,
39/1.96488040299172750380/1.88821407747841085722,
40/1.44295034378190778490/2.74120236186057963934,
41/2.73086423938344768914/1.24535424642142000806,
42/3.54173205820341152616/1.83058358642595919719,
43/2.13859791660781572986/3.45958558439673069529,
44/2.20893418017362686001/2.09834253080358745791,
45/3.90318718721096358237/2.21492423213046008001,
46/3.86735535362073701293/3.21428206579243758156,
47/3.01980199899359336158/2.68357187080812797930,
48/2.53880932248356305792/3.74743007216201595710,
49/2.90458175299953413884/2.81672575333973762568,
50/3.80866585827123227403/3.67131876792213329708}
\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 {
29/360.00/490.75/0.4/Blue,
33/310.75/441.58/0.4/Green,
5/261.58/336.32/0.4/Orange,
1/216.32/352.20/0.4/Violet,
11/172.20/293.01/0.4/Teal,
14/53.01/199.08/0.4/Lime,
28/300.00/382.29/0.4/LightBlue,
34/141.58/419.13/0.4/LightCoral}
\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, 2/4,
3/2, 3/4,
4/5,
5/37, 5/38,
6/7, 6/1,
7/1,
8/7, 8/6,
9/7, 9/8,
10/9, 10/8,
11/9, 11/10,
12/13, 12/11,
13/11,
14/13, 14/12,
15/13, 15/14,
16/17, 16/15,
17/15, 17/19,
18/19, 18/17, 18/16,
20/21, 20/19,
21/23, 21/19,
22/23, 22/21, 22/20,
24/25, 24/23,
25/23,
26/25, 26/24,
27/25, 27/26,
28/27, 28/26,
29/27, 29/28,
30/31, 30/29,
31/29,
32/31, 32/30,
33/31, 33/32,
34/35, 34/33,
35/33,
36/35, 36/34,
37/35, 37/36,
38/37, 38/36,
39/32, 39/30,
40/34, 40/39, 40/43,
41/28, 41/39, 41/42,
42/24, 42/22,
43/4, 43/38,
44/40, 44/41,
45/20, 45/18, 45/46,
46/14, 46/16,
47/44, 47/42, 47/46, 47/45,
48/6, 48/3, 48/50,
49/43, 49/44, 49/48, 49/50,
50/12, 50/10}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,50}
\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);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-46) -- (p-16);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-48) -- (p-50);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-49) -- (p-50);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
29/360.00/490.75/0.4/Blue,
33/310.75/441.58/0.4/Green,
5/261.58/336.32/0.4/Orange,
1/216.32/352.20/0.4/Violet,
11/172.20/293.01/0.4/Teal,
14/53.01/199.08/0.4/Lime,
28/300.00/382.29/0.4/LightBlue,
34/141.58/419.13/0.4/LightCoral}
{
\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 {
1/66,
2/126,
3/306,
4/306,
5/186,
6/262,
7/142,
8/262,
9/82,
10/322,
11/22,
12/203,
13/83,
14/203,
15/57,
16/117,
17/357,
18/177,
19/15,
20/135,
21/15,
22/195,
23/330,
24/90,
25/270,
26/30,
27/210,
28/150,
29/210,
30/41,
31/161,
32/101,
33/161,
34/292,
35/232,
36/352,
37/232,
38/352,
39/41,
40/93,
41/354,
42/73,
43/14,
44/275,
45/302,
46/62,
47/182,
48/144,
49/257,
50/297}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>Tahmen(2,3,2,2,2,3,2,3)</Bildtext>
%<Ausrichten von="1" nach="2"/>
%<Winkel size="18" color="blue" id="blauerWinkel" value="15.522486812413007"/>
%<Feinjustieren Anzahl="1"/>
%<Rechenweg>
%P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(2,1); Rahmen(2,3,2,2,2,3,2,3);
%</Rechenweg>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/2.02/0.00,
2/3.02/0.00,
3/2.52/0.87,
4/3.52/0.87,
5/4.02/0.00,
6/2.32/0.95,
7/1.34/0.74,
8/1.65/1.69,
9/0.67/1.48,
10/0.98/2.43,
11/0.00/2.22,
12/0.90/2.66,
13/0.07/3.22,
14/0.97/3.66,
15/0.14/4.22,
16/1.12/4.00,
17/0.82/4.95,
18/1.79/4.74,
19/1.49/5.69,
20/2.14/4.93,
21/2.48/5.87,
22/3.12/5.10,
23/3.46/6.04,
24/3.33/5.05,
25/4.25/5.43,
26/4.12/4.44,
27/5.05/4.82,
28/4.92/3.83,
29/5.84/4.21,
30/5.03/3.63,
31/5.93/3.22,
32/5.12/2.64,
33/6.03/2.22,
34/5.05/2.43,
35/5.36/1.48,
36/4.38/1.69,
37/4.69/0.74,
38/3.71/0.95}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- 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, 5/37,
6/1,
7/1, 7/6,
8/7, 8/6,
9/7, 9/8,
10/9, 10/8,
11/9, 11/10,
12/11,
13/11, 13/12,
14/13, 14/12,
15/13, 15/14,
16/15,
17/15, 17/16,
18/17, 18/16,
19/17, 19/18,
20/19,
21/19, 21/20,
22/21, 22/20,
23/21, 23/22,
24/23,
25/23, 25/24,
26/25, 26/24,
27/25, 27/26,
28/27, 28/26,
29/27, 29/28, 29/31,
30/31, 30/29,
31/33,
32/33, 32/31, 32/30,
34/35, 34/33, 34/36,
35/33,
36/37, 36/35, 36/38,
37/35,
38/5, 38/37}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,38}
\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);
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/210,
2/330,
3/150,
4/30,
5/330,
6/42,
7/222,
8/342,
9/222,
10/42,
11/162,
12/296,
13/176,
14/56,
15/197,
16/317,
17/137,
18/317,
19/77,
20/280,
21/40,
22/340,
23/112,
24/172,
25/352,
26/172,
27/52,
28/232,
29/352,
30/185,
31/5,
32/245,
33/18,
34/138,
35/18,
36/138,
37/18,
38/198}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/e456cb978639164c3a13f1b7c1b3c23b.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>Tahmen(2,3,2,2,2,3,2,3)</Bildtext>
%<Ausrichten von=\"1\" nach=\"2\"/>
%<Winkel size=\"18\" color=\"blue\" id=\"blauerWinkel\" value=\"15.522486812413007\"/>
%<Feinjustieren Anzahl=\"1\"/>
%<Rechenweg>
%P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(2,1); Rahmen(2,3,2,2,2,3,2,3);
%</Rechenweg>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/2.02/0.00,
2/3.02/0.00,
3/2.52/0.87,
4/3.52/0.87,
5/4.02/0.00,
6/2.32/0.95,
7/1.34/0.74,
8/1.65/1.69,
9/0.67/1.48,
10/0.98/2.43,
11/0.00/2.22,
12/0.90/2.66,
13/0.07/3.22,
14/0.97/3.66,
15/0.14/4.22,
16/1.12/4.00,
17/0.82/4.95,
18/1.79/4.74,
19/1.49/5.69,
20/2.14/4.93,
21/2.48/5.87,
22/3.12/5.10,
23/3.46/6.04,
24/3.33/5.05,
25/4.25/5.43,
26/4.12/4.44,
27/5.05/4.82,
28/4.92/3.83,
29/5.84/4.21,
30/5.03/3.63,
31/5.93/3.22,
32/5.12/2.64,
33/6.03/2.22,
34/5.05/2.43,
35/5.36/1.48,
36/4.38/1.69,
37/4.69/0.74,
38/3.71/0.95}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- 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, 5/37,
6/1,
7/1, 7/6,
8/7, 8/6,
9/7, 9/8,
10/9, 10/8,
11/9, 11/10,
12/11,
13/11, 13/12,
14/13, 14/12,
15/13, 15/14,
16/15,
17/15, 17/16,
18/17, 18/16,
19/17, 19/18,
20/19,
21/19, 21/20,
22/21, 22/20,
23/21, 23/22,
24/23,
25/23, 25/24,
26/25, 26/24,
27/25, 27/26,
28/27, 28/26,
29/27, 29/28, 29/31,
30/31, 30/29,
31/33,
32/33, 32/31, 32/30,
34/35, 34/33, 34/36,
35/33,
36/37, 36/35, 36/38,
37/35,
38/5, 38/37}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,38}
\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);
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/210,
2/330,
3/150,
4/30,
5/330,
6/42,
7/222,
8/342,
9/222,
10/42,
11/162,
12/296,
13/176,
14/56,
15/197,
16/317,
17/137,
18/317,
19/77,
20/280,
21/40,
22/340,
23/112,
24/172,
25/352,
26/172,
27/52,
28/232,
29/352,
30/185,
31/5,
32/245,
33/18,
34/138,
35/18,
36/138,
37/18,
38/198}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>Tahmen(2,3,2,2,2,3,2,3)</Bildtext>
%<Ausrichten von="1" nach="2"/>
%<Winkel size="18" color="blue" id="blauerWinkel" value="15.522486812413007"/>
%<Feinjustieren Anzahl="1"/>
%<Rechenweg>
%P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(2,1); Rahmen(2,3,4,3,3,4,3);
%</Rechenweg>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/2.21/0.00,
2/3.21/0.00,
3/2.71/0.87,
4/3.71/0.87,
5/4.21/0.00,
6/2.43/0.98,
7/1.47/0.68,
8/1.69/1.65,
9/0.74/1.35,
10/0.954/2.327,
11/0.00/2.03,
12/0.929/2.395,
13/0.15/3.02,
14/1.07/3.38,
15/0.29/4.01,
16/1.22/4.37,
17/0.44/4.99,
18/1.365/5.363,
19/0.58/5.98,
20/1.405/5.418,
21/1.48/6.41,
22/2.31/5.85,
23/2.39/6.85,
24/3.21/6.28,
25/3.29/7.28,
26/3.35/6.28,
27/4.18/6.83,
28/4.25/5.84,
29/5.08/6.39,
30/5.146/5.394,
31/5.98/5.95,
32/5.179/5.347,
33/6.10/4.96,
34/5.30/4.35,
35/6.22/3.96,
36/5.42/3.36,
37/6.34/2.97,
38/5.546/2.369,
39/6.47/1.98,
40/5.520/2.300,
41/5.72/1.32,
42/4.77/1.64,
43/4.96/0.66,
44/4.02/0.98}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- 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, 5/43,
6/1,
7/1, 7/6,
8/7, 8/6,
9/7, 9/8,
10/9, 10/8,
11/9, 11/10,
12/11,
13/11, 13/12,
14/13, 14/12,
15/13, 15/14,
16/15, 16/14,
17/15, 17/16,
18/17, 18/16,
19/17, 19/18,
20/19,
21/19, 21/20,
22/21, 22/20,
23/21, 23/22,
24/23, 24/22,
25/23, 25/24,
26/25,
27/25, 27/26,
28/27, 28/26,
29/27, 29/28,
30/29, 30/28,
31/29, 31/30, 31/33,
32/33, 32/31,
33/35,
34/35, 34/33, 34/32,
35/37,
36/37, 36/35, 36/34,
37/39,
38/39, 38/37, 38/36,
40/41, 40/39, 40/42,
41/39,
42/43, 42/41, 42/44,
43/41,
44/5, 44/43}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,44}
\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);
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/288,
2/330,
3/150,
4/30,
5/330,
6/48,
7/288,
8/348,
9/288,
10/48,
11/168,
12/352,
13/232,
14/352,
15/232,
16/352,
17/232,
18/352,
19/176,
20/296,
21/56,
22/296,
23/56,
24/296,
25/56,
26/244,
27/4,
28/184,
29/124,
30/244,
31/4,
32/127,
33/67,
34/247,
35/7,
36/247,
37/307,
38/187,
39/307,
40/71,
41/11,
42/131,
43/311,
44/131}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/484628cca71d907a45c3a66e47bb93d7.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>Tahmen(2,3,2,2,2,3,2,3)</Bildtext>
%<Ausrichten von=\"1\" nach=\"2\"/>
%<Winkel size=\"18\" color=\"blue\" id=\"blauerWinkel\" value=\"15.522486812413007\"/>
%<Feinjustieren Anzahl=\"1\"/>
%<Rechenweg>
%P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(2,1); Rahmen(2,3,4,3,3,4,3);
%</Rechenweg>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/2.21/0.00,
2/3.21/0.00,
3/2.71/0.87,
4/3.71/0.87,
5/4.21/0.00,
6/2.43/0.98,
7/1.47/0.68,
8/1.69/1.65,
9/0.74/1.35,
10/0.954/2.327,
11/0.00/2.03,
12/0.929/2.395,
13/0.15/3.02,
14/1.07/3.38,
15/0.29/4.01,
16/1.22/4.37,
17/0.44/4.99,
18/1.365/5.363,
19/0.58/5.98,
20/1.405/5.418,
21/1.48/6.41,
22/2.31/5.85,
23/2.39/6.85,
24/3.21/6.28,
25/3.29/7.28,
26/3.35/6.28,
27/4.18/6.83,
28/4.25/5.84,
29/5.08/6.39,
30/5.146/5.394,
31/5.98/5.95,
32/5.179/5.347,
33/6.10/4.96,
34/5.30/4.35,
35/6.22/3.96,
36/5.42/3.36,
37/6.34/2.97,
38/5.546/2.369,
39/6.47/1.98,
40/5.520/2.300,
41/5.72/1.32,
42/4.77/1.64,
43/4.96/0.66,
44/4.02/0.98}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- 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, 5/43,
6/1,
7/1, 7/6,
8/7, 8/6,
9/7, 9/8,
10/9, 10/8,
11/9, 11/10,
12/11,
13/11, 13/12,
14/13, 14/12,
15/13, 15/14,
16/15, 16/14,
17/15, 17/16,
18/17, 18/16,
19/17, 19/18,
20/19,
21/19, 21/20,
22/21, 22/20,
23/21, 23/22,
24/23, 24/22,
25/23, 25/24,
26/25,
27/25, 27/26,
28/27, 28/26,
29/27, 29/28,
30/29, 30/28,
31/29, 31/30, 31/33,
32/33, 32/31,
33/35,
34/35, 34/33, 34/32,
35/37,
36/37, 36/35, 36/34,
37/39,
38/39, 38/37, 38/36,
40/41, 40/39, 40/42,
41/39,
42/43, 42/41, 42/44,
43/41,
44/5, 44/43}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,44}
\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);
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/288,
2/330,
3/150,
4/30,
5/330,
6/48,
7/288,
8/348,
9/288,
10/48,
11/168,
12/352,
13/232,
14/352,
15/232,
16/352,
17/232,
18/352,
19/176,
20/296,
21/56,
22/296,
23/56,
24/296,
25/56,
26/244,
27/4,
28/184,
29/124,
30/244,
31/4,
32/127,
33/67,
34/247,
35/7,
36/247,
37/307,
38/187,
39/307,
40/71,
41/11,
42/131,
43/311,
44/131}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>Automatisch generierte Eingabe zu: Fig.5 4-regular planar graph with 51 vertices. This graph is rigid and asymmetric.</Bildtext>
%<Ausrichten von="27" nach="25"/>
%<Winkel size="18" color="blue" id="blauerWinkel" value="45.00000000000001"/>
%<Winkel size="18" color="green" id="gruenerWinkel" value="45"/>
%<Winkel size="18" color="orange" id="orangerWinkel" value="45.00000000000001"/>
%<Winkel size="18" color="violet" id="vierterWinkel" value="45.00000000000001"/>
%<Winkel size="18" color="teal" id="fuenfterWinkel" value="45"/>
%<Winkel size="18" color="lime" id="sechsterWinkel" value="45.00000000000001"/>
%<Winkel size="18" color="LightBlue" id="siebenterWinkel" value="188.97052392937874"/>
%<Winkel size="18" color="LightCoral" id="achterWinkel" value="44.999999999999986"/>
%<Winkel size="18" color="LightCyan" id="neunterWinkel" value="190.36480284682804"/>
%<Winkel size="18" color="LightGoldenrodYellow" id="zehnterWinkel" value="44.999999999999986"/>
%<Winkel size="18" color="LightGreen" id="elfterWinkel" value="45.00000000000001"/>
%<Winkel size="18" color="LightGray" id="zwoelfterWinkel" value="44.999999999999964"/>
%<Winkel size="18" color="LightPink" id="dreizehnterWinkel" value="45.00000000000001"/>
%<Winkel size="18" color="LightSalmon" id="vierzehnterWinkel" value="45"/>
%<Winkel size="18" color="LightSeaGreen" id="fuenfzehnterWinkel" value="148.07258660286803"/>
%<Winkel size="18" color="LightSkyBlue" id="sechzehnterWinkel" value="45"/>
%<Winkel size="18" color="LightSlateGray" id="siebzehnterWinkel" value="60.55491794481753"/>
%<Winkel size="18" color="LightSteelBlue" id="achtzehnterWinkel" value="45"/>
%<Winkel size="18" color="Crimson" id="Winkel19" value="279.2750456296003"/>
%<Winkel size="18" color="DarkBlue" id="Winkel20" value="44.999999999999936"/>
%<Winkel size="18" color="DarkCyan" id="Winkel21" value="45"/>
%<Winkel size="18" color="DarkGoldenrod" id="Winkel22" value="45"/>
%<Winkel size="18" color="DarkGray" id="Winkel23" value="139.96219911442307"/>
%<Winkel size="18" color="DarkGreen" id="Winkel24" value="45"/>
%<Winkel size="18" color="DarkKhaki" id="Winkel25" value="45"/>
%<Winkel size="18" color="DarkMagenta" id="Winkel26" value="45.00000000000001"/>
%<Winkel size="18" color="DarkOliveGreen" id="Winkel27" value="44.84747990654853"/>
%<Winkel size="18" color="DarkOrange" id="Winkel28" value="45"/>
%<Winkel size="18" color="DarkOrchid" id="Winkel29" value="45"/>
%<Winkel size="18" color="DarkRed" id="Winkel30" value="45.00000000000001"/>
%<Winkel size="18" color="DarkSalmon" id="Winkel31" value="45"/>
%<Winkel size="18" color="DarkSeaGreen" id="Winkel32" value="45"/>
%<Winkel size="18" color="DarkSlateBlue" id="Winkel33" value="291.60856120518304"/>
%<Winkel size="18" color="DarkSlateGray" id="Winkel34" value="45.00000000000001"/>
%<Winkel size="18" color="DarkTurquoise" id="Winkel35" value="240"/>
%<Winkel size="18" color="DarkViolet" id="Winkel36" value="45"/>
%<Winkel size="18" color="DeepPink" id="Winkel37" value="45"/>
%<Winkel size="18" color="DeepSkyBlue" id="Winkel38" value="45"/>
%<Winkel size="18" color="DimGray" id="Winkel39" value="45.00000000000001"/>
%<Winkel size="18" color="DodgerBlue" id="Winkel40" value="45"/>
%<Winkel size="18" color="FireBrick" id="Winkel41" value="45.00000000000001"/>
%<Winkel size="18" color="FloralWhite" id="Winkel42" value="45"/>
%<Winkel size="18" color="ForestGreen" id="Winkel43" value="277.44333062292696"/>
%<Winkel size="18" color="Fuchsia" id="Winkel44" value="45"/>
%<Winkel size="18" color="Gainsboro" id="Winkel45" value="45"/>
%<Winkel size="18" color="GhostWhite" id="Winkel46" value="45.00000000000001"/>
%<Winkel size="18" color="Gold" id="Winkel47" value="45.00000000000001"/>
%<Winkel size="18" color="Goldenrod" id="Winkel48" value="45"/>
%<Winkel size="18" color="Gray" id="Winkel49" value="45.00000000000001"/>
%<Winkel size="18" color="Green" id="Winkel50" value="45"/>
%<Winkel size="18" color="GreenYellow" id="Winkel51" value="45.00000000000001"/>
%<Winkel size="18" color="Honeydew" id="Winkel52" value="45"/>
%<Winkel size="18" color="HotPink" id="Winkel53" value="45"/>
%<Winkel size="18" color="IndianRed" id="Winkel54" value="45.00000000000001"/>
%<Winkel size="18" color="Indigo" id="Winkel55" value="45"/>
%<Winkel size="18" color="Ivory" id="Winkel56" value="45.00000000000001"/>
%<Winkel size="18" color="Khaki" id="Winkel57" value="44.911592050559506"/>
%<Winkel size="18" color="Lavender" id="Winkel58" value="45"/>
%<Winkel size="18" color="LavenderBlush" id="Winkel59" value="45"/>
%<Winkel size="18" color="LawnGreen" id="Winkel60" value="45"/>
%<Winkel size="18" color="LemonChiffon" id="Winkel61" value="45"/>
%<Winkel size="18" color="LightBlue" id="Winkel62" value="45"/>
%<Winkel size="18" color="LightCoral" id="Winkel63" value="287.2475101574122"/>
%<Winkel size="18" color="LightCyan" id="Winkel64" value="45"/>
%<Winkel size="18" color="LightGoldenrodYellow" id="Winkel65" value="45.000000000000064"/>
%<Winkel size="18" color="LightGreen" id="Winkel66" value="44.99999999999999"/>
%<Winkel size="18" color="LightGray" id="Winkel67" value="44.99999999999999"/>
%<Winkel size="18" color="LightPink" id="Winkel68" value="45"/>
%<Winkel size="18" color="LightSalmon" id="Winkel69" value="45"/>
%<Winkel size="18" color="LightSeaGreen" id="Winkel70" value="45"/>
%<Winkel size="18" color="LightSkyBlue" id="Winkel71" value="271.0449756281402"/>
%<Winkel size="18" color="LightSlateGray" id="Winkel72" value="45"/>
%<Winkel size="18" color="LightSteelBlue" id="Winkel73" value="45.00000000000001"/>
%<Winkel size="18" color="LightYellow" id="Winkel74" value="45.00000000000001"/>
%<Winkel size="18" color="Lime" id="Winkel75" value="45.00000000000001"/>
%<Winkel size="18" color="LimeGreen" id="Winkel76" value="45.00000000000001"/>
%<Winkel size="18" color="Linen" id="Winkel77" value="45.00000000000001"/>
%<Winkel size="18" color="Maroon" id="Winkel78" value="45"/>
%<Winkel size="18" color="MediumAquamarine" id="Winkel79" value="289.6799787422597"/>
%<Winkel size="18" color="MediumBlue" id="Winkel80" value="45.00000000000001"/>
%<Winkel size="18" color="MediumOrchid" id="Winkel81" value="45.00000000000001"/>
%<Winkel size="18" color="MediumPurple" id="Winkel82" value="45"/>
%<Winkel size="18" color="MediumSeaGreen" id="Winkel83" value="45.00000000000001"/>
%<Winkel size="18" color="MediumSlateBlue" id="Winkel84" value="45.00000000000001"/>
%<Winkel size="18" color="MediumSpringGreen" id="Winkel85" value="45"/>
%<Winkel size="18" color="MediumTurquoise" id="Winkel86" value="45"/>
%<Winkel size="18" color="MediumVioletRed" id="Winkel87" value="276.5301804195562"/>
%<Winkel size="18" color="MidnightBlue" id="Winkel88" value="45.00000000000001"/>
%<Winkel size="18" color="MintCream" id="Winkel89" value="45.00000000000001"/>
%<Winkel size="18" color="MistyRose" id="Winkel90" value="44.99999999999999"/>
%<Winkel size="18" color="Moccasin" id="Winkel91" value="45"/>
%<Winkel size="18" color="NavajoWhite" id="Winkel92" value="45"/>
%<Winkel size="18" color="Navy" id="Winkel93" value="45.00000000000001"/>
%<Winkel size="18" color="OldLace" id="Winkel94" value="45"/>
%<Winkel size="18" color="Olive" id="Winkel95" value="45"/>
%<Winkel size="18" color="OliveDrab" id="Winkel96" value="45"/>
%<Winkel size="18" color="Orange" id="Winkel97" value="351.60856120518304"/>
%<Winkel size="18" color="OrangeRed" id="Winkel98" value="45.00000000000001"/>
%<Feinjustieren Anzahl="101,98"/>
%<Rechenweg>
%P[1]=[-90.47502624995381,373.3560161118893]; P[2]=[-159.99984570994133,323.7312977681336]; D=ab(1,2); A(2,1); Q(3,1,2,jum(blauerWinkel)*D,jum(gruenerWinkel)*D); Q(4,3,2,jum(orangerWinkel)*D,jum(vierterWinkel)*D); Q(5,4,2,jum(fuenfterWinkel)*D,jum(sechsterWinkel)*D); M(45,3,1,siebenterWinkel,0,jum(achterWinkel)*D); M(49,45,3,neunterWinkel,0,jum(zehnterWinkel)*D); Q(43,4,49,jum(elfterWinkel)*D,jum(zwoelfterWinkel)*D); Q(48,45,49,jum(dreizehnterWinkel)*D,jum(vierzehnterWinkel)*D); M(46,48,45,fuenfzehnterWinkel,0,jum(sechzehnterWinkel)*D); M(50,46,48,siebzehnterWinkel,0,jum(achtzehnterWinkel)*D); M(51,50,46,Winkel19,0,jum(Winkel20)*D); Q(47,50,51,jum(Winkel21)*D,jum(Winkel22)*D); M(44,49,45,Winkel23,0,jum(Winkel24)*D); Q(40,44,43,jum(Winkel25)*D,jum(Winkel26)*D); Q(42,50,44,jum(Winkel27)*D,jum(Winkel28)*D); Q(41,42,44,jum(Winkel29)*D,jum(Winkel30)*D); Q(39,41,40,jum(Winkel31)*D,jum(Winkel32)*D); M(37,5,4,Winkel33,0,jum(Winkel34)*D); M(36,37,5,Winkel35,0,jum(Winkel36)*D); Q(34,40,36,jum(Winkel37)*D,jum(Winkel38)*D); Q(35,34,36,jum(Winkel39)*D,jum(Winkel40)*D); Q(33,34,35,jum(Winkel41)*D,jum(Winkel42)*D); M(31,33,34,Winkel43,0,jum(Winkel44)*D); Q(30,39,31,jum(Winkel45)*D,jum(Winkel46)*D); Q(32,31,30,jum(Winkel47)*D,jum(Winkel48)*D); Q(29,30,31,jum(Winkel49)*D,jum(Winkel50)*D); Q(28,29,41,jum(Winkel51)*D,jum(Winkel52)*D); Q(27,28,29,jum(Winkel53)*D,jum(Winkel54)*D); Q(26,28,27,jum(Winkel55)*D,jum(Winkel56)*D); Q(24,42,26,jum(Winkel57)*D,jum(Winkel58)*D); Q(25,24,26,jum(Winkel59)*D,jum(Winkel60)*D); Q(23,24,25,jum(Winkel61)*D,jum(Winkel62)*D); M(21,23,24,Winkel63,0,jum(Winkel64)*D); Q(20,51,21,jum(Winkel65)*D,jum(Winkel66)*D); Q(22,23,21,jum(Winkel67)*D,jum(Winkel68)*D); Q(19,20,21,jum(Winkel69)*D,jum(Winkel70)*D); M(17,19,20,Winkel71,0,jum(Winkel72)*D); Q(16,47,17,jum(Winkel73)*D,jum(Winkel74)*D); Q(18,19,17,jum(Winkel75)*D,jum(Winkel76)*D); Q(15,16,17,jum(Winkel77)*D,jum(Winkel78)*D); M(13,15,16,Winkel79,0,jum(Winkel80)*D); Q(12,46,13,jum(Winkel81)*D,jum(Winkel82)*D); Q(14,13,12,jum(Winkel83)*D,jum(Winkel84)*D); Q(11,12,13,jum(Winkel85)*D,jum(Winkel86)*D); M(9,11,12,Winkel87,0,jum(Winkel88)*D); Q(10,11,9,jum(Winkel89)*D,jum(Winkel90)*D); Q(8,10,9,jum(Winkel91)*D,jum(Winkel92)*D); Q(6,8,1,jum(Winkel93)*D,jum(Winkel94)*D); Q(7,1,6,jum(Winkel95)*D,jum(Winkel96)*D); M(38,5,4,Winkel97,0,jum(Winkel98)*D);
%R(3,1,"green");
%R(3,2,"green");
%R(4,3,"green");
%R(4,2,"green");
%R(5,4,"green");
%R(5,2,"green");
%R(45,3,"green");
%R(43,4,"green");
%R(48,49,"green");
%R(46,48,"green");
%R(50,46,"green");
%R(47,50,"green");
%R(47,51,"green");
%R(44,49,"green");
%R(40,44,"green");
%R(40,43,"green");
%R(42,44,"green");
%R(41,42,"green");
%R(41,44,"green");
%R(39,41,"green");
%R(39,40,"green");
%R(37,5,"green");
%R(36,37,"green");
%R(34,40,"green");
%R(34,36,"green");
%R(35,34,"green");
%R(35,36,"green");
%A(35,37); R(35,37,"green");
%R(33,34,"green");
%R(33,35,"green");
%R(31,33,"green");
%R(30,39,"green");
%R(30,31,"green");
%R(32,31,"green");
%R(32,30,"green");
%A(32,33); R(32,33,"green");
%A(32,39); R(32,39,"green");
%R(29,30,"green");
%R(29,31,"green");
%R(28,29,"green");
%R(28,41,"green");
%R(27,28,"green");
%R(27,29,"green");
%R(26,28,"green");
%R(26,27,"green");
%R(24,26,"green");
%R(25,24,"green");
%R(25,26,"green");
%A(25,27); R(25,27,"green");
%R(23,24,"green");
%R(23,25,"green");
%R(21,23,"green");
%R(20,21,"green");
%R(22,23,"green");
%R(22,21,"green");
%A(22,20); R(22,20,"green");
%A(22,51); R(22,51,"green");
%R(19,20,"green");
%R(19,21,"green");
%R(17,19,"green");
%R(16,47,"green");
%R(16,17,"green");
%R(18,19,"green");
%R(18,17,"green");
%A(18,16); R(18,16,"green");
%A(18,47); R(18,47,"green");
%R(15,16,"green");
%R(15,17,"green");
%R(13,15,"green");
%R(12,46,"green");
%R(12,13,"green");
%R(14,13,"green");
%R(14,12,"green");
%A(14,15); R(14,15,"green");
%A(14,46); R(14,46,"green");
%R(11,12,"green");
%R(11,13,"green");
%R(9,11,"green");
%R(10,11,"green");
%R(10,9,"green");
%A(10,48); R(10,48,"green");
%R(8,10,"green");
%R(8,9,"green");
%R(6,8,"green");
%R(6,1,"green");
%A(6,45); R(6,45,"green");
%R(7,1,"green");
%R(7,6,"green");
%A(7,8); R(7,8,"green");
%A(7,9); R(7,9,"green");
%R(38,5,"green");
%A(38,37); R(38,37,"green");
%A(38,36); R(38,36,"green");
%R(20,51,"green");
%R(49,45,"green");
%R(43,49,"green");
%R(51,50,"green");
%R(48,45,"green");
%R(24,42,"green");
%R(42,50,"green");
%A(38,43); R(38,43,"green");
%</Rechenweg>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Crimson}{rgb}{0.86,0.08,0.23}
\definecolor{DarkGray}{rgb}{0.66,0.66,0.66}
\definecolor{DarkSlateBlue}{rgb}{0.28,0.24,0.54}
\definecolor{DarkTurquoise}{rgb}{0.00,0.80,0.82}
\definecolor{ForestGreen}{rgb}{0.13,0.54,0.13}
\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{LightSeaGreen}{rgb}{0.13,0.70,0.66}
\definecolor{LightSkyBlue}{rgb}{0.53,0.80,0.98}
\definecolor{LightSlateGray}{rgb}{0.46,0.53,0.60}
\definecolor{MediumAquamarine}{rgb}{0.40,0.80,0.66}
\definecolor{MediumVioletRed}{rgb}{0.78,0.08,0.52}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.78/5.81,
2/0.96/5.22,
3/1.87/4.81,
4/1.06/4.23,
5/0.15/4.64,
6/2.03/4.84,
7/2.74/5.54,
8/2.99/4.57,
9/3.71/5.27,
10/3.96/4.30,
11/4.67/5.00,
12/4.29/4.08,
13/5.28/4.22,
14/4.91/3.29,
15/5.90/3.43,
16/4.95/3.11,
17/5.70/2.45,
18/4.75/2.13,
19/5.49/1.47,
20/4.52/1.69,
21/4.81/0.73,
22/3.84/0.96,
23/4.13/0.00,
24/3.64/0.87,
25/3.13/0.00,
26/2.64/0.87,
27/2.13/0.00,
28/1.635/0.867,
29/1.13/0.00,
30/1.564/0.904,
31/0.57/0.82,
32/1.00/1.73,
33/0.00/1.65,
34/0.89/2.10,
35/0.05/2.65,
36/0.94/3.10,
37/0.10/3.65,
38/0.99/4.10,
39/1.99/1.81,
40/1.65/2.75,
41/2.62/1.03,
42/3.27/1.79,
43/1.92/3.71,
44/2.28/1.97,
45/2.12/3.84,
46/3.92/3.15,
47/4.00/2.80,
48/3.12/3.75,
49/2.54/2.93,
50/3.00/2.75,
51/3.54/1.91}
\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 {
3/95.52/284.49/0.4/LightBlue,
45/104.49/294.85/0.4/LightCyan,
48/174.85/322.93/0.4/LightSeaGreen,
46/142.93/203.48/0.4/LightSlateGray,
50/23.48/302.76/0.4/Crimson,
49/114.85/254.82/0.4/DarkGray,
5/335.52/627.13/0.4/DarkSlateBlue,
37/87.13/327.13/0.4/DarkTurquoise,
33/27.13/304.57/0.4/ForestGreen,
23/119.99/407.23/0.4/LightCoral,
19/167.23/438.28/0.4/LightSkyBlue,
15/198.28/487.96/0.4/MediumAquamarine,
11/247.96/524.49/0.4/MediumVioletRed,
5/335.52/687.13/0.3/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,
6/8, 6/1, 6/45,
7/1, 7/6, 7/8, 7/9,
8/10, 8/9,
9/11,
10/11, 10/9, 10/48,
11/12, 11/13,
12/46, 12/13,
13/15,
14/13, 14/12, 14/15, 14/46,
15/16, 15/17,
16/47, 16/17,
17/19,
18/19, 18/17, 18/16, 18/47,
19/20, 19/21,
20/51, 20/21,
21/23,
22/23, 22/21, 22/20, 22/51,
23/24, 23/25,
24/42, 24/26,
25/24, 25/26, 25/27,
26/28, 26/27,
27/28, 27/29,
28/29, 28/41,
29/30, 29/31,
30/39, 30/31,
31/33,
32/31, 32/30, 32/33, 32/39,
33/34, 33/35,
34/40, 34/36,
35/34, 35/36, 35/37,
36/37,
37/5,
38/5, 38/37, 38/36, 38/43,
39/41, 39/40,
40/44, 40/43,
41/42, 41/44,
42/50, 42/44,
43/4, 43/49,
44/49,
45/3,
46/48,
47/50, 47/51,
48/45, 48/49,
49/45,
50/46,
51/50}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,51}
\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);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-24) -- (p-42);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-38) -- (p-43);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-42) -- (p-50);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
3/95.52/284.49/0.4/LightBlue,
45/104.49/294.85/0.4/LightCyan,
48/174.85/322.93/0.4/LightSeaGreen,
46/142.93/203.48/0.4/LightSlateGray,
50/23.48/302.76/0.4/Crimson,
49/114.85/254.82/0.4/DarkGray,
5/335.52/627.13/0.4/DarkSlateBlue,
37/87.13/327.13/0.4/DarkTurquoise,
33/27.13/304.57/0.4/ForestGreen,
23/119.99/407.23/0.4/LightCoral,
19/167.23/438.28/0.4/LightSkyBlue,
15/198.28/487.96/0.4/MediumAquamarine,
11/247.96/524.49/0.4/MediumVioletRed,
5/335.52/687.13/0.3/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 {
1/66,
2/66,
3/306,
4/246,
5/117,
6/194,
7/14,
8/254,
9/74,
10/314,
11/14,
12/98,
13/338,
14/278,
15/338,
16/48,
17/348,
18/168,
19/17,
20/17,
21/17,
22/197,
23/330,
24/30,
25/330,
26/30,
27/210,
28/90,
29/210,
30/35,
31/275,
32/155,
33/237,
34/357,
35/177,
36/357,
37/177,
38/57,
39/35,
40/77,
41/260,
42/20,
43/104,
44/284,
45/145,
46/218,
47/33,
48/25,
49/265,
50/153,
51/273}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/e2b82b8cef8a50ec91c5852939444d8a.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>Automatisch generierte Eingabe zu: Fig.5 4-regular planar graph with 51 vertices. This graph is rigid and asymmetric.</Bildtext>
%<Ausrichten von=\"27\" nach=\"25\"/>
%<Winkel size=\"18\" color=\"blue\" id=\"blauerWinkel\" value=\"45.00000000000001\"/>
%<Winkel size=\"18\" color=\"green\" id=\"gruenerWinkel\" value=\"45\"/>
%<Winkel size=\"18\" color=\"orange\" id=\"orangerWinkel\" value=\"45.00000000000001\"/>
%<Winkel size=\"18\" color=\"violet\" id=\"vierterWinkel\" value=\"45.00000000000001\"/>
%<Winkel size=\"18\" color=\"teal\" id=\"fuenfterWinkel\" value=\"45\"/>
%<Winkel size=\"18\" color=\"lime\" id=\"sechsterWinkel\" value=\"45.00000000000001\"/>
%<Winkel size=\"18\" color=\"LightBlue\" id=\"siebenterWinkel\" value=\"188.97052392937874\"/>
%<Winkel size=\"18\" color=\"LightCoral\" id=\"achterWinkel\" value=\"44.999999999999986\"/>
%<Winkel size=\"18\" color=\"LightCyan\" id=\"neunterWinkel\" value=\"190.36480284682804\"/>
%<Winkel size=\"18\" color=\"LightGoldenrodYellow\" id=\"zehnterWinkel\" value=\"44.999999999999986\"/>
%<Winkel size=\"18\" color=\"LightGreen\" id=\"elfterWinkel\" value=\"45.00000000000001\"/>
%<Winkel size=\"18\" color=\"LightGray\" id=\"zwoelfterWinkel\" value=\"44.999999999999964\"/>
%<Winkel size=\"18\" color=\"LightPink\" id=\"dreizehnterWinkel\" value=\"45.00000000000001\"/>
%<Winkel size=\"18\" color=\"LightSalmon\" id=\"vierzehnterWinkel\" value=\"45\"/>
%<Winkel size=\"18\" color=\"LightSeaGreen\" id=\"fuenfzehnterWinkel\" value=\"148.07258660286803\"/>
%<Winkel size=\"18\" color=\"LightSkyBlue\" id=\"sechzehnterWinkel\" value=\"45\"/>
%<Winkel size=\"18\" color=\"LightSlateGray\" id=\"siebzehnterWinkel\" value=\"60.55491794481753\"/>
%<Winkel size=\"18\" color=\"LightSteelBlue\" id=\"achtzehnterWinkel\" value=\"45\"/>
%<Winkel size=\"18\" color=\"Crimson\" id=\"Winkel19\" value=\"279.2750456296003\"/>
%<Winkel size=\"18\" color=\"DarkBlue\" id=\"Winkel20\" value=\"44.999999999999936\"/>
%<Winkel size=\"18\" color=\"DarkCyan\" id=\"Winkel21\" value=\"45\"/>
%<Winkel size=\"18\" color=\"DarkGoldenrod\" id=\"Winkel22\" value=\"45\"/>
%<Winkel size=\"18\" color=\"DarkGray\" id=\"Winkel23\" value=\"139.96219911442307\"/>
%<Winkel size=\"18\" color=\"DarkGreen\" id=\"Winkel24\" value=\"45\"/>
%<Winkel size=\"18\" color=\"DarkKhaki\" id=\"Winkel25\" value=\"45\"/>
%<Winkel size=\"18\" color=\"DarkMagenta\" id=\"Winkel26\" value=\"45.00000000000001\"/>
%<Winkel size=\"18\" color=\"DarkOliveGreen\" id=\"Winkel27\" value=\"44.84747990654853\"/>
%<Winkel size=\"18\" color=\"DarkOrange\" id=\"Winkel28\" value=\"45\"/>
%<Winkel size=\"18\" color=\"DarkOrchid\" id=\"Winkel29\" value=\"45\"/>
%<Winkel size=\"18\" color=\"DarkRed\" id=\"Winkel30\" value=\"45.00000000000001\"/>
%<Winkel size=\"18\" color=\"DarkSalmon\" id=\"Winkel31\" value=\"45\"/>
%<Winkel size=\"18\" color=\"DarkSeaGreen\" id=\"Winkel32\" value=\"45\"/>
%<Winkel size=\"18\" color=\"DarkSlateBlue\" id=\"Winkel33\" value=\"291.60856120518304\"/>
%<Winkel size=\"18\" color=\"DarkSlateGray\" id=\"Winkel34\" value=\"45.00000000000001\"/>
%<Winkel size=\"18\" color=\"DarkTurquoise\" id=\"Winkel35\" value=\"240\"/>
%<Winkel size=\"18\" color=\"DarkViolet\" id=\"Winkel36\" value=\"45\"/>
%<Winkel size=\"18\" color=\"DeepPink\" id=\"Winkel37\" value=\"45\"/>
%<Winkel size=\"18\" color=\"DeepSkyBlue\" id=\"Winkel38\" value=\"45\"/>
%<Winkel size=\"18\" color=\"DimGray\" id=\"Winkel39\" value=\"45.00000000000001\"/>
%<Winkel size=\"18\" color=\"DodgerBlue\" id=\"Winkel40\" value=\"45\"/>
%<Winkel size=\"18\" color=\"FireBrick\" id=\"Winkel41\" value=\"45.00000000000001\"/>
%<Winkel size=\"18\" color=\"FloralWhite\" id=\"Winkel42\" value=\"45\"/>
%<Winkel size=\"18\" color=\"ForestGreen\" id=\"Winkel43\" value=\"277.44333062292696\"/>
%<Winkel size=\"18\" color=\"Fuchsia\" id=\"Winkel44\" value=\"45\"/>
%<Winkel size=\"18\" color=\"Gainsboro\" id=\"Winkel45\" value=\"45\"/>
%<Winkel size=\"18\" color=\"GhostWhite\" id=\"Winkel46\" value=\"45.00000000000001\"/>
%<Winkel size=\"18\" color=\"Gold\" id=\"Winkel47\" value=\"45.00000000000001\"/>
%<Winkel size=\"18\" color=\"Goldenrod\" id=\"Winkel48\" value=\"45\"/>
%<Winkel size=\"18\" color=\"Gray\" id=\"Winkel49\" value=\"45.00000000000001\"/>
%<Winkel size=\"18\" color=\"Green\" id=\"Winkel50\" value=\"45\"/>
%<Winkel size=\"18\" color=\"GreenYellow\" id=\"Winkel51\" value=\"45.00000000000001\"/>
%<Winkel size=\"18\" color=\"Honeydew\" id=\"Winkel52\" value=\"45\"/>
%<Winkel size=\"18\" color=\"HotPink\" id=\"Winkel53\" value=\"45\"/>
%<Winkel size=\"18\" color=\"IndianRed\" id=\"Winkel54\" value=\"45.00000000000001\"/>
%<Winkel size=\"18\" color=\"Indigo\" id=\"Winkel55\" value=\"45\"/>
%<Winkel size=\"18\" color=\"Ivory\" id=\"Winkel56\" value=\"45.00000000000001\"/>
%<Winkel size=\"18\" color=\"Khaki\" id=\"Winkel57\" value=\"44.911592050559506\"/>
%<Winkel size=\"18\" color=\"Lavender\" id=\"Winkel58\" value=\"45\"/>
%<Winkel size=\"18\" color=\"LavenderBlush\" id=\"Winkel59\" value=\"45\"/>
%<Winkel size=\"18\" color=\"LawnGreen\" id=\"Winkel60\" value=\"45\"/>
%<Winkel size=\"18\" color=\"LemonChiffon\" id=\"Winkel61\" value=\"45\"/>
%<Winkel size=\"18\" color=\"LightBlue\" id=\"Winkel62\" value=\"45\"/>
%<Winkel size=\"18\" color=\"LightCoral\" id=\"Winkel63\" value=\"287.2475101574122\"/>
%<Winkel size=\"18\" color=\"LightCyan\" id=\"Winkel64\" value=\"45\"/>
%<Winkel size=\"18\" color=\"LightGoldenrodYellow\" id=\"Winkel65\" value=\"45.000000000000064\"/>
%<Winkel size=\"18\" color=\"LightGreen\" id=\"Winkel66\" value=\"44.99999999999999\"/>
%<Winkel size=\"18\" color=\"LightGray\" id=\"Winkel67\" value=\"44.99999999999999\"/>
%<Winkel size=\"18\" color=\"LightPink\" id=\"Winkel68\" value=\"45\"/>
%<Winkel size=\"18\" color=\"LightSalmon\" id=\"Winkel69\" value=\"45\"/>
%<Winkel size=\"18\" color=\"LightSeaGreen\" id=\"Winkel70\" value=\"45\"/>
%<Winkel size=\"18\" color=\"LightSkyBlue\" id=\"Winkel71\" value=\"271.0449756281402\"/>
%<Winkel size=\"18\" color=\"LightSlateGray\" id=\"Winkel72\" value=\"45\"/>
%<Winkel size=\"18\" color=\"LightSteelBlue\" id=\"Winkel73\" value=\"45.00000000000001\"/>
%<Winkel size=\"18\" color=\"LightYellow\" id=\"Winkel74\" value=\"45.00000000000001\"/>
%<Winkel size=\"18\" color=\"Lime\" id=\"Winkel75\" value=\"45.00000000000001\"/>
%<Winkel size=\"18\" color=\"LimeGreen\" id=\"Winkel76\" value=\"45.00000000000001\"/>
%<Winkel size=\"18\" color=\"Linen\" id=\"Winkel77\" value=\"45.00000000000001\"/>
%<Winkel size=\"18\" color=\"Maroon\" id=\"Winkel78\" value=\"45\"/>
%<Winkel size=\"18\" color=\"MediumAquamarine\" id=\"Winkel79\" value=\"289.6799787422597\"/>
%<Winkel size=\"18\" color=\"MediumBlue\" id=\"Winkel80\" value=\"45.00000000000001\"/>
%<Winkel size=\"18\" color=\"MediumOrchid\" id=\"Winkel81\" value=\"45.00000000000001\"/>
%<Winkel size=\"18\" color=\"MediumPurple\" id=\"Winkel82\" value=\"45\"/>
%<Winkel size=\"18\" color=\"MediumSeaGreen\" id=\"Winkel83\" value=\"45.00000000000001\"/>
%<Winkel size=\"18\" color=\"MediumSlateBlue\" id=\"Winkel84\" value=\"45.00000000000001\"/>
%<Winkel size=\"18\" color=\"MediumSpringGreen\" id=\"Winkel85\" value=\"45\"/>
%<Winkel size=\"18\" color=\"MediumTurquoise\" id=\"Winkel86\" value=\"45\"/>
%<Winkel size=\"18\" color=\"MediumVioletRed\" id=\"Winkel87\" value=\"276.5301804195562\"/>
%<Winkel size=\"18\" color=\"MidnightBlue\" id=\"Winkel88\" value=\"45.00000000000001\"/>
%<Winkel size=\"18\" color=\"MintCream\" id=\"Winkel89\" value=\"45.00000000000001\"/>
%<Winkel size=\"18\" color=\"MistyRose\" id=\"Winkel90\" value=\"44.99999999999999\"/>
%<Winkel size=\"18\" color=\"Moccasin\" id=\"Winkel91\" value=\"45\"/>
%<Winkel size=\"18\" color=\"NavajoWhite\" id=\"Winkel92\" value=\"45\"/>
%<Winkel size=\"18\" color=\"Navy\" id=\"Winkel93\" value=\"45.00000000000001\"/>
%<Winkel size=\"18\" color=\"OldLace\" id=\"Winkel94\" value=\"45\"/>
%<Winkel size=\"18\" color=\"Olive\" id=\"Winkel95\" value=\"45\"/>
%<Winkel size=\"18\" color=\"OliveDrab\" id=\"Winkel96\" value=\"45\"/>
%<Winkel size=\"18\" color=\"Orange\" id=\"Winkel97\" value=\"351.60856120518304\"/>
%<Winkel size=\"18\" color=\"OrangeRed\" id=\"Winkel98\" value=\"45.00000000000001\"/>
%<Feinjustieren Anzahl=\"101,98\"/>
%<Rechenweg>
%P[1]=[-90.47502624995381,373.3560161118893]; P[2]=[-159.99984570994133,323.7312977681336]; D=ab(1,2); A(2,1); Q(3,1,2,jum(blauerWinkel)*D,jum(gruenerWinkel)*D); Q(4,3,2,jum(orangerWinkel)*D,jum(vierterWinkel)*D); Q(5,4,2,jum(fuenfterWinkel)*D,jum(sechsterWinkel)*D); M(45,3,1,siebenterWinkel,0,jum(achterWinkel)*D); M(49,45,3,neunterWinkel,0,jum(zehnterWinkel)*D); Q(43,4,49,jum(elfterWinkel)*D,jum(zwoelfterWinkel)*D); Q(48,45,49,jum(dreizehnterWinkel)*D,jum(vierzehnterWinkel)*D); M(46,48,45,fuenfzehnterWinkel,0,jum(sechzehnterWinkel)*D); M(50,46,48,siebzehnterWinkel,0,jum(achtzehnterWinkel)*D); M(51,50,46,Winkel19,0,jum(Winkel20)*D); Q(47,50,51,jum(Winkel21)*D,jum(Winkel22)*D); M(44,49,45,Winkel23,0,jum(Winkel24)*D); Q(40,44,43,jum(Winkel25)*D,jum(Winkel26)*D); Q(42,50,44,jum(Winkel27)*D,jum(Winkel28)*D); Q(41,42,44,jum(Winkel29)*D,jum(Winkel30)*D); Q(39,41,40,jum(Winkel31)*D,jum(Winkel32)*D); M(37,5,4,Winkel33,0,jum(Winkel34)*D); M(36,37,5,Winkel35,0,jum(Winkel36)*D); Q(34,40,36,jum(Winkel37)*D,jum(Winkel38)*D); Q(35,34,36,jum(Winkel39)*D,jum(Winkel40)*D); Q(33,34,35,jum(Winkel41)*D,jum(Winkel42)*D); M(31,33,34,Winkel43,0,jum(Winkel44)*D); Q(30,39,31,jum(Winkel45)*D,jum(Winkel46)*D); Q(32,31,30,jum(Winkel47)*D,jum(Winkel48)*D); Q(29,30,31,jum(Winkel49)*D,jum(Winkel50)*D); Q(28,29,41,jum(Winkel51)*D,jum(Winkel52)*D); Q(27,28,29,jum(Winkel53)*D,jum(Winkel54)*D); Q(26,28,27,jum(Winkel55)*D,jum(Winkel56)*D); Q(24,42,26,jum(Winkel57)*D,jum(Winkel58)*D); Q(25,24,26,jum(Winkel59)*D,jum(Winkel60)*D); Q(23,24,25,jum(Winkel61)*D,jum(Winkel62)*D); M(21,23,24,Winkel63,0,jum(Winkel64)*D); Q(20,51,21,jum(Winkel65)*D,jum(Winkel66)*D); Q(22,23,21,jum(Winkel67)*D,jum(Winkel68)*D); Q(19,20,21,jum(Winkel69)*D,jum(Winkel70)*D); M(17,19,20,Winkel71,0,jum(Winkel72)*D); Q(16,47,17,jum(Winkel73)*D,jum(Winkel74)*D); Q(18,19,17,jum(Winkel75)*D,jum(Winkel76)*D); Q(15,16,17,jum(Winkel77)*D,jum(Winkel78)*D); M(13,15,16,Winkel79,0,jum(Winkel80)*D); Q(12,46,13,jum(Winkel81)*D,jum(Winkel82)*D); Q(14,13,12,jum(Winkel83)*D,jum(Winkel84)*D); Q(11,12,13,jum(Winkel85)*D,jum(Winkel86)*D); M(9,11,12,Winkel87,0,jum(Winkel88)*D); Q(10,11,9,jum(Winkel89)*D,jum(Winkel90)*D); Q(8,10,9,jum(Winkel91)*D,jum(Winkel92)*D); Q(6,8,1,jum(Winkel93)*D,jum(Winkel94)*D); Q(7,1,6,jum(Winkel95)*D,jum(Winkel96)*D); M(38,5,4,Winkel97,0,jum(Winkel98)*D);
%R(3,1,\"green\");
%R(3,2,\"green\");
%R(4,3,\"green\");
%R(4,2,\"green\");
%R(5,4,\"green\");
%R(5,2,\"green\");
%R(45,3,\"green\");
%R(43,4,\"green\");
%R(48,49,\"green\");
%R(46,48,\"green\");
%R(50,46,\"green\");
%R(47,50,\"green\");
%R(47,51,\"green\");
%R(44,49,\"green\");
%R(40,44,\"green\");
%R(40,43,\"green\");
%R(42,44,\"green\");
%R(41,42,\"green\");
%R(41,44,\"green\");
%R(39,41,\"green\");
%R(39,40,\"green\");
%R(37,5,\"green\");
%R(36,37,\"green\");
%R(34,40,\"green\");
%R(34,36,\"green\");
%R(35,34,\"green\");
%R(35,36,\"green\");
%A(35,37); R(35,37,\"green\");
%R(33,34,\"green\");
%R(33,35,\"green\");
%R(31,33,\"green\");
%R(30,39,\"green\");
%R(30,31,\"green\");
%R(32,31,\"green\");
%R(32,30,\"green\");
%A(32,33); R(32,33,\"green\");
%A(32,39); R(32,39,\"green\");
%R(29,30,\"green\");
%R(29,31,\"green\");
%R(28,29,\"green\");
%R(28,41,\"green\");
%R(27,28,\"green\");
%R(27,29,\"green\");
%R(26,28,\"green\");
%R(26,27,\"green\");
%R(24,26,\"green\");
%R(25,24,\"green\");
%R(25,26,\"green\");
%A(25,27); R(25,27,\"green\");
%R(23,24,\"green\");
%R(23,25,\"green\");
%R(21,23,\"green\");
%R(20,21,\"green\");
%R(22,23,\"green\");
%R(22,21,\"green\");
%A(22,20); R(22,20,\"green\");
%A(22,51); R(22,51,\"green\");
%R(19,20,\"green\");
%R(19,21,\"green\");
%R(17,19,\"green\");
%R(16,47,\"green\");
%R(16,17,\"green\");
%R(18,19,\"green\");
%R(18,17,\"green\");
%A(18,16); R(18,16,\"green\");
%A(18,47); R(18,47,\"green\");
%R(15,16,\"green\");
%R(15,17,\"green\");
%R(13,15,\"green\");
%R(12,46,\"green\");
%R(12,13,\"green\");
%R(14,13,\"green\");
%R(14,12,\"green\");
%A(14,15); R(14,15,\"green\");
%A(14,46); R(14,46,\"green\");
%R(11,12,\"green\");
%R(11,13,\"green\");
%R(9,11,\"green\");
%R(10,11,\"green\");
%R(10,9,\"green\");
%A(10,48); R(10,48,\"green\");
%R(8,10,\"green\");
%R(8,9,\"green\");
%R(6,8,\"green\");
%R(6,1,\"green\");
%A(6,45); R(6,45,\"green\");
%R(7,1,\"green\");
%R(7,6,\"green\");
%A(7,8); R(7,8,\"green\");
%A(7,9); R(7,9,\"green\");
%R(38,5,\"green\");
%A(38,37); R(38,37,\"green\");
%A(38,36); R(38,36,\"green\");
%R(20,51,\"green\");
%R(49,45,\"green\");
%R(43,49,\"green\");
%R(51,50,\"green\");
%R(48,45,\"green\");
%R(24,42,\"green\");
%R(42,50,\"green\");
%A(38,43); R(38,43,\"green\");
%</Rechenweg>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Crimson}{rgb}{0.86,0.08,0.23}
\definecolor{DarkGray}{rgb}{0.66,0.66,0.66}
\definecolor{DarkSlateBlue}{rgb}{0.28,0.24,0.54}
\definecolor{DarkTurquoise}{rgb}{0.00,0.80,0.82}
\definecolor{ForestGreen}{rgb}{0.13,0.54,0.13}
\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{LightSeaGreen}{rgb}{0.13,0.70,0.66}
\definecolor{LightSkyBlue}{rgb}{0.53,0.80,0.98}
\definecolor{LightSlateGray}{rgb}{0.46,0.53,0.60}
\definecolor{MediumAquamarine}{rgb}{0.40,0.80,0.66}
\definecolor{MediumVioletRed}{rgb}{0.78,0.08,0.52}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.78/5.81,
2/0.96/5.22,
3/1.87/4.81,
4/1.06/4.23,
5/0.15/4.64,
6/2.03/4.84,
7/2.74/5.54,
8/2.99/4.57,
9/3.71/5.27,
10/3.96/4.30,
11/4.67/5.00,
12/4.29/4.08,
13/5.28/4.22,
14/4.91/3.29,
15/5.90/3.43,
16/4.95/3.11,
17/5.70/2.45,
18/4.75/2.13,
19/5.49/1.47,
20/4.52/1.69,
21/4.81/0.73,
22/3.84/0.96,
23/4.13/0.00,
24/3.64/0.87,
25/3.13/0.00,
26/2.64/0.87,
27/2.13/0.00,
28/1.635/0.867,
29/1.13/0.00,
30/1.564/0.904,
31/0.57/0.82,
32/1.00/1.73,
33/0.00/1.65,
34/0.89/2.10,
35/0.05/2.65,
36/0.94/3.10,
37/0.10/3.65,
38/0.99/4.10,
39/1.99/1.81,
40/1.65/2.75,
41/2.62/1.03,
42/3.27/1.79,
43/1.92/3.71,
44/2.28/1.97,
45/2.12/3.84,
46/3.92/3.15,
47/4.00/2.80,
48/3.12/3.75,
49/2.54/2.93,
50/3.00/2.75,
51/3.54/1.91}
\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 {
3/95.52/284.49/0.4/LightBlue,
45/104.49/294.85/0.4/LightCyan,
48/174.85/322.93/0.4/LightSeaGreen,
46/142.93/203.48/0.4/LightSlateGray,
50/23.48/302.76/0.4/Crimson,
49/114.85/254.82/0.4/DarkGray,
5/335.52/627.13/0.4/DarkSlateBlue,
37/87.13/327.13/0.4/DarkTurquoise,
33/27.13/304.57/0.4/ForestGreen,
23/119.99/407.23/0.4/LightCoral,
19/167.23/438.28/0.4/LightSkyBlue,
15/198.28/487.96/0.4/MediumAquamarine,
11/247.96/524.49/0.4/MediumVioletRed,
5/335.52/687.13/0.3/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,
6/8, 6/1, 6/45,
7/1, 7/6, 7/8, 7/9,
8/10, 8/9,
9/11,
10/11, 10/9, 10/48,
11/12, 11/13,
12/46, 12/13,
13/15,
14/13, 14/12, 14/15, 14/46,
15/16, 15/17,
16/47, 16/17,
17/19,
18/19, 18/17, 18/16, 18/47,
19/20, 19/21,
20/51, 20/21,
21/23,
22/23, 22/21, 22/20, 22/51,
23/24, 23/25,
24/42, 24/26,
25/24, 25/26, 25/27,
26/28, 26/27,
27/28, 27/29,
28/29, 28/41,
29/30, 29/31,
30/39, 30/31,
31/33,
32/31, 32/30, 32/33, 32/39,
33/34, 33/35,
34/40, 34/36,
35/34, 35/36, 35/37,
36/37,
37/5,
38/5, 38/37, 38/36, 38/43,
39/41, 39/40,
40/44, 40/43,
41/42, 41/44,
42/50, 42/44,
43/4, 43/49,
44/49,
45/3,
46/48,
47/50, 47/51,
48/45, 48/49,
49/45,
50/46,
51/50}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,51}
\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);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-24) -- (p-42);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-38) -- (p-43);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-42) -- (p-50);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
3/95.52/284.49/0.4/LightBlue,
45/104.49/294.85/0.4/LightCyan,
48/174.85/322.93/0.4/LightSeaGreen,
46/142.93/203.48/0.4/LightSlateGray,
50/23.48/302.76/0.4/Crimson,
49/114.85/254.82/0.4/DarkGray,
5/335.52/627.13/0.4/DarkSlateBlue,
37/87.13/327.13/0.4/DarkTurquoise,
33/27.13/304.57/0.4/ForestGreen,
23/119.99/407.23/0.4/LightCoral,
19/167.23/438.28/0.4/LightSkyBlue,
15/198.28/487.96/0.4/MediumAquamarine,
11/247.96/524.49/0.4/MediumVioletRed,
5/335.52/687.13/0.3/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 {
1/66,
2/66,
3/306,
4/246,
5/117,
6/194,
7/14,
8/254,
9/74,
10/314,
11/14,
12/98,
13/338,
14/278,
15/338,
16/48,
17/348,
18/168,
19/17,
20/17,
21/17,
22/197,
23/330,
24/30,
25/330,
26/30,
27/210,
28/90,
29/210,
30/35,
31/275,
32/155,
33/237,
34/357,
35/177,
36/357,
37/177,
38/57,
39/35,
40/77,
41/260,
42/20,
43/104,
44/284,
45/145,
46/218,
47/33,
48/25,
49/265,
50/153,
51/273}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>Automatisch generierte Eingabe zu: Fig.5 4-regular planar graph with 51 vertices. This graph is rigid and asymmetric.</Bildtext>
%<Ausrichten von="27" nach="25"/>
%<Winkel size="18" color="blue" id="blauerWinkel" value="44.999920611762484"/>
%<Winkel size="18" color="green" id="gruenerWinkel" value="45.002776263842804"/>
%<Winkel size="18" color="orange" id="orangerWinkel" value="44.997677044551736"/>
%<Winkel size="18" color="violet" id="vierterWinkel" value="44.997217462432886"/>
%<Winkel size="18" color="teal" id="fuenfterWinkel" value="44.964114597046155"/>
%<Winkel size="18" color="lime" id="sechsterWinkel" value="45.003410751395116"/>
%<Winkel size="18" color="LightBlue" id="siebenterWinkel" value="189.02909873461255"/>
%<Winkel size="18" color="LightCoral" id="achterWinkel" value="45.0025009013814"/>
%<Winkel size="18" color="LightCyan" id="neunterWinkel" value="190.27191701356222"/>
%<Winkel size="18" color="LightGoldenrodYellow" id="zehnterWinkel" value="45.00242725379248"/>
%<Winkel size="18" color="LightGreen" id="elfterWinkel" value="44.96361886469813"/>
%<Winkel size="18" color="LightGray" id="zwoelfterWinkel" value="44.99923604666663"/>
%<Winkel size="18" color="LightPink" id="dreizehnterWinkel" value="44.99958274352372"/>
%<Winkel size="18" color="LightSalmon" id="vierzehnterWinkel" value="45.00303367258632"/>
%<Winkel size="18" color="LightSeaGreen" id="fuenfzehnterWinkel" value="148.1707562195201"/>
%<Winkel size="18" color="LightSkyBlue" id="sechzehnterWinkel" value="44.998549834471156"/>
%<Winkel size="18" color="LightSlateGray" id="siebzehnterWinkel" value="59.4802915376566"/>
%<Winkel size="18" color="LightSteelBlue" id="achtzehnterWinkel" value="44.98221884179663"/>
%<Winkel size="18" color="Crimson" id="Winkel19" value="279.95734983872"/>
%<Winkel size="18" color="DarkBlue" id="Winkel20" value="45.02359654018318"/>
%<Winkel size="18" color="DarkCyan" id="Winkel21" value="45.01054274439624"/>
%<Winkel size="18" color="DarkGoldenrod" id="Winkel22" value="45.006151840124616"/>
%<Winkel size="18" color="DarkGray" id="Winkel23" value="138.67939484606057"/>
%<Winkel size="18" color="DarkGreen" id="Winkel24" value="45.00426683264632"/>
%<Winkel size="18" color="DarkKhaki" id="Winkel25" value="45.00283002600061"/>
%<Winkel size="18" color="DarkMagenta" id="Winkel26" value="44.99474964094099"/>
%<Winkel size="18" color="DarkOliveGreen" id="Winkel27" value="44.97285235768148"/>
%<Winkel size="18" color="DarkOrange" id="Winkel28" value="44.998152625124"/>
%<Winkel size="18" color="DarkOrchid" id="Winkel29" value="44.9978685851894"/>
%<Winkel size="18" color="DarkRed" id="Winkel30" value="45.00702731059546"/>
%<Winkel size="18" color="DarkSalmon" id="Winkel31" value="44.99364081531139"/>
%<Winkel size="18" color="DarkSeaGreen" id="Winkel32" value="44.99394299743615"/>
%<Winkel size="18" color="DarkSlateBlue" id="Winkel33" value="291.2031149062783"/>
%<Winkel size="18" color="DarkSlateGray" id="Winkel34" value="44.997316090854"/>
%<Winkel size="18" color="DarkTurquoise" id="Winkel35" value="239.90543256360937"/>
%<Winkel size="18" color="DarkViolet" id="Winkel36" value="44.99774626122254"/>
%<Winkel size="18" color="DeepPink" id="Winkel37" value="44.9976483408938"/>
%<Winkel size="18" color="DeepSkyBlue" id="Winkel38" value="45.00291709319561"/>
%<Winkel size="18" color="DimGray" id="Winkel39" value="44.99774701219944"/>
%<Winkel size="18" color="DodgerBlue" id="Winkel40" value="45.00225301098184"/>
%<Winkel size="18" color="FireBrick" id="Winkel41" value="45.00030513259907"/>
%<Winkel size="18" color="FloralWhite" id="Winkel42" value="45.001820989790474"/>
%<Winkel size="18" color="ForestGreen" id="Winkel43" value="278.0124973106346"/>
%<Winkel size="18" color="Fuchsia" id="Winkel44" value="45.00221405169269"/>
%<Winkel size="18" color="Gainsboro" id="Winkel45" value="44.99931540429439"/>
%<Winkel size="18" color="GhostWhite" id="Winkel46" value="44.99999986762294"/>
%<Winkel size="18" color="Gold" id="Winkel47" value="44.99999966468424"/>
%<Winkel size="18" color="Goldenrod" id="Winkel48" value="45.0000000925683"/>
%<Winkel size="18" color="Gray" id="Winkel49" value="44.99931551633651"/>
%<Winkel size="18" color="Green" id="Winkel50" value="45.00221394990952"/>
%<Winkel size="18" color="GreenYellow" id="Winkel51" value="44.99861047545535"/>
%<Winkel size="18" color="Honeydew" id="Winkel52" value="45.000244853879096"/>
%<Winkel size="18" color="HotPink" id="Winkel53" value="45.001435894252424"/>
%<Winkel size="18" color="IndianRed" id="Winkel54" value="45.00224600929001"/>
%<Winkel size="18" color="Indigo" id="Winkel55" value="44.9983455998264"/>
%<Winkel size="18" color="Ivory" id="Winkel56" value="44.99856352137355"/>
%<Winkel size="18" color="Khaki" id="Winkel57" value="44.97310563968774"/>
%<Winkel size="18" color="Lavender" id="Winkel58" value="44.99690912519378"/>
%<Winkel size="18" color="LavenderBlush" id="Winkel59" value="44.998555777552816"/>
%<Winkel size="18" color="LawnGreen" id="Winkel60" value="45.00143585925098"/>
%<Winkel size="18" color="LemonChiffon" id="Winkel61" value="44.97256667637732"/>
%<Winkel size="18" color="LightBlue" id="Winkel62" value="45.00512163501002"/>
%<Winkel size="18" color="LightCoral" id="Winkel63" value="286.8851736098871"/>
%<Winkel size="18" color="LightCyan" id="Winkel64" value="44.998461079534195"/>
%<Winkel size="18" color="LightGoldenrodYellow" id="Winkel65" value="45.00229929814892"/>
%<Winkel size="18" color="LightGreen" id="Winkel66" value="45.000015346597394"/>
%<Winkel size="18" color="LightGray" id="Winkel67" value="45.02597683970119"/>
%<Winkel size="18" color="LightPink" id="Winkel68" value="44.99998251478087"/>
%<Winkel size="18" color="LightSalmon" id="Winkel69" value="45.00228513708102"/>
%<Winkel size="18" color="LightSeaGreen" id="Winkel70" value="44.99844466400142"/>
%<Winkel size="18" color="LightSkyBlue" id="Winkel71" value="270.99162765460375"/>
%<Winkel size="18" color="LightSlateGray" id="Winkel72" value="44.99948390712597"/>
%<Winkel size="18" color="LightSteelBlue" id="Winkel73" value="45.01539868857148"/>
%<Winkel size="18" color="LightYellow" id="Winkel74" value="44.99999418126762"/>
%<Winkel size="18" color="Lime" id="Winkel75" value="44.9982863889359"/>
%<Winkel size="18" color="LimeGreen" id="Winkel76" value="45.000005481021006"/>
%<Winkel size="18" color="Linen" id="Winkel77" value="45.01539819857957"/>
%<Winkel size="18" color="Maroon" id="Winkel78" value="44.99948955766944"/>
%<Winkel size="18" color="MediumAquamarine" id="Winkel79" value="289.99322923649487"/>
%<Winkel size="18" color="MediumBlue" id="Winkel80" value="45.00253129883014"/>
%<Winkel size="18" color="MediumOrchid" id="Winkel81" value="44.99604815610316"/>
%<Winkel size="18" color="MediumPurple" id="Winkel82" value="45.00000518160969"/>
%<Winkel size="18" color="MediumSeaGreen" id="Winkel83" value="44.99999214009517"/>
%<Winkel size="18" color="MediumSlateBlue" id="Winkel84" value="44.99999661842605"/>
%<Winkel size="18" color="MediumSpringGreen" id="Winkel85" value="44.996043874768155"/>
%<Winkel size="18" color="MediumTurquoise" id="Winkel86" value="45.002524778080556"/>
%<Winkel size="18" color="MediumVioletRed" id="Winkel87" value="276.52326052517077"/>
%<Winkel size="18" color="MidnightBlue" id="Winkel88" value="45.00107661009278"/>
%<Winkel size="18" color="MintCream" id="Winkel89" value="45.00280317052216"/>
%<Winkel size="18" color="MistyRose" id="Winkel90" value="44.99979508777183"/>
%<Winkel size="18" color="Moccasin" id="Winkel91" value="44.99954396507075"/>
%<Winkel size="18" color="NavajoWhite" id="Winkel92" value="45.00020497862781"/>
%<Winkel size="18" color="Navy" id="Winkel93" value="44.99974896203554"/>
%<Winkel size="18" color="OldLace" id="Winkel94" value="44.99951860070741"/>
%<Winkel size="18" color="Olive" id="Winkel95" value="45.00066670648813"/>
%<Winkel size="18" color="OliveDrab" id="Winkel96" value="45.00020495363063"/>
%<Winkel size="18" color="Orange" id="Winkel97" value="351.1703336066315"/>
%<Winkel size="18" color="OrangeRed" id="Winkel98" value="45.03552899056538"/>
%<Feinjustieren Anzahl="101,98"/>
%<Rechenweg>
%P[1]=[-90.47502624995381,373.3560161118893]; P[2]=[-159.99984570994133,323.7312977681336]; D=ab(1,2); A(2,1); Q(3,1,2,jum(blauerWinkel)*D,jum(gruenerWinkel)*D); Q(4,3,2,jum(orangerWinkel)*D,jum(vierterWinkel)*D); Q(5,4,2,jum(fuenfterWinkel)*D,jum(sechsterWinkel)*D); M(45,3,1,siebenterWinkel,0,jum(achterWinkel)*D); M(49,45,3,neunterWinkel,0,jum(zehnterWinkel)*D); Q(43,4,49,jum(elfterWinkel)*D,jum(zwoelfterWinkel)*D); Q(48,45,49,jum(dreizehnterWinkel)*D,jum(vierzehnterWinkel)*D); M(46,48,45,fuenfzehnterWinkel,0,jum(sechzehnterWinkel)*D); M(50,46,48,siebzehnterWinkel,0,jum(achtzehnterWinkel)*D); M(51,50,46,Winkel19,0,jum(Winkel20)*D); Q(47,50,51,jum(Winkel21)*D,jum(Winkel22)*D); M(44,49,45,Winkel23,0,jum(Winkel24)*D); Q(40,44,43,jum(Winkel25)*D,jum(Winkel26)*D); Q(42,50,44,jum(Winkel27)*D,jum(Winkel28)*D); Q(41,42,44,jum(Winkel29)*D,jum(Winkel30)*D); Q(39,41,40,jum(Winkel31)*D,jum(Winkel32)*D); M(37,5,4,Winkel33,0,jum(Winkel34)*D); M(36,37,5,Winkel35,0,jum(Winkel36)*D); Q(34,40,36,jum(Winkel37)*D,jum(Winkel38)*D); Q(35,34,36,jum(Winkel39)*D,jum(Winkel40)*D); Q(33,34,35,jum(Winkel41)*D,jum(Winkel42)*D); M(31,33,34,Winkel43,0,jum(Winkel44)*D); Q(30,39,31,jum(Winkel45)*D,jum(Winkel46)*D); Q(32,31,30,jum(Winkel47)*D,jum(Winkel48)*D); Q(29,30,31,jum(Winkel49)*D,jum(Winkel50)*D); Q(28,29,41,jum(Winkel51)*D,jum(Winkel52)*D); Q(27,28,29,jum(Winkel53)*D,jum(Winkel54)*D); Q(26,28,27,jum(Winkel55)*D,jum(Winkel56)*D); Q(24,42,26,jum(Winkel57)*D,jum(Winkel58)*D); Q(25,24,26,jum(Winkel59)*D,jum(Winkel60)*D); Q(23,24,25,jum(Winkel61)*D,jum(Winkel62)*D); M(21,23,24,Winkel63,0,jum(Winkel64)*D); Q(20,51,21,jum(Winkel65)*D,jum(Winkel66)*D); Q(22,23,21,jum(Winkel67)*D,jum(Winkel68)*D); Q(19,20,21,jum(Winkel69)*D,jum(Winkel70)*D); M(17,19,20,Winkel71,0,jum(Winkel72)*D); Q(16,47,17,jum(Winkel73)*D,jum(Winkel74)*D); Q(18,19,17,jum(Winkel75)*D,jum(Winkel76)*D); Q(15,16,17,jum(Winkel77)*D,jum(Winkel78)*D); M(13,15,16,Winkel79,0,jum(Winkel80)*D); Q(12,46,13,jum(Winkel81)*D,jum(Winkel82)*D); Q(14,13,12,jum(Winkel83)*D,jum(Winkel84)*D); Q(11,12,13,jum(Winkel85)*D,jum(Winkel86)*D); M(9,11,12,Winkel87,0,jum(Winkel88)*D); Q(10,11,9,jum(Winkel89)*D,jum(Winkel90)*D); Q(8,10,9,jum(Winkel91)*D,jum(Winkel92)*D); Q(6,8,1,jum(Winkel93)*D,jum(Winkel94)*D); Q(7,1,6,jum(Winkel95)*D,jum(Winkel96)*D); M(38,5,4,Winkel97,0,jum(Winkel98)*D);
%R(3,1,"green");
%R(3,2,"green");
%R(4,3,"green");
%R(4,2,"green");
%R(5,4,"green");
%R(5,2,"green");
%R(45,3,"green");
%R(43,4,"green");
%R(48,49,"green");
%R(46,48,"green");
%R(50,46,"green");
%R(47,50,"green");
%R(47,51,"green");
%R(44,49,"green");
%R(40,44,"green");
%R(40,43,"green");
%R(42,44,"green");
%R(41,42,"green");
%R(41,44,"green");
%R(39,41,"green");
%R(39,40,"green");
%R(37,5,"green");
%R(36,37,"green");
%R(34,40,"green");
%R(34,36,"green");
%R(35,34,"green");
%R(35,36,"green");
%A(35,37); R(35,37,"green");
%R(33,34,"green");
%R(33,35,"green");
%R(31,33,"green");
%R(30,39,"green");
%R(30,31,"green");
%R(32,31,"green");
%R(32,30,"green");
%A(32,33); R(32,33,"green");
%A(32,39); R(32,39,"green");
%R(29,30,"green");
%R(29,31,"green");
%R(28,29,"green");
%R(28,41,"green");
%R(27,28,"green");
%R(27,29,"green");
%R(26,28,"green");
%R(26,27,"green");
%R(24,26,"green");
%R(25,24,"green");
%R(25,26,"green");
%A(25,27); R(25,27,"green");
%R(23,24,"green");
%R(23,25,"green");
%R(21,23,"green");
%R(20,21,"green");
%R(22,23,"green");
%R(22,21,"green");
%A(22,20); R(22,20,"green");
%A(22,51); R(22,51,"green");
%R(19,20,"green");
%R(19,21,"green");
%R(17,19,"green");
%R(16,47,"green");
%R(16,17,"green");
%R(18,19,"green");
%R(18,17,"green");
%A(18,16); R(18,16,"green");
%A(18,47); R(18,47,"green");
%R(15,16,"green");
%R(15,17,"green");
%R(13,15,"green");
%R(12,46,"green");
%R(12,13,"green");
%R(14,13,"green");
%R(14,12,"green");
%A(14,15); R(14,15,"green");
%A(14,46); R(14,46,"green");
%R(11,12,"green");
%R(11,13,"green");
%R(9,11,"green");
%R(10,11,"green");
%R(10,9,"green");
%A(10,48); R(10,48,"green");
%R(8,10,"green");
%R(8,9,"green");
%R(6,8,"green");
%R(6,1,"green");
%A(6,45); R(6,45,"green");
%R(7,1,"green");
%R(7,6,"green");
%A(7,8); R(7,8,"green");
%A(7,9); R(7,9,"green");
%R(38,5,"green");
%A(38,37); R(38,37,"green");
%A(38,36); R(38,36,"green");
%R(20,51,"green");
%R(49,45,"green");
%R(43,49,"green");
%R(51,50,"green");
%R(48,45,"green");
%R(24,42,"green");
%R(42,50,"green");
%A(38,43); R(38,43,"green");
%</Rechenweg>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Crimson}{rgb}{0.86,0.08,0.23}
\definecolor{DarkGray}{rgb}{0.66,0.66,0.66}
\definecolor{DarkSlateBlue}{rgb}{0.28,0.24,0.54}
\definecolor{DarkTurquoise}{rgb}{0.00,0.80,0.82}
\definecolor{ForestGreen}{rgb}{0.13,0.54,0.13}
\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{LightSeaGreen}{rgb}{0.13,0.70,0.66}
\definecolor{LightSkyBlue}{rgb}{0.53,0.80,0.98}
\definecolor{LightSlateGray}{rgb}{0.46,0.53,0.60}
\definecolor{MediumAquamarine}{rgb}{0.40,0.80,0.66}
\definecolor{MediumVioletRed}{rgb}{0.78,0.08,0.52}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.80/5.80,
2/0.99/5.22,
3/1.90/4.81,
4/1.08/4.23,
5/0.17/4.64,
6/2.05/4.83,
7/2.76/5.54,
8/3.01/4.57,
9/3.73/5.27,
10/3.98/4.30,
11/4.69/5.00,
12/4.32/4.07,
13/5.31/4.21,
14/4.93/3.29,
15/5.92/3.42,
16/4.97/3.12,
17/5.71/2.45,
18/4.76/2.14,
19/5.50/1.47,
20/4.53/1.69,
21/4.82/0.74,
22/3.85/0.96,
23/4.14/0.01,
24/3.64/0.87,
25/3.14/0.00,
26/2.64/0.87,
27/2.14/0.00,
28/1.637/0.867,
29/1.14/0.00,
30/1.566/0.904,
31/0.57/0.82,
32/1.00/1.73,
33/0.00/1.64,
34/0.89/2.09,
35/0.06/2.64,
36/0.95/3.09,
37/0.12/3.64,
38/1.01/4.09,
39/1.99/1.81,
40/1.65/2.75,
41/2.62/1.03,
42/3.27/1.80,
43/1.93/3.71,
44/2.28/1.97,
45/2.15/3.84,
46/3.94/3.15,
47/4.02/2.81,
48/3.14/3.75,
49/2.57/2.93,
50/3.02/2.77,
51/3.55/1.92}
\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 {
3/95.52/284.55/0.4/LightBlue,
45/104.55/294.83/0.4/LightCyan,
48/174.83/323.00/0.4/LightSeaGreen,
46/143.00/202.48/0.4/LightSlateGray,
50/22.48/302.44/0.4/Crimson,
49/114.83/253.51/0.4/DarkGray,
5/335.58/626.78/0.4/DarkSlateBlue,
37/86.78/326.69/0.4/DarkTurquoise,
33/26.69/304.70/0.4/ForestGreen,
23/120.15/407.04/0.4/LightCoral,
19/166.97/437.96/0.4/LightSkyBlue,
15/197.95/487.94/0.4/MediumAquamarine,
11/247.99/524.51/0.4/MediumVioletRed,
5/335.58/686.75/0.3/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,
6/8, 6/1, 6/45,
7/1, 7/6, 7/8, 7/9,
8/10, 8/9,
9/11,
10/11, 10/9, 10/48,
11/12, 11/13,
12/46, 12/13,
13/15,
14/13, 14/12, 14/15, 14/46,
15/16, 15/17,
16/47, 16/17,
17/19,
18/19, 18/17, 18/16, 18/47,
19/20, 19/21,
20/51, 20/21,
21/23,
22/23, 22/21, 22/20, 22/51,
23/24, 23/25,
24/42, 24/26,
25/24, 25/26, 25/27,
26/28, 26/27,
27/28, 27/29,
28/29, 28/41,
29/30, 29/31,
30/39, 30/31,
31/33,
32/31, 32/30, 32/33, 32/39,
33/34, 33/35,
34/40, 34/36,
35/34, 35/36, 35/37,
36/37,
37/5,
38/5, 38/37, 38/36, 38/43,
39/41, 39/40,
40/44, 40/43,
41/42, 41/44,
42/50, 42/44,
43/4, 43/49,
44/49,
45/3,
46/48,
47/50, 47/51,
48/45, 48/49,
49/45,
50/46,
51/50}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,51}
\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);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-5) -- (p-4);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-5) -- (p-2);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-10) -- (p-48);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-11) -- (p-12);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-12) -- (p-46);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-14) -- (p-15);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-14) -- (p-46);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-15) -- (p-16);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-16) -- (p-47);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-22) -- (p-23);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-22) -- (p-51);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-23) -- (p-24);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-23) -- (p-25);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-24) -- (p-42);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-24) -- (p-26);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-25) -- (p-27);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-34) -- (p-36);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-38) -- (p-5);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-38) -- (p-36);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-38) -- (p-43);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-39) -- (p-41);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-39) -- (p-40);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-40) -- (p-43);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-41) -- (p-44);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-42) -- (p-50);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-43) -- (p-4);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-44) -- (p-49);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-47) -- (p-50);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-47) -- (p-51);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-48) -- (p-49);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-50) -- (p-46);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-51) -- (p-50);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
3/95.52/284.55/0.4/LightBlue,
45/104.55/294.83/0.4/LightCyan,
48/174.83/323.00/0.4/LightSeaGreen,
46/143.00/202.48/0.4/LightSlateGray,
50/22.48/302.44/0.4/Crimson,
49/114.83/253.51/0.4/DarkGray,
5/335.58/626.78/0.4/DarkSlateBlue,
37/86.78/326.69/0.4/DarkTurquoise,
33/26.69/304.70/0.4/ForestGreen,
23/120.15/407.04/0.4/LightCoral,
19/166.97/437.96/0.4/LightSkyBlue,
15/197.95/487.94/0.4/MediumAquamarine,
11/247.99/524.51/0.4/MediumVioletRed,
5/335.58/686.75/0.3/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 {
1/135,
2/66,
3/6,
4/246,
5/117,
6/195,
7/15,
8/195,
9/15,
10/255,
11/15,
12/98,
13/98,
14/278,
15/48,
16/48,
17/48,
18/228,
19/17,
20/137,
21/317,
22/137,
23/257,
24/30,
25/210,
26/150,
27/330,
28/150,
29/275,
30/275,
31/275,
32/95,
33/237,
34/297,
35/237,
36/57,
37/117,
38/357,
39/35,
40/78,
41/260,
42/20,
43/104,
44/140,
45/145,
46/218,
47/168,
48/25,
49/265,
50/152,
51/137}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/0773e68f16563295e6895db022608f8b.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>Automatisch generierte Eingabe zu: Fig.5 4-regular planar graph with 51 vertices. This graph is rigid and asymmetric.</Bildtext>
%<Ausrichten von=\"27\" nach=\"25\"/>
%<Winkel size=\"18\" color=\"blue\" id=\"blauerWinkel\" value=\"44.999920611762484\"/>
%<Winkel size=\"18\" color=\"green\" id=\"gruenerWinkel\" value=\"45.002776263842804\"/>
%<Winkel size=\"18\" color=\"orange\" id=\"orangerWinkel\" value=\"44.997677044551736\"/>
%<Winkel size=\"18\" color=\"violet\" id=\"vierterWinkel\" value=\"44.997217462432886\"/>
%<Winkel size=\"18\" color=\"teal\" id=\"fuenfterWinkel\" value=\"44.964114597046155\"/>
%<Winkel size=\"18\" color=\"lime\" id=\"sechsterWinkel\" value=\"45.003410751395116\"/>
%<Winkel size=\"18\" color=\"LightBlue\" id=\"siebenterWinkel\" value=\"189.02909873461255\"/>
%<Winkel size=\"18\" color=\"LightCoral\" id=\"achterWinkel\" value=\"45.0025009013814\"/>
%<Winkel size=\"18\" color=\"LightCyan\" id=\"neunterWinkel\" value=\"190.27191701356222\"/>
%<Winkel size=\"18\" color=\"LightGoldenrodYellow\" id=\"zehnterWinkel\" value=\"45.00242725379248\"/>
%<Winkel size=\"18\" color=\"LightGreen\" id=\"elfterWinkel\" value=\"44.96361886469813\"/>
%<Winkel size=\"18\" color=\"LightGray\" id=\"zwoelfterWinkel\" value=\"44.99923604666663\"/>
%<Winkel size=\"18\" color=\"LightPink\" id=\"dreizehnterWinkel\" value=\"44.99958274352372\"/>
%<Winkel size=\"18\" color=\"LightSalmon\" id=\"vierzehnterWinkel\" value=\"45.00303367258632\"/>
%<Winkel size=\"18\" color=\"LightSeaGreen\" id=\"fuenfzehnterWinkel\" value=\"148.1707562195201\"/>
%<Winkel size=\"18\" color=\"LightSkyBlue\" id=\"sechzehnterWinkel\" value=\"44.998549834471156\"/>
%<Winkel size=\"18\" color=\"LightSlateGray\" id=\"siebzehnterWinkel\" value=\"59.4802915376566\"/>
%<Winkel size=\"18\" color=\"LightSteelBlue\" id=\"achtzehnterWinkel\" value=\"44.98221884179663\"/>
%<Winkel size=\"18\" color=\"Crimson\" id=\"Winkel19\" value=\"279.95734983872\"/>
%<Winkel size=\"18\" color=\"DarkBlue\" id=\"Winkel20\" value=\"45.02359654018318\"/>
%<Winkel size=\"18\" color=\"DarkCyan\" id=\"Winkel21\" value=\"45.01054274439624\"/>
%<Winkel size=\"18\" color=\"DarkGoldenrod\" id=\"Winkel22\" value=\"45.006151840124616\"/>
%<Winkel size=\"18\" color=\"DarkGray\" id=\"Winkel23\" value=\"138.67939484606057\"/>
%<Winkel size=\"18\" color=\"DarkGreen\" id=\"Winkel24\" value=\"45.00426683264632\"/>
%<Winkel size=\"18\" color=\"DarkKhaki\" id=\"Winkel25\" value=\"45.00283002600061\"/>
%<Winkel size=\"18\" color=\"DarkMagenta\" id=\"Winkel26\" value=\"44.99474964094099\"/>
%<Winkel size=\"18\" color=\"DarkOliveGreen\" id=\"Winkel27\" value=\"44.97285235768148\"/>
%<Winkel size=\"18\" color=\"DarkOrange\" id=\"Winkel28\" value=\"44.998152625124\"/>
%<Winkel size=\"18\" color=\"DarkOrchid\" id=\"Winkel29\" value=\"44.9978685851894\"/>
%<Winkel size=\"18\" color=\"DarkRed\" id=\"Winkel30\" value=\"45.00702731059546\"/>
%<Winkel size=\"18\" color=\"DarkSalmon\" id=\"Winkel31\" value=\"44.99364081531139\"/>
%<Winkel size=\"18\" color=\"DarkSeaGreen\" id=\"Winkel32\" value=\"44.99394299743615\"/>
%<Winkel size=\"18\" color=\"DarkSlateBlue\" id=\"Winkel33\" value=\"291.2031149062783\"/>
%<Winkel size=\"18\" color=\"DarkSlateGray\" id=\"Winkel34\" value=\"44.997316090854\"/>
%<Winkel size=\"18\" color=\"DarkTurquoise\" id=\"Winkel35\" value=\"239.90543256360937\"/>
%<Winkel size=\"18\" color=\"DarkViolet\" id=\"Winkel36\" value=\"44.99774626122254\"/>
%<Winkel size=\"18\" color=\"DeepPink\" id=\"Winkel37\" value=\"44.9976483408938\"/>
%<Winkel size=\"18\" color=\"DeepSkyBlue\" id=\"Winkel38\" value=\"45.00291709319561\"/>
%<Winkel size=\"18\" color=\"DimGray\" id=\"Winkel39\" value=\"44.99774701219944\"/>
%<Winkel size=\"18\" color=\"DodgerBlue\" id=\"Winkel40\" value=\"45.00225301098184\"/>
%<Winkel size=\"18\" color=\"FireBrick\" id=\"Winkel41\" value=\"45.00030513259907\"/>
%<Winkel size=\"18\" color=\"FloralWhite\" id=\"Winkel42\" value=\"45.001820989790474\"/>
%<Winkel size=\"18\" color=\"ForestGreen\" id=\"Winkel43\" value=\"278.0124973106346\"/>
%<Winkel size=\"18\" color=\"Fuchsia\" id=\"Winkel44\" value=\"45.00221405169269\"/>
%<Winkel size=\"18\" color=\"Gainsboro\" id=\"Winkel45\" value=\"44.99931540429439\"/>
%<Winkel size=\"18\" color=\"GhostWhite\" id=\"Winkel46\" value=\"44.99999986762294\"/>
%<Winkel size=\"18\" color=\"Gold\" id=\"Winkel47\" value=\"44.99999966468424\"/>
%<Winkel size=\"18\" color=\"Goldenrod\" id=\"Winkel48\" value=\"45.0000000925683\"/>
%<Winkel size=\"18\" color=\"Gray\" id=\"Winkel49\" value=\"44.99931551633651\"/>
%<Winkel size=\"18\" color=\"Green\" id=\"Winkel50\" value=\"45.00221394990952\"/>
%<Winkel size=\"18\" color=\"GreenYellow\" id=\"Winkel51\" value=\"44.99861047545535\"/>
%<Winkel size=\"18\" color=\"Honeydew\" id=\"Winkel52\" value=\"45.000244853879096\"/>
%<Winkel size=\"18\" color=\"HotPink\" id=\"Winkel53\" value=\"45.001435894252424\"/>
%<Winkel size=\"18\" color=\"IndianRed\" id=\"Winkel54\" value=\"45.00224600929001\"/>
%<Winkel size=\"18\" color=\"Indigo\" id=\"Winkel55\" value=\"44.9983455998264\"/>
%<Winkel size=\"18\" color=\"Ivory\" id=\"Winkel56\" value=\"44.99856352137355\"/>
%<Winkel size=\"18\" color=\"Khaki\" id=\"Winkel57\" value=\"44.97310563968774\"/>
%<Winkel size=\"18\" color=\"Lavender\" id=\"Winkel58\" value=\"44.99690912519378\"/>
%<Winkel size=\"18\" color=\"LavenderBlush\" id=\"Winkel59\" value=\"44.998555777552816\"/>
%<Winkel size=\"18\" color=\"LawnGreen\" id=\"Winkel60\" value=\"45.00143585925098\"/>
%<Winkel size=\"18\" color=\"LemonChiffon\" id=\"Winkel61\" value=\"44.97256667637732\"/>
%<Winkel size=\"18\" color=\"LightBlue\" id=\"Winkel62\" value=\"45.00512163501002\"/>
%<Winkel size=\"18\" color=\"LightCoral\" id=\"Winkel63\" value=\"286.8851736098871\"/>
%<Winkel size=\"18\" color=\"LightCyan\" id=\"Winkel64\" value=\"44.998461079534195\"/>
%<Winkel size=\"18\" color=\"LightGoldenrodYellow\" id=\"Winkel65\" value=\"45.00229929814892\"/>
%<Winkel size=\"18\" color=\"LightGreen\" id=\"Winkel66\" value=\"45.000015346597394\"/>
%<Winkel size=\"18\" color=\"LightGray\" id=\"Winkel67\" value=\"45.02597683970119\"/>
%<Winkel size=\"18\" color=\"LightPink\" id=\"Winkel68\" value=\"44.99998251478087\"/>
%<Winkel size=\"18\" color=\"LightSalmon\" id=\"Winkel69\" value=\"45.00228513708102\"/>
%<Winkel size=\"18\" color=\"LightSeaGreen\" id=\"Winkel70\" value=\"44.99844466400142\"/>
%<Winkel size=\"18\" color=\"LightSkyBlue\" id=\"Winkel71\" value=\"270.99162765460375\"/>
%<Winkel size=\"18\" color=\"LightSlateGray\" id=\"Winkel72\" value=\"44.99948390712597\"/>
%<Winkel size=\"18\" color=\"LightSteelBlue\" id=\"Winkel73\" value=\"45.01539868857148\"/>
%<Winkel size=\"18\" color=\"LightYellow\" id=\"Winkel74\" value=\"44.99999418126762\"/>
%<Winkel size=\"18\" color=\"Lime\" id=\"Winkel75\" value=\"44.9982863889359\"/>
%<Winkel size=\"18\" color=\"LimeGreen\" id=\"Winkel76\" value=\"45.000005481021006\"/>
%<Winkel size=\"18\" color=\"Linen\" id=\"Winkel77\" value=\"45.01539819857957\"/>
%<Winkel size=\"18\" color=\"Maroon\" id=\"Winkel78\" value=\"44.99948955766944\"/>
%<Winkel size=\"18\" color=\"MediumAquamarine\" id=\"Winkel79\" value=\"289.99322923649487\"/>
%<Winkel size=\"18\" color=\"MediumBlue\" id=\"Winkel80\" value=\"45.00253129883014\"/>
%<Winkel size=\"18\" color=\"MediumOrchid\" id=\"Winkel81\" value=\"44.99604815610316\"/>
%<Winkel size=\"18\" color=\"MediumPurple\" id=\"Winkel82\" value=\"45.00000518160969\"/>
%<Winkel size=\"18\" color=\"MediumSeaGreen\" id=\"Winkel83\" value=\"44.99999214009517\"/>
%<Winkel size=\"18\" color=\"MediumSlateBlue\" id=\"Winkel84\" value=\"44.99999661842605\"/>
%<Winkel size=\"18\" color=\"MediumSpringGreen\" id=\"Winkel85\" value=\"44.996043874768155\"/>
%<Winkel size=\"18\" color=\"MediumTurquoise\" id=\"Winkel86\" value=\"45.002524778080556\"/>
%<Winkel size=\"18\" color=\"MediumVioletRed\" id=\"Winkel87\" value=\"276.52326052517077\"/>
%<Winkel size=\"18\" color=\"MidnightBlue\" id=\"Winkel88\" value=\"45.00107661009278\"/>
%<Winkel size=\"18\" color=\"MintCream\" id=\"Winkel89\" value=\"45.00280317052216\"/>
%<Winkel size=\"18\" color=\"MistyRose\" id=\"Winkel90\" value=\"44.99979508777183\"/>
%<Winkel size=\"18\" color=\"Moccasin\" id=\"Winkel91\" value=\"44.99954396507075\"/>
%<Winkel size=\"18\" color=\"NavajoWhite\" id=\"Winkel92\" value=\"45.00020497862781\"/>
%<Winkel size=\"18\" color=\"Navy\" id=\"Winkel93\" value=\"44.99974896203554\"/>
%<Winkel size=\"18\" color=\"OldLace\" id=\"Winkel94\" value=\"44.99951860070741\"/>
%<Winkel size=\"18\" color=\"Olive\" id=\"Winkel95\" value=\"45.00066670648813\"/>
%<Winkel size=\"18\" color=\"OliveDrab\" id=\"Winkel96\" value=\"45.00020495363063\"/>
%<Winkel size=\"18\" color=\"Orange\" id=\"Winkel97\" value=\"351.1703336066315\"/>
%<Winkel size=\"18\" color=\"OrangeRed\" id=\"Winkel98\" value=\"45.03552899056538\"/>
%<Feinjustieren Anzahl=\"101,98\"/>
%<Rechenweg>
%P[1]=[-90.47502624995381,373.3560161118893]; P[2]=[-159.99984570994133,323.7312977681336]; D=ab(1,2); A(2,1); Q(3,1,2,jum(blauerWinkel)*D,jum(gruenerWinkel)*D); Q(4,3,2,jum(orangerWinkel)*D,jum(vierterWinkel)*D); Q(5,4,2,jum(fuenfterWinkel)*D,jum(sechsterWinkel)*D); M(45,3,1,siebenterWinkel,0,jum(achterWinkel)*D); M(49,45,3,neunterWinkel,0,jum(zehnterWinkel)*D); Q(43,4,49,jum(elfterWinkel)*D,jum(zwoelfterWinkel)*D); Q(48,45,49,jum(dreizehnterWinkel)*D,jum(vierzehnterWinkel)*D); M(46,48,45,fuenfzehnterWinkel,0,jum(sechzehnterWinkel)*D); M(50,46,48,siebzehnterWinkel,0,jum(achtzehnterWinkel)*D); M(51,50,46,Winkel19,0,jum(Winkel20)*D); Q(47,50,51,jum(Winkel21)*D,jum(Winkel22)*D); M(44,49,45,Winkel23,0,jum(Winkel24)*D); Q(40,44,43,jum(Winkel25)*D,jum(Winkel26)*D); Q(42,50,44,jum(Winkel27)*D,jum(Winkel28)*D); Q(41,42,44,jum(Winkel29)*D,jum(Winkel30)*D); Q(39,41,40,jum(Winkel31)*D,jum(Winkel32)*D); M(37,5,4,Winkel33,0,jum(Winkel34)*D); M(36,37,5,Winkel35,0,jum(Winkel36)*D); Q(34,40,36,jum(Winkel37)*D,jum(Winkel38)*D); Q(35,34,36,jum(Winkel39)*D,jum(Winkel40)*D); Q(33,34,35,jum(Winkel41)*D,jum(Winkel42)*D); M(31,33,34,Winkel43,0,jum(Winkel44)*D); Q(30,39,31,jum(Winkel45)*D,jum(Winkel46)*D); Q(32,31,30,jum(Winkel47)*D,jum(Winkel48)*D); Q(29,30,31,jum(Winkel49)*D,jum(Winkel50)*D); Q(28,29,41,jum(Winkel51)*D,jum(Winkel52)*D); Q(27,28,29,jum(Winkel53)*D,jum(Winkel54)*D); Q(26,28,27,jum(Winkel55)*D,jum(Winkel56)*D); Q(24,42,26,jum(Winkel57)*D,jum(Winkel58)*D); Q(25,24,26,jum(Winkel59)*D,jum(Winkel60)*D); Q(23,24,25,jum(Winkel61)*D,jum(Winkel62)*D); M(21,23,24,Winkel63,0,jum(Winkel64)*D); Q(20,51,21,jum(Winkel65)*D,jum(Winkel66)*D); Q(22,23,21,jum(Winkel67)*D,jum(Winkel68)*D); Q(19,20,21,jum(Winkel69)*D,jum(Winkel70)*D); M(17,19,20,Winkel71,0,jum(Winkel72)*D); Q(16,47,17,jum(Winkel73)*D,jum(Winkel74)*D); Q(18,19,17,jum(Winkel75)*D,jum(Winkel76)*D); Q(15,16,17,jum(Winkel77)*D,jum(Winkel78)*D); M(13,15,16,Winkel79,0,jum(Winkel80)*D); Q(12,46,13,jum(Winkel81)*D,jum(Winkel82)*D); Q(14,13,12,jum(Winkel83)*D,jum(Winkel84)*D); Q(11,12,13,jum(Winkel85)*D,jum(Winkel86)*D); M(9,11,12,Winkel87,0,jum(Winkel88)*D); Q(10,11,9,jum(Winkel89)*D,jum(Winkel90)*D); Q(8,10,9,jum(Winkel91)*D,jum(Winkel92)*D); Q(6,8,1,jum(Winkel93)*D,jum(Winkel94)*D); Q(7,1,6,jum(Winkel95)*D,jum(Winkel96)*D); M(38,5,4,Winkel97,0,jum(Winkel98)*D);
%R(3,1,\"green\");
%R(3,2,\"green\");
%R(4,3,\"green\");
%R(4,2,\"green\");
%R(5,4,\"green\");
%R(5,2,\"green\");
%R(45,3,\"green\");
%R(43,4,\"green\");
%R(48,49,\"green\");
%R(46,48,\"green\");
%R(50,46,\"green\");
%R(47,50,\"green\");
%R(47,51,\"green\");
%R(44,49,\"green\");
%R(40,44,\"green\");
%R(40,43,\"green\");
%R(42,44,\"green\");
%R(41,42,\"green\");
%R(41,44,\"green\");
%R(39,41,\"green\");
%R(39,40,\"green\");
%R(37,5,\"green\");
%R(36,37,\"green\");
%R(34,40,\"green\");
%R(34,36,\"green\");
%R(35,34,\"green\");
%R(35,36,\"green\");
%A(35,37); R(35,37,\"green\");
%R(33,34,\"green\");
%R(33,35,\"green\");
%R(31,33,\"green\");
%R(30,39,\"green\");
%R(30,31,\"green\");
%R(32,31,\"green\");
%R(32,30,\"green\");
%A(32,33); R(32,33,\"green\");
%A(32,39); R(32,39,\"green\");
%R(29,30,\"green\");
%R(29,31,\"green\");
%R(28,29,\"green\");
%R(28,41,\"green\");
%R(27,28,\"green\");
%R(27,29,\"green\");
%R(26,28,\"green\");
%R(26,27,\"green\");
%R(24,26,\"green\");
%R(25,24,\"green\");
%R(25,26,\"green\");
%A(25,27); R(25,27,\"green\");
%R(23,24,\"green\");
%R(23,25,\"green\");
%R(21,23,\"green\");
%R(20,21,\"green\");
%R(22,23,\"green\");
%R(22,21,\"green\");
%A(22,20); R(22,20,\"green\");
%A(22,51); R(22,51,\"green\");
%R(19,20,\"green\");
%R(19,21,\"green\");
%R(17,19,\"green\");
%R(16,47,\"green\");
%R(16,17,\"green\");
%R(18,19,\"green\");
%R(18,17,\"green\");
%A(18,16); R(18,16,\"green\");
%A(18,47); R(18,47,\"green\");
%R(15,16,\"green\");
%R(15,17,\"green\");
%R(13,15,\"green\");
%R(12,46,\"green\");
%R(12,13,\"green\");
%R(14,13,\"green\");
%R(14,12,\"green\");
%A(14,15); R(14,15,\"green\");
%A(14,46); R(14,46,\"green\");
%R(11,12,\"green\");
%R(11,13,\"green\");
%R(9,11,\"green\");
%R(10,11,\"green\");
%R(10,9,\"green\");
%A(10,48); R(10,48,\"green\");
%R(8,10,\"green\");
%R(8,9,\"green\");
%R(6,8,\"green\");
%R(6,1,\"green\");
%A(6,45); R(6,45,\"green\");
%R(7,1,\"green\");
%R(7,6,\"green\");
%A(7,8); R(7,8,\"green\");
%A(7,9); R(7,9,\"green\");
%R(38,5,\"green\");
%A(38,37); R(38,37,\"green\");
%A(38,36); R(38,36,\"green\");
%R(20,51,\"green\");
%R(49,45,\"green\");
%R(43,49,\"green\");
%R(51,50,\"green\");
%R(48,45,\"green\");
%R(24,42,\"green\");
%R(42,50,\"green\");
%A(38,43); R(38,43,\"green\");
%</Rechenweg>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
\definecolor{Crimson}{rgb}{0.86,0.08,0.23}
\definecolor{DarkGray}{rgb}{0.66,0.66,0.66}
\definecolor{DarkSlateBlue}{rgb}{0.28,0.24,0.54}
\definecolor{DarkTurquoise}{rgb}{0.00,0.80,0.82}
\definecolor{ForestGreen}{rgb}{0.13,0.54,0.13}
\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{LightSeaGreen}{rgb}{0.13,0.70,0.66}
\definecolor{LightSkyBlue}{rgb}{0.53,0.80,0.98}
\definecolor{LightSlateGray}{rgb}{0.46,0.53,0.60}
\definecolor{MediumAquamarine}{rgb}{0.40,0.80,0.66}
\definecolor{MediumVioletRed}{rgb}{0.78,0.08,0.52}
\definecolor{Orange}{rgb}{1.00,0.64,0.00}
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/1.80/5.80,
2/0.99/5.22,
3/1.90/4.81,
4/1.08/4.23,
5/0.17/4.64,
6/2.05/4.83,
7/2.76/5.54,
8/3.01/4.57,
9/3.73/5.27,
10/3.98/4.30,
11/4.69/5.00,
12/4.32/4.07,
13/5.31/4.21,
14/4.93/3.29,
15/5.92/3.42,
16/4.97/3.12,
17/5.71/2.45,
18/4.76/2.14,
19/5.50/1.47,
20/4.53/1.69,
21/4.82/0.74,
22/3.85/0.96,
23/4.14/0.01,
24/3.64/0.87,
25/3.14/0.00,
26/2.64/0.87,
27/2.14/0.00,
28/1.637/0.867,
29/1.14/0.00,
30/1.566/0.904,
31/0.57/0.82,
32/1.00/1.73,
33/0.00/1.64,
34/0.89/2.09,
35/0.06/2.64,
36/0.95/3.09,
37/0.12/3.64,
38/1.01/4.09,
39/1.99/1.81,
40/1.65/2.75,
41/2.62/1.03,
42/3.27/1.80,
43/1.93/3.71,
44/2.28/1.97,
45/2.15/3.84,
46/3.94/3.15,
47/4.02/2.81,
48/3.14/3.75,
49/2.57/2.93,
50/3.02/2.77,
51/3.55/1.92}
\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 {
3/95.52/284.55/0.4/LightBlue,
45/104.55/294.83/0.4/LightCyan,
48/174.83/323.00/0.4/LightSeaGreen,
46/143.00/202.48/0.4/LightSlateGray,
50/22.48/302.44/0.4/Crimson,
49/114.83/253.51/0.4/DarkGray,
5/335.58/626.78/0.4/DarkSlateBlue,
37/86.78/326.69/0.4/DarkTurquoise,
33/26.69/304.70/0.4/ForestGreen,
23/120.15/407.04/0.4/LightCoral,
19/166.97/437.96/0.4/LightSkyBlue,
15/197.95/487.94/0.4/MediumAquamarine,
11/247.99/524.51/0.4/MediumVioletRed,
5/335.58/686.75/0.3/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,
6/8, 6/1, 6/45,
7/1, 7/6, 7/8, 7/9,
8/10, 8/9,
9/11,
10/11, 10/9, 10/48,
11/12, 11/13,
12/46, 12/13,
13/15,
14/13, 14/12, 14/15, 14/46,
15/16, 15/17,
16/47, 16/17,
17/19,
18/19, 18/17, 18/16, 18/47,
19/20, 19/21,
20/51, 20/21,
21/23,
22/23, 22/21, 22/20, 22/51,
23/24, 23/25,
24/42, 24/26,
25/24, 25/26, 25/27,
26/28, 26/27,
27/28, 27/29,
28/29, 28/41,
29/30, 29/31,
30/39, 30/31,
31/33,
32/31, 32/30, 32/33, 32/39,
33/34, 33/35,
34/40, 34/36,
35/34, 35/36, 35/37,
36/37,
37/5,
38/5, 38/37, 38/36, 38/43,
39/41, 39/40,
40/44, 40/43,
41/42, 41/44,
42/50, 42/44,
43/4, 43/49,
44/49,
45/3,
46/48,
47/50, 47/51,
48/45, 48/49,
49/45,
50/46,
51/50}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,51}
\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);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-5) -- (p-4);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-5) -- (p-2);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-10) -- (p-48);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-11) -- (p-12);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-12) -- (p-46);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-14) -- (p-15);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-14) -- (p-46);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-15) -- (p-16);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-16) -- (p-47);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-22) -- (p-23);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-22) -- (p-51);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-23) -- (p-24);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-23) -- (p-25);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-24) -- (p-42);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-24) -- (p-26);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-25) -- (p-27);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-34) -- (p-36);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-38) -- (p-5);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-38) -- (p-36);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-38) -- (p-43);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-39) -- (p-41);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-39) -- (p-40);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-40) -- (p-43);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-41) -- (p-44);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-42) -- (p-50);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-43) -- (p-4);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-44) -- (p-49);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-47) -- (p-50);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-47) -- (p-51);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-48) -- (p-49);
\draw[cyan,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-50) -- (p-46);
\draw[magenta,ultra thick,dash pattern=on 0.01cm off 0.09cm] (p-51) -- (p-50);
%Winkel als \draw[->,red] (p-1) +(0:0.3 cm) arc (0:60:0.3 cm);
\foreach \i/\a/\b/\r/\c in {
3/95.52/284.55/0.4/LightBlue,
45/104.55/294.83/0.4/LightCyan,
48/174.83/323.00/0.4/LightSeaGreen,
46/143.00/202.48/0.4/LightSlateGray,
50/22.48/302.44/0.4/Crimson,
49/114.83/253.51/0.4/DarkGray,
5/335.58/626.78/0.4/DarkSlateBlue,
37/86.78/326.69/0.4/DarkTurquoise,
33/26.69/304.70/0.4/ForestGreen,
23/120.15/407.04/0.4/LightCoral,
19/166.97/437.96/0.4/LightSkyBlue,
15/197.95/487.94/0.4/MediumAquamarine,
11/247.99/524.51/0.4/MediumVioletRed,
5/335.58/686.75/0.3/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 {
1/135,
2/66,
3/6,
4/246,
5/117,
6/195,
7/15,
8/195,
9/15,
10/255,
11/15,
12/98,
13/98,
14/278,
15/48,
16/48,
17/48,
18/228,
19/17,
20/137,
21/317,
22/137,
23/257,
24/30,
25/210,
26/150,
27/330,
28/150,
29/275,
30/275,
31/275,
32/95,
33/237,
34/297,
35/237,
36/57,
37/117,
38/357,
39/35,
40/78,
41/260,
42/20,
43/104,
44/140,
45/145,
46/218,
47/168,
48/25,
49/265,
50/152,
51/137}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>Rahmen(2,3,2,2,2,3,2,3)</Bildtext>
%<Ausrichten von="1" nach="2"/>
%<Winkel size="18" color="blue" id="blauerWinkel" value="15.522486812413007"/>
%<Feinjustieren Anzahl="1"/>
%<Rechenweg>
%P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(2,1);
%//Rahmen(2,3,2,2,2,3,2,3);
%//Rahmen(2,3,4,3,3,4,3);
%Rahmen(2,3,4,3,3,4,4);
%//Rahmen(3,3,3,3,3,3,3,3);
%//Rahmen(2,2,2,2,4,3,4,4);
%</Rechenweg>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/2.64/0.00,
2/3.64/0.00,
3/3.14/0.87,
4/4.140/0.866,
5/4.64/0.00,
6/2.73/1.00,
7/1.82/0.58,
8/1.92/1.57,
9/1.01/1.15,
10/1.10/2.15,
11/0.19/1.73,
12/1.03/2.27,
13/0.14/2.73,
14/0.98/3.27,
15/0.10/3.73,
16/0.94/4.27,
17/0.05/4.73,
18/0.889/5.269,
19/0.00/5.73,
20/0.925/5.346,
21/0.79/6.34,
22/1.72/5.96,
23/1.58/6.95,
24/2.51/6.57,
25/2.38/7.56,
26/2.71/6.61,
27/3.36/7.37,
28/3.69/6.43,
29/4.34/7.19,
30/4.672/6.242,
31/5.32/7.00,
32/4.721/6.202,
33/5.71/6.08,
34/5.11/5.28,
35/6.10/5.16,
36/5.50/4.36,
37/6.49/4.24,
38/5.888/3.438,
39/6.88/3.31,
40/5.882/3.385,
41/6.32/2.49,
42/5.32/2.56,
43/5.76/1.66,
44/4.76/1.73,
45/5.20/0.83,
46/4.203/0.899}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- 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, 5/45,
6/1,
7/1, 7/6,
8/7, 8/6,
9/7, 9/8,
10/9, 10/8,
11/9, 11/10,
12/11,
13/11, 13/12,
14/13, 14/12,
15/13, 15/14,
16/15, 16/14,
17/15, 17/16,
18/17, 18/16,
19/17, 19/18,
20/19,
21/19, 21/20,
22/21, 22/20,
23/21, 23/22,
24/23, 24/22,
25/23, 25/24,
26/25,
27/25, 27/26,
28/27, 28/26,
29/27, 29/28,
30/29, 30/28,
31/29, 31/30, 31/33,
32/33, 32/31,
33/35,
34/35, 34/33, 34/32,
35/37,
36/37, 36/35, 36/34,
37/39,
38/39, 38/37, 38/36,
40/41, 40/39, 40/42,
41/39,
42/43, 42/41, 42/44,
43/41,
44/45, 44/43, 44/46,
45/43,
46/5, 46/45}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,46}
\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);
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/210,
2/330,
3/150,
4/30,
5/330,
6/55,
7/235,
8/55,
9/235,
10/55,
11/175,
12/303,
13/243,
14/63,
15/243,
16/63,
17/243,
18/63,
19/188,
20/308,
21/128,
22/248,
23/68,
24/308,
25/68,
26/199,
27/139,
28/199,
29/139,
30/319,
31/83,
32/143,
33/23,
34/143,
35/323,
36/263,
37/83,
38/263,
39/26,
40/86,
41/326,
42/146,
43/26,
44/206,
45/26,
46/146}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/e329c52bb514d7591e57607a4bc121e3.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>Rahmen(2,3,2,2,2,3,2,3)</Bildtext>
%<Ausrichten von=\"1\" nach=\"2\"/>
%<Winkel size=\"18\" color=\"blue\" id=\"blauerWinkel\" value=\"15.522486812413007\"/>
%<Feinjustieren Anzahl=\"1\"/>
%<Rechenweg>
%P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(2,1);
%//Rahmen(2,3,2,2,2,3,2,3);
%//Rahmen(2,3,4,3,3,4,3);
%Rahmen(2,3,4,3,3,4,4);
%//Rahmen(3,3,3,3,3,3,3,3);
%//Rahmen(2,2,2,2,4,3,4,4);
%</Rechenweg>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/2.64/0.00,
2/3.64/0.00,
3/3.14/0.87,
4/4.140/0.866,
5/4.64/0.00,
6/2.73/1.00,
7/1.82/0.58,
8/1.92/1.57,
9/1.01/1.15,
10/1.10/2.15,
11/0.19/1.73,
12/1.03/2.27,
13/0.14/2.73,
14/0.98/3.27,
15/0.10/3.73,
16/0.94/4.27,
17/0.05/4.73,
18/0.889/5.269,
19/0.00/5.73,
20/0.925/5.346,
21/0.79/6.34,
22/1.72/5.96,
23/1.58/6.95,
24/2.51/6.57,
25/2.38/7.56,
26/2.71/6.61,
27/3.36/7.37,
28/3.69/6.43,
29/4.34/7.19,
30/4.672/6.242,
31/5.32/7.00,
32/4.721/6.202,
33/5.71/6.08,
34/5.11/5.28,
35/6.10/5.16,
36/5.50/4.36,
37/6.49/4.24,
38/5.888/3.438,
39/6.88/3.31,
40/5.882/3.385,
41/6.32/2.49,
42/5.32/2.56,
43/5.76/1.66,
44/4.76/1.73,
45/5.20/0.83,
46/4.203/0.899}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- 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, 5/45,
6/1,
7/1, 7/6,
8/7, 8/6,
9/7, 9/8,
10/9, 10/8,
11/9, 11/10,
12/11,
13/11, 13/12,
14/13, 14/12,
15/13, 15/14,
16/15, 16/14,
17/15, 17/16,
18/17, 18/16,
19/17, 19/18,
20/19,
21/19, 21/20,
22/21, 22/20,
23/21, 23/22,
24/23, 24/22,
25/23, 25/24,
26/25,
27/25, 27/26,
28/27, 28/26,
29/27, 29/28,
30/29, 30/28,
31/29, 31/30, 31/33,
32/33, 32/31,
33/35,
34/35, 34/33, 34/32,
35/37,
36/37, 36/35, 36/34,
37/39,
38/39, 38/37, 38/36,
40/41, 40/39, 40/42,
41/39,
42/43, 42/41, 42/44,
43/41,
44/45, 44/43, 44/46,
45/43,
46/5, 46/45}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,46}
\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);
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/210,
2/330,
3/150,
4/30,
5/330,
6/55,
7/235,
8/55,
9/235,
10/55,
11/175,
12/303,
13/243,
14/63,
15/243,
16/63,
17/243,
18/63,
19/188,
20/308,
21/128,
22/248,
23/68,
24/308,
25/68,
26/199,
27/139,
28/199,
29/139,
30/319,
31/83,
32/143,
33/23,
34/143,
35/323,
36/263,
37/83,
38/263,
39/26,
40/86,
41/326,
42/146,
43/26,
44/206,
45/26,
46/146}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>Rahmen(2,3,2,2,2,3,2,3)</Bildtext>
%<Ausrichten von="1" nach="2"/>
%<Winkel size="18" color="blue" id="blauerWinkel" value="15.522486812413007"/>
%<Feinjustieren Anzahl="1"/>
%<Rechenweg>
%P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(2,1);
%//Rahmen(2,3,2,2,2,3,2,3);
%//Rahmen(2,3,4,3,3,4,3);
%//Rahmen(2,3,4,3,3,4,4);
%//Rahmen(3,3,3,3,3,3,3,3);
%Rahmen(2,2,2,2,4,3,4,4);
%</Rechenweg>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/3.01/0.00,
2/4.01/0.00,
3/3.51/0.87,
4/4.506/0.866,
5/5.01/0.00,
6/2.97/1.00,
7/2.12/0.47,
8/2.09/1.47,
9/1.24/0.94,
10/1.68/1.84,
11/0.68/1.77,
12/1.12/2.67,
13/0.13/2.60,
14/0.96/3.15,
15/0.06/3.60,
16/0.90/4.15,
17/0.00/4.60,
18/0.97/4.37,
19/0.69/5.32,
20/1.66/5.09,
21/1.37/6.05,
22/2.34/5.82,
23/2.06/6.78,
24/3.031/6.549,
25/2.74/7.51,
26/3.086/6.568,
27/3.73/7.33,
28/4.07/6.40,
29/4.71/7.16,
30/5.056/6.223,
31/5.70/6.99,
32/5.096/6.191,
33/6.09/6.07,
34/5.49/5.27,
35/6.48/5.15,
36/5.88/4.35,
37/6.87/4.23,
38/6.266/3.429,
39/7.26/3.31,
40/6.261/3.380,
41/6.70/2.48,
42/5.70/2.55,
43/6.13/1.65,
44/5.13/1.73,
45/5.57/0.83,
46/4.572/0.901}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- 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, 5/45,
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,
14/13,
15/13, 15/14,
16/15, 16/14,
17/15, 17/16,
18/17,
19/17, 19/18,
20/19, 20/18,
21/19, 21/20,
22/21, 22/20,
23/21, 23/22,
24/23, 24/22,
25/23, 25/24,
26/25,
27/25, 27/26,
28/27, 28/26,
29/27, 29/28,
30/29, 30/28,
31/29, 31/30, 31/33,
32/33, 32/31,
33/35,
34/35, 34/33, 34/32,
35/37,
36/37, 36/35, 36/34,
37/39,
38/39, 38/37, 38/36,
40/41, 40/39, 40/42,
41/39,
42/43, 42/41, 42/44,
43/41,
44/45, 44/43, 44/46,
45/43,
46/5, 46/45}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,46}
\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);
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/210,
2/330,
3/150,
4/30,
5/330,
6/2,
7/182,
8/122,
9/274,
10/34,
11/274,
12/34,
13/154,
14/304,
15/124,
16/64,
17/197,
18/257,
19/197,
20/317,
21/137,
22/257,
23/197,
24/317,
25/140,
26/260,
27/80,
28/320,
29/80,
30/260,
31/20,
32/143,
33/23,
34/203,
35/323,
36/143,
37/323,
38/203,
39/26,
40/146,
41/326,
42/86,
43/26,
44/86,
45/266,
46/146}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/c1f2be07b0dae055f1a7db28eaf4a103.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>Rahmen(2,3,2,2,2,3,2,3)</Bildtext>
%<Ausrichten von=\"1\" nach=\"2\"/>
%<Winkel size=\"18\" color=\"blue\" id=\"blauerWinkel\" value=\"15.522486812413007\"/>
%<Feinjustieren Anzahl=\"1\"/>
%<Rechenweg>
%P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(2,1);
%//Rahmen(2,3,2,2,2,3,2,3);
%//Rahmen(2,3,4,3,3,4,3);
%//Rahmen(2,3,4,3,3,4,4);
%//Rahmen(3,3,3,3,3,3,3,3);
%Rahmen(2,2,2,2,4,3,4,4);
%</Rechenweg>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/3.01/0.00,
2/4.01/0.00,
3/3.51/0.87,
4/4.506/0.866,
5/5.01/0.00,
6/2.97/1.00,
7/2.12/0.47,
8/2.09/1.47,
9/1.24/0.94,
10/1.68/1.84,
11/0.68/1.77,
12/1.12/2.67,
13/0.13/2.60,
14/0.96/3.15,
15/0.06/3.60,
16/0.90/4.15,
17/0.00/4.60,
18/0.97/4.37,
19/0.69/5.32,
20/1.66/5.09,
21/1.37/6.05,
22/2.34/5.82,
23/2.06/6.78,
24/3.031/6.549,
25/2.74/7.51,
26/3.086/6.568,
27/3.73/7.33,
28/4.07/6.40,
29/4.71/7.16,
30/5.056/6.223,
31/5.70/6.99,
32/5.096/6.191,
33/6.09/6.07,
34/5.49/5.27,
35/6.48/5.15,
36/5.88/4.35,
37/6.87/4.23,
38/6.266/3.429,
39/7.26/3.31,
40/6.261/3.380,
41/6.70/2.48,
42/5.70/2.55,
43/6.13/1.65,
44/5.13/1.73,
45/5.57/0.83,
46/4.572/0.901}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- 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, 5/45,
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,
14/13,
15/13, 15/14,
16/15, 16/14,
17/15, 17/16,
18/17,
19/17, 19/18,
20/19, 20/18,
21/19, 21/20,
22/21, 22/20,
23/21, 23/22,
24/23, 24/22,
25/23, 25/24,
26/25,
27/25, 27/26,
28/27, 28/26,
29/27, 29/28,
30/29, 30/28,
31/29, 31/30, 31/33,
32/33, 32/31,
33/35,
34/35, 34/33, 34/32,
35/37,
36/37, 36/35, 36/34,
37/39,
38/39, 38/37, 38/36,
40/41, 40/39, 40/42,
41/39,
42/43, 42/41, 42/44,
43/41,
44/45, 44/43, 44/46,
45/43,
46/5, 46/45}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,46}
\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);
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/210,
2/330,
3/150,
4/30,
5/330,
6/2,
7/182,
8/122,
9/274,
10/34,
11/274,
12/34,
13/154,
14/304,
15/124,
16/64,
17/197,
18/257,
19/197,
20/317,
21/137,
22/257,
23/197,
24/317,
25/140,
26/260,
27/80,
28/320,
29/80,
30/260,
31/20,
32/143,
33/23,
34/203,
35/323,
36/143,
37/323,
38/203,
39/26,
40/146,
41/326,
42/86,
43/26,
44/86,
45/266,
46/146}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
![<math>
%Eingabe war:
%<Streichholzgraph>
%<Bildtext>Rahmen(2,3,2,2,2,3,2,3)</Bildtext>
%<Ausrichten von="1" nach="2"/>
%<Winkel size="18" color="blue" id="blauerWinkel" value="15.522486812413007"/>
%<Feinjustieren Anzahl="1"/>
%<Rechenweg>
%P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(2,1);
%//Rahmen(2,3,2,2,2,3,2,3);
%//Rahmen(2,3,4,3,3,4,3);
%//Rahmen(2,3,4,3,3,4,4);
%//Rahmen(3,3,3,3,3,3,3,3);
%Rahmen(2,4,2,4,3,4,4); Z(8,10);
%</Rechenweg>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/2.97/0.00,
2/3.97/0.00,
3/3.47/0.87,
4/4.467/0.866,
5/4.97/0.00,
6/3.20/0.97,
7/2.24/0.69,
8/2.48/1.66,
9/1.52/1.38,
10/1.75/2.35,
11/0.79/2.07,
12/1.02/3.04,
13/0.07/2.75,
14/0.91/3.28,
15/0.03/3.75,
16/0.88/4.28,
17/0.00/4.75,
18/0.97/4.50,
19/0.71/5.46,
20/1.67/5.20,
21/1.41/6.17,
22/2.38/5.91,
23/2.12/6.88,
24/3.085/6.619,
25/2.82/7.58,
26/3.144/6.637,
27/3.81/7.39,
28/4.12/6.44,
29/4.79/7.19,
30/5.105/6.242,
31/5.77/6.99,
32/5.148/6.205,
33/6.14/6.06,
34/5.52/5.28,
35/6.51/5.14,
36/5.89/4.35,
37/6.88/4.21,
38/6.266/3.421,
39/7.26/3.28,
40/6.260/3.366,
41/6.68/2.46,
42/5.69/2.55,
43/6.11/1.64,
44/5.12/1.73,
45/5.54/0.82,
46/4.543/0.906}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- 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, 5/45,
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,
14/13,
15/13, 15/14,
16/15, 16/14,
17/15, 17/16,
18/17,
19/17, 19/18,
20/19, 20/18,
21/19, 21/20,
22/21, 22/20,
23/21, 23/22,
24/23, 24/22,
25/23, 25/24,
26/25,
27/25, 27/26,
28/27, 28/26,
29/27, 29/28,
30/29, 30/28,
31/29, 31/30, 31/33,
32/33, 32/31,
33/35,
34/35, 34/33, 34/32,
35/37,
36/37, 36/35, 36/34,
37/39,
38/39, 38/37, 38/36,
40/41, 40/39, 40/42,
41/39,
42/43, 42/41, 42/44,
43/41,
44/45, 44/43, 44/46,
45/43,
46/5, 46/45}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,46}
\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);
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/210,
2/330,
3/150,
4/30,
5/330,
6/46,
7/166,
8/46,
9/166,
10/46,
11/226,
12/46,
13/242,
14/2,
15/182,
16/2,
17/122,
18/255,
19/75,
20/255,
21/195,
22/15,
23/135,
24/315,
25/75,
26/199,
27/19,
28/199,
29/19,
30/259,
31/19,
32/142,
33/22,
34/202,
35/322,
36/262,
37/322,
38/202,
39/25,
40/145,
41/25,
42/145,
43/25,
44/145,
45/25,
46/145}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}
</math>](/matheplanet/nuke/html/latexrender/pictures/33d400f177f0b47dfedd24b1958d5601.png "%Eingabe war:
%<Streichholzgraph>
%<Bildtext>Rahmen(2,3,2,2,2,3,2,3)</Bildtext>
%<Ausrichten von=\"1\" nach=\"2\"/>
%<Winkel size=\"18\" color=\"blue\" id=\"blauerWinkel\" value=\"15.522486812413007\"/>
%<Feinjustieren Anzahl=\"1\"/>
%<Rechenweg>
%P[1]=[0,0]; P[2]=[50,0]; D=ab(1,2); A(2,1);
%//Rahmen(2,3,2,2,2,3,2,3);
%//Rahmen(2,3,4,3,3,4,3);
%//Rahmen(2,3,4,3,3,4,4);
%//Rahmen(3,3,3,3,3,3,3,3);
%Rahmen(2,4,2,4,3,4,4); Z(8,10);
%</Rechenweg>
%</Streichholzgraph>
%Ende der Eingabe.
\begin{tikzpicture}[draw=grey,font=\sffamily\scriptsize]
%Koordinaten als \coordinate (p-1) at (0,0);
\foreach \i/\x/\y in {
1/2.97/0.00,
2/3.97/0.00,
3/3.47/0.87,
4/4.467/0.866,
5/4.97/0.00,
6/3.20/0.97,
7/2.24/0.69,
8/2.48/1.66,
9/1.52/1.38,
10/1.75/2.35,
11/0.79/2.07,
12/1.02/3.04,
13/0.07/2.75,
14/0.91/3.28,
15/0.03/3.75,
16/0.88/4.28,
17/0.00/4.75,
18/0.97/4.50,
19/0.71/5.46,
20/1.67/5.20,
21/1.41/6.17,
22/2.38/5.91,
23/2.12/6.88,
24/3.085/6.619,
25/2.82/7.58,
26/3.144/6.637,
27/3.81/7.39,
28/4.12/6.44,
29/4.79/7.19,
30/5.105/6.242,
31/5.77/6.99,
32/5.148/6.205,
33/6.14/6.06,
34/5.52/5.28,
35/6.51/5.14,
36/5.89/4.35,
37/6.88/4.21,
38/6.266/3.421,
39/7.26/3.28,
40/6.260/3.366,
41/6.68/2.46,
42/5.69/2.55,
43/6.11/1.64,
44/5.12/1.73,
45/5.54/0.82,
46/4.543/0.906}
\coordinate (p-\i) at (\x,\y);
%Innenflächen als \filldraw[yellow,shift={+(0.1,0.1)}] (p-1) -- (p-2) -- (p-3) -- 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, 5/45,
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,
14/13,
15/13, 15/14,
16/15, 16/14,
17/15, 17/16,
18/17,
19/17, 19/18,
20/19, 20/18,
21/19, 21/20,
22/21, 22/20,
23/21, 23/22,
24/23, 24/22,
25/23, 25/24,
26/25,
27/25, 27/26,
28/27, 28/26,
29/27, 29/28,
30/29, 30/28,
31/29, 31/30, 31/33,
32/33, 32/31,
33/35,
34/35, 34/33, 34/32,
35/37,
36/37, 36/35, 36/34,
37/39,
38/39, 38/37, 38/36,
40/41, 40/39, 40/42,
41/39,
42/43, 42/41, 42/44,
43/41,
44/45, 44/43, 44/46,
45/43,
46/5, 46/45}
\draw[gray,thick] (p-\i) -- (p-\j);
%Punkte als \fill[red] (p-1) circle (1.125pt)
\foreach \i in {1,...,46}
\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);
%Punktnummern als \node[anchor=30] (P1) at (p-1) {1};
\foreach \i/\a in {
1/210,
2/330,
3/150,
4/30,
5/330,
6/46,
7/166,
8/46,
9/166,
10/46,
11/226,
12/46,
13/242,
14/2,
15/182,
16/2,
17/122,
18/255,
19/75,
20/255,
21/195,
22/15,
23/135,
24/315,
25/75,
26/199,
27/19,
28/199,
29/19,
30/259,
31/19,
32/142,
33/22,
34/202,
35/322,
36/262,
37/322,
38/202,
39/25,
40/145,
41/25,
42/145,
43/25,
44/145,
45/25,
46/145}
\node[anchor=\a] (P\i) at (p-\i) {\i};
\end{tikzpicture}")
