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 Streichholzgraphen 4-regulär und 4/n-regulär (n>4) und 2/5 |
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Slash
Aktiv 
Dabei seit: 23.03.2005
Mitteilungen: 6929
Aus: New York
 |      Beitrag No.1400, vom Themenstarter, eingetragen 2018-09-16 08:35
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Hier der Teilgraph für einen Ring aus 27 Stück.
  
\geo ebene(773.31,302.32) x(4.48,21.96) y(11.06,17.9) form(.) #//Eingabe war: #<Streichholzgraph> #<Bildtext>Teilgraph für 4/4 Ring aus 27 Stück.</Bildtext> #<Winkel size=''18'' color=''green'' id=''gruenerWinkel'' value=''1.918489353803068''/> #<Winkel size=''18'' color=''orange'' id=''orangerWinkel'' value=''83.0827717574036''/> #<Winkel size=''18'' color=''blue'' id=''blauerWinkel'' value=''8.298673786669271''/> #<Feinjustieren Anzahl=''3''/> #<Rechenweg> #P[1]=[-188.46939747023382,47.016293202594795]; #P[2]=[-148.92775969342222,66.81341984485638]; D=ab(1,2); A(2,1,Bew(1)); #N(3,1,2); #M(4,1,3,blauerWinkel); N(5,1,4); A(3,4,ab(4,3,[1,5])); #A(2,8,ab(5,7,[1,8])); A(10,14,ab(5,7,[1,14])); N(27,26,22); N(28,26,27); #N(29,27,22); #M(30,7,6,gruenerWinkel); N(31,7,30); #M(32,31,30,orangerWinkel); N(33,31,32); #A(30,32,ab(32,30,7,[30,33])); #A(36,34,ab(7,33,[30,36])); #A(42,40,ab(7,33,[30,42])); #A(54,52,ab(7,33,[30,30])); N(55,52,54); N(56,52,55); N(57,55,28); #RA(54,28); #A(56,29,ab(56,29,[1,56],''gespiegelt'')); #RA(57,111); RA(57,85); #</Rechenweg> #</Streichholzgraph> #//Ende der Eingabe, weiter mit fedgeo: p(5.737979261812533,11.06321991448935,P1) p(6.632168358232203,11.510909382585456,P2) p(5.797363357644397,12.06145512182389,P3) p(5.652662976233746,12.059573833242641,P4) p(4.8324533142226125,11.487510803198239,P5) p(5.7120470720656105,13.057809040577181,P6) p(4.81785797564594,12.610119572481075,P7) p(6.617573019655531,12.633518151868293,P8) p(7.537694305822123,11.086618493876568,P9) p(8.431883402241793,11.534307961972676,P10) p(7.597078401653986,12.08485370121111,P11) p(7.452378020243335,12.082972412629859,P12) p(7.5117621160752,13.081207619964399,P13) p(8.417288063665119,12.656916731255512,P14) p(9.337409349831713,11.110017073263787,P15) p(10.231598446251382,11.557706541359893,P16) p(9.396793445663576,12.108252280598327,P17) p(9.252093064252925,12.106370992017078,P18) p(9.311477160084788,13.104606199351618,P19) p(10.21700310767471,12.68031531064273,P20) p(11.137124393841303,11.133415652651006,P21) p(12.03131349026097,11.581105120747113,P22) p(11.196508489673166,12.131650859985546,P23) p(11.051808108262515,12.129769571404296,P24) p(11.111192204094378,13.128004778738838,P25) p(12.016718151684298,12.703713890029949,P26) p(12.851523152272105,12.153168150791515,P27) p(12.910907248103968,13.151403358126055,P28) p(12.93683943785089,11.156814232038226,P29) p(5.696558234121846,13.087493488561936,P30) p(4.8437901664538074,13.609783276673593,P31) p(5.464981714211505,14.393442042332726,P32) p(4.47571754137349,14.539580320477501,P33) p(6.34368197268741,14.870815958413587,P34) p(6.317749781879543,13.87115225422107,P35) p(6.6858224069598595,12.941355210417163,P36) p(7.564522665435766,13.418729126498022,P37) p(6.711754597767726,13.941018914609678,P38) p(7.332946145525423,14.724677680268812,P39) p(8.211646404001328,15.202051596349673,P40) p(8.185714213193464,14.202387892157155,P41) p(8.55378683827378,13.27259084835325,P42) p(9.432487096749686,13.74996476443411,P43) p(8.579719029081645,14.272254552545768,P44) p(9.200910576839343,15.055913318204901,P45) p(10.079610835315249,15.533287234285762,P46) p(10.053678644507382,14.533623530093244,P47) p(10.421751269587698,13.603826486289336,P48) p(11.300451528063604,14.081200402370197,P49) p(10.447683460395565,14.603490190481853,P50) p(11.068875008153261,15.387148956140987,P51) p(11.947575266629167,15.864522872221848,P52) p(11.9216430758213,14.864859168029332,P53) p(12.289715700901619,13.935062124225427,P54) p(12.315647891709489,14.934725828417944,P55) p(12.936839439467182,15.71838459407708,P56) p(12.936839438911809,14.151067062318575,P57) p(20.135699613822922,11.06321990938784,P58) p(19.241510517720506,11.510909378117612,P59) p(20.076315518698465,12.06145511676446,P60) p(20.221015900107776,12.059573828080666,P61) p(21.041225561713517,11.487510797455016,P62) p(20.161631804983323,13.057809035457291,P63) p(21.05582090108573,12.610119566727512,P64) p(19.256105857092727,12.63351814739011,P65) p(18.335984569829915,11.086618490050434,P66) p(17.441795473727502,11.53430795878021,P67) p(18.276600474705454,12.084853697427057,P68) p(18.42130085611477,12.082972408743265,P69) p(18.36191676099031,13.081207616119887,P70) p(17.456390813099716,12.656916728052707,P71) p(16.5362695258369,11.11001707071303,P72) p(15.642080429734493,11.55770653944281,P73) p(16.47688543071245,12.108252278089655,P74) p(16.621585812121765,12.10637098940586,P75) p(16.562201716997308,13.104606196782484,P76) p(15.656675769106709,12.680315308715304,P77) p(14.736554481843896,11.133415651375628,P78) p(13.84236538574148,11.581105120105407,P79) p(14.677170386719439,12.131650858752252,P80) p(14.821870768128758,12.12976957006846,P81) p(14.762486673004299,13.128004777445083,P82) p(13.856960725113701,12.7037138893779,P83) p(13.022155724135763,12.153168150731057,P84) p(12.96277162901129,13.151403358107679,P85) p(20.17712064294812,13.087493483431068,P86) p(21.029888710986285,13.609783270938408,P87) p(20.408697163783934,14.393442037037754,P88) p(21.39796133672551,14.53958031448148,P89) p(19.529996905646318,14.870815953741308,P90) p(19.555929095745768,13.871152249530411,P91) p(19.187856470006547,12.941355205987342,P92) p(18.309156211868935,13.418729122690898,P93) p(19.161924279907097,13.941018910198235,P94) p(18.540732732704747,14.724677676297581,P95) p(17.662032474567134,15.202051593001137,P96) p(17.68796466466658,14.202387888790245,P97) p(17.31989203892736,13.272590845247175,P98) p(16.441191780789747,13.74996476195073,P99) p(17.29395984882791,14.272254549458069,P100) p(16.672768301625556,15.055913315557412,P101) p(15.794068043487945,15.533287232260971,P102) p(15.820000233587393,14.533623528050075,P103) p(15.45192760784817,13.603826484507005,P104) p(14.57322734971056,14.081200401210562,P105) p(15.425995417748723,14.603490188717899,P106) p(14.80480387054637,15.387148954817246,P107) p(13.92610361240876,15.864522871520801,P108) p(13.952035802508208,14.864859167309906,P109) p(13.583963176768984,13.935062123766839,P110) p(13.55803098666953,14.934725827977733,P111) nolabel() s(P1,P2) s(P9,P2) s(P12,P2) s(P1,P3) s(P2,P3) s(P6,P3) s(P1,P4) s(P6,P4) s(P7,P4) s(P1,P5) s(P4,P5) s(P6,P7) s(P6,P8) s(P3,P8) s(P13,P8) s(P9,P10) s(P15,P10) s(P18,P10) s(P9,P11) s(P10,P11) s(P13,P11) s(P9,P12) s(P13,P12) s(P8,P12) s(P11,P14) s(P13,P14) s(P19,P14) s(P15,P16) s(P21,P16) s(P24,P16) s(P15,P17) s(P16,P17) s(P19,P17) s(P15,P18) s(P19,P18) s(P14,P18) s(P17,P20) s(P19,P20) s(P25,P20) s(P21,P22) s(P21,P23) s(P22,P23) s(P25,P23) s(P20,P24) s(P21,P24) s(P25,P24) s(P23,P26) s(P25,P26) s(P26,P27) s(P22,P27) s(P26,P28) s(P27,P28) s(P27,P29) s(P22,P29) s(P79,P29) s(P84,P29) s(P7,P30) s(P35,P30) s(P7,P31) s(P30,P31) s(P31,P32) s(P34,P32) s(P31,P33) s(P32,P33) s(P38,P34) s(P39,P34) s(P34,P35) s(P32,P35) s(P35,P36) s(P30,P36) s(P36,P37) s(P41,P37) s(P36,P38) s(P37,P38) s(P38,P39) s(P40,P39) s(P44,P40) s(P45,P40) s(P39,P41) s(P40,P41) s(P37,P42) s(P41,P42) s(P42,P43) s(P47,P43) s(P42,P44) s(P43,P44) s(P44,P45) s(P46,P45) s(P50,P46) s(P51,P46) s(P45,P47) s(P46,P47) s(P43,P48) s(P47,P48) s(P48,P49) s(P53,P49) s(P48,P50) s(P49,P50) s(P50,P51) s(P52,P51) s(P51,P53) s(P52,P53) s(P49,P54) s(P53,P54) s(P28,P54) s(P52,P55) s(P54,P55) s(P52,P56) s(P55,P56) s(P108,P56) s(P111,P56) s(P55,P57) s(P28,P57) s(P111,P57) s(P85,P57) s(P58,P59) s(P66,P59) s(P69,P59) s(P58,P60) s(P59,P60) s(P63,P60) s(P58,P61) s(P63,P61) s(P64,P61) s(P58,P62) s(P61,P62) s(P63,P64) s(P60,P65) s(P63,P65) s(P70,P65) s(P66,P67) s(P72,P67) s(P75,P67) s(P66,P68) s(P67,P68) s(P70,P68) s(P65,P69) s(P66,P69) s(P70,P69) s(P68,P71) s(P70,P71) s(P76,P71) s(P72,P73) s(P78,P73) s(P81,P73) s(P72,P74) s(P73,P74) s(P76,P74) s(P71,P75) s(P72,P75) s(P76,P75) s(P74,P77) s(P76,P77) s(P82,P77) s(P78,P79) s(P78,P80) s(P79,P80) s(P82,P80) s(P77,P81) s(P78,P81) s(P82,P81) s(P80,P83) s(P82,P83) s(P79,P84) s(P83,P84) s(P83,P85) s(P84,P85) s(P64,P86) s(P91,P86) s(P64,P87) s(P86,P87) s(P87,P88) s(P90,P88) s(P87,P89) s(P88,P89) s(P94,P90) s(P95,P90) s(P88,P91) s(P90,P91) s(P86,P92) s(P91,P92) s(P92,P93) s(P97,P93) s(P92,P94) s(P93,P94) s(P94,P95) s(P96,P95) s(P100,P96) s(P101,P96) s(P95,P97) s(P96,P97) s(P93,P98) s(P97,P98) s(P98,P99) s(P103,P99) s(P98,P100) s(P99,P100) s(P100,P101) s(P102,P101) s(P106,P102) s(P107,P102) s(P101,P103) s(P102,P103) s(P99,P104) s(P103,P104) s(P104,P105) s(P109,P105) s(P104,P106) s(P105,P106) s(P106,P107) s(P108,P107) s(P107,P109) s(P108,P109) s(P85,P110) s(P105,P110) s(P109,P110) s(P108,P111) s(P110,P111) pen(2) color(#008000) m(P6,P7,MA10) m(P7,P30,MB10) f(P7,MA10,MB10) color(#FFA500) m(P30,P31,MA11) m(P31,P32,MB11) b(P31,MA11,MB11) color(#0000FF) m(P3,P1,MA12) m(P1,P4,MB12) f(P1,MA12,MB12) pen(2) color(#008000) s(P54,P28) abstand(P54,P28,A18) print(abs(P54,P28):,4.48,17.9) print(A18,5.95,17.9) color(#008000) s(P57,P111) abstand(P57,P111,A18) print(abs(P57,P111):,4.48,17.561) print(A18,5.95,17.561) color(#008000) s(P57,P85) abstand(P57,P85,A18) print(abs(P57,P85):,4.48,17.221) print(A18,5.95,17.221) print(min=0.9999999999999853,4.48,16.882) print(max=1.000000000000035,4.48,16.543) \geooff \geoprint()
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haribo
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Dabei seit: 25.10.2012
Mitteilungen: 1687
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 | Beitrag No.1401, eingetragen 2018-09-16 11:05
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Slash
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Dabei seit: 23.03.2005
Mitteilungen: 6929
Aus: New York
| Beitrag No.1402, vom Themenstarter, eingetragen 2018-09-16 12:43
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Vielleicht ist ein Beweis, dass so ein Ring-Graph bzw. ein 4/4 mit den geforderten Eigenschaften überhaupt nicht möglich ist, gar nicht mal so schwer. Es geht nur zwingend mit diesen "Girlanden", da sich die Dreiecke nicht anders verbinden lassen. Und man muss irgendwie eine Keilform für den Teilgraph erhalten. Das geht aber nicht ohen Rauten oder größere Dreiecke, da die Winkel der Girlanden begrenzt sind. Ein Beweis wäre bestimmt ähnlich dem Beweis, dass kein regulärer SHG mit Grad > 4 existiert.
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StefanVogel
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Dabei seit: 26.11.2005
Mitteilungen: 3081
Aus: Raun
| Beitrag No.1403, eingetragen 2018-09-17 04:55
|
Hallo Slash, wie hast du geschafft, dass im #1400 der Winkel zwischen den Vektoren P33-P5 und P89-P62 gleich 13.33333333333...° ist, so dass sich der Kreis schließt?
Button "GAP" und folgende liefert zu diesem Graph als Ergebnis einen zusätzlichen Freiheitsgrad, also möglicherweise beweglich.
Button neue Eingabe "egal wie" erzeugt 5 bewegliche Winkel, mit denen nur 4 Kanten eingestellt werden müssen. Es bleibt ein beweglicher Winkel übrig.
In deiner Eingabe ist wegen Symmetrie der Abstand |P57-P85| automatisch 1, wenn schon |P54-P28| und |P57-P111| auf 1 eingestellt sind. Auch da bleibt ein frei wählbarer Winkel übrig.
Mit dem stelle ich jetzt nochmal zusätzlich den Winkel 360°/27=13.33333333333...° ein, indem ich in deiner Eingabe vor RA(57,85); die Zeile RW(33,5,89,62,360/27); einfüge (dann Button "Feinjustieren(3)"). Anstelle von 360/27 funktionieren auch 360/26, 360/25, 360/24. Das ergibt einen Kreis aus minimal 24 Teilgraphen. Ab 360/23 wird der grüne Winkel kleiner 0, Überschneidung. Ausgabe |P33-P5| ist immer noch der Fehler im Zusammenhang mit RW(33,5,...), Entschuldigung.
111 Knoten, 4×Grad 2, 107×Grad 4
218 Kanten, minimal 0.99999999999999511502, maximal 1.00000000000001376677
einstellbare Kanten R(j,k):
|P54-P28|=1.00000000000000599520
|P57-P111|=1.00000000000000710543
|P33-P5|=3.07284700991616821497
|P57-P85|=1.00000000000000000000
\geo ebene(761.55,223.98) x(2.55,20.05) y(9.86,15.01) form(.) #//Eingabe war: #<Streichholzgraph> #<Bildtext>#1400 mit RW(...)</Bildtext> #<Winkel size=''18'' color=''green'' id=''gruenerWinkel'' value=''1.9184897329371173''/> #<Winkel size=''18'' color=''orange'' id=''orangerWinkel'' value=''83.08277062444888''/> #<Winkel size=''18'' color=''blue'' id=''blauerWinkel'' value=''8.298673467286031''/> #<Feinjustieren Anzahl=''3''/> #<Rechenweg> #P[1]=[-269.27456157256296,-6.115758229361575]; #P[2]=[-230.35424151520107,13.370296179461945]; D=ab(1,2); A(2,1,Bew(1)); #N(3,1,2); #M(4,1,3,blauerWinkel); N(5,1,4); A(3,4,ab(4,3,[1,5])); #A(2,8,ab(5,7,[1,8])); A(10,14,ab(5,7,[1,14])); N(27,26,22); N(28,26,27); #N(29,27,22); #M(30,7,6,gruenerWinkel); N(31,7,30); #M(32,31,30,orangerWinkel); N(33,31,32); #A(30,32,ab(32,30,7,[30,33])); #A(36,34,ab(7,33,[30,36])); #A(42,40,ab(7,33,[30,42])); #A(54,52,ab(7,33,[30,30])); N(55,52,54); N(56,52,55); N(57,55,28); #RA(54,28); #A(56,29,ab(56,29,[1,56],''gespiegelt'')); #RA(57,111); RW(33,5,89,62,360/27); #RA(57,85); #</Rechenweg> #</Streichholzgraph> #//Ende der Eingabe, weiter mit fedgeo: nolabel() p(3.81,9.86,P1) p(4.71,10.31,P2) p(3.87,10.86,P3) p(3.73,10.86,P4) p(2.91,10.28,P5,label) p(3.79,11.85,P6) p(2.89,11.41,P7) p(4.69,11.43,P8) p(5.61,9.88,P9) p(6.51,10.33,P10) p(5.67,10.88,P11) p(5.53,10.88,P12) p(5.59,11.88,P13) p(6.49,11.45,P14) p(7.41,9.91,P15) p(8.31,10.35,P16) p(7.47,10.90,P17) p(7.33,10.90,P18) p(7.39,11.90,P19) p(8.29,11.48,P20) p(9.21,9.93,P21) p(10.11,10.38,P22) p(9.27,10.93,P23) p(9.13,10.93,P24) p(9.19,11.92,P25) p(10.09,11.50,P26) p(10.93,10.95,P27) p(10.99,11.95,P28) print(_P28,10.19,12.25) p(11.01,9.95,P29) p(3.77,11.88,P30) p(2.92,12.41,P31) p(3.54,13.19,P32) p(2.55,13.34,P33,label) p(4.42,13.67,P34) p(4.39,12.67,P35) p(4.76,11.74,P36) p(5.64,12.22,P37) p(4.79,12.74,P38) p(5.41,13.52,P39) p(6.29,14.00,P40) p(6.26,13.00,P41) p(6.63,12.07,P42) p(7.51,12.55,P43) p(6.66,13.07,P44) p(7.28,13.85,P45) p(8.16,14.33,P46) p(8.13,13.33,P47) p(8.50,12.40,P48) p(9.38,12.88,P49) p(8.52,13.40,P50) p(9.14,14.18,P51) p(10.02,14.66,P52) p(10.00,13.66,P53) p(10.37,12.73,P54,label) p(10.39,13.73,P55) p(11.01,14.51,P56) p(11.01,12.95,P57,label) p(18.21,9.86,P58) p(17.32,10.31,P59) p(18.15,10.86,P60) p(18.30,10.86,P61) p(19.12,10.28,P62,label) p(18.24,11.85,P63) p(19.13,11.41,P64) p(17.33,11.43,P65) p(16.41,9.88,P66) p(15.52,10.33,P67) p(16.35,10.88,P68) p(16.50,10.88,P69) p(16.44,11.88,P70) p(15.53,11.45,P71) p(14.61,9.91,P72) p(13.72,10.35,P73) p(14.55,10.90,P74) p(14.70,10.90,P75) p(14.64,11.90,P76) p(13.73,11.48,P77) p(12.81,9.93,P78) p(11.92,10.38,P79) p(12.75,10.93,P80) p(12.90,10.93,P81) p(12.84,11.92,P82) p(11.93,11.50,P83) p(11.10,10.95,P84) p(11.04,11.95,P85,label) p(18.25,11.88,P86) p(19.11,12.41,P87) p(18.48,13.19,P88) p(19.47,13.34,P89,label) p(17.61,13.67,P90) p(17.63,12.67,P91) p(17.26,11.74,P92) p(16.38,12.22,P93) p(17.24,12.74,P94) p(16.62,13.52,P95) p(15.74,14.00,P96) p(15.76,13.00,P97) p(15.40,12.07,P98) p(14.52,12.55,P99) p(15.37,13.07,P100) p(14.75,13.85,P101) p(13.87,14.33,P102) p(13.90,13.33,P103) p(13.53,12.40,P104) p(12.65,12.88,P105) p(13.50,13.40,P106) p(12.88,14.18,P107) p(12.00,14.66,P108) p(12.03,13.66,P109) p(11.66,12.73,P110) p(11.63,13.73,P111,label) nolabel() s(P1,P2) s(P9,P2) s(P12,P2) s(P1,P3) s(P2,P3) s(P6,P3) s(P1,P4) s(P6,P4) s(P7,P4) s(P1,P5) s(P4,P5) s(P6,P7) s(P6,P8) s(P3,P8) s(P13,P8) s(P9,P10) s(P15,P10) s(P18,P10) s(P9,P11) s(P10,P11) s(P13,P11) s(P9,P12) s(P13,P12) s(P8,P12) s(P11,P14) s(P13,P14) s(P19,P14) s(P15,P16) s(P21,P16) s(P24,P16) s(P15,P17) s(P16,P17) s(P19,P17) s(P15,P18) s(P19,P18) s(P14,P18) s(P17,P20) s(P19,P20) s(P25,P20) s(P21,P22) s(P21,P23) s(P22,P23) s(P25,P23) s(P20,P24) s(P21,P24) s(P25,P24) s(P23,P26) s(P25,P26) s(P26,P27) s(P22,P27) s(P26,P28) s(P27,P28) s(P27,P29) s(P22,P29) s(P79,P29) s(P84,P29) s(P7,P30) s(P35,P30) s(P7,P31) s(P30,P31) s(P31,P32) s(P34,P32) s(P31,P33) s(P32,P33) s(P38,P34) s(P39,P34) s(P34,P35) s(P32,P35) s(P35,P36) s(P30,P36) s(P36,P37) s(P41,P37) s(P36,P38) s(P37,P38) s(P38,P39) s(P40,P39) s(P44,P40) s(P45,P40) s(P39,P41) s(P40,P41) s(P37,P42) s(P41,P42) s(P42,P43) s(P47,P43) s(P42,P44) s(P43,P44) s(P44,P45) s(P46,P45) s(P50,P46) s(P51,P46) s(P45,P47) s(P46,P47) s(P43,P48) s(P47,P48) s(P48,P49) s(P53,P49) s(P48,P50) s(P49,P50) s(P50,P51) s(P52,P51) s(P51,P53) s(P52,P53) s(P49,P54) s(P53,P54) s(P28,P54) s(P52,P55) s(P54,P55) s(P52,P56) s(P55,P56) s(P108,P56) s(P111,P56) s(P55,P57) s(P28,P57) s(P111,P57) s(P85,P57) s(P58,P59) s(P66,P59) s(P69,P59) s(P58,P60) s(P59,P60) s(P63,P60) s(P58,P61) s(P63,P61) s(P64,P61) s(P58,P62) s(P61,P62) s(P63,P64) s(P60,P65) s(P63,P65) s(P70,P65) s(P66,P67) s(P72,P67) s(P75,P67) s(P66,P68) s(P67,P68) s(P70,P68) s(P65,P69) s(P66,P69) s(P70,P69) s(P68,P71) s(P70,P71) s(P76,P71) s(P72,P73) s(P78,P73) s(P81,P73) s(P72,P74) s(P73,P74) s(P76,P74) s(P71,P75) s(P72,P75) s(P76,P75) s(P74,P77) s(P76,P77) s(P82,P77) s(P78,P79) s(P78,P80) s(P79,P80) s(P82,P80) s(P77,P81) s(P78,P81) s(P82,P81) s(P80,P83) s(P82,P83) s(P79,P84) s(P83,P84) s(P83,P85) s(P84,P85) s(P64,P86) s(P91,P86) s(P64,P87) s(P86,P87) s(P87,P88) s(P90,P88) s(P87,P89) s(P88,P89) s(P94,P90) s(P95,P90) s(P88,P91) s(P90,P91) s(P86,P92) s(P91,P92) s(P92,P93) s(P97,P93) s(P92,P94) s(P93,P94) s(P94,P95) s(P96,P95) s(P100,P96) s(P101,P96) s(P95,P97) s(P96,P97) s(P93,P98) s(P97,P98) s(P98,P99) s(P103,P99) s(P98,P100) s(P99,P100) s(P100,P101) s(P102,P101) s(P106,P102) s(P107,P102) s(P101,P103) s(P102,P103) s(P99,P104) s(P103,P104) s(P104,P105) s(P109,P105) s(P104,P106) s(P105,P106) s(P106,P107) s(P108,P107) s(P107,P109) s(P108,P109) s(P85,P110) s(P105,P110) s(P109,P110) s(P108,P111) s(P110,P111) pen(2) color(#008000) m(P6,P7,MA10) m(P7,P30,MB10) f(P7,MA10,MB10) color(#FFA500) m(P30,P31,MA11) m(P31,P32,MB11) b(P31,MA11,MB11) color(#0000FF) m(P3,P1,MA12) m(P1,P4,MB12) f(P1,MA12,MB12) pen(2) color(#32CD32) s(P54,P28) color(#32CD32) s(P57,P111) color(#EE82EE) s(P33,P5) color(#32CD32) s(P57,P85) color(blue) color(orange) color(red) \geooff \geoprint()
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Dabei seit: 23.03.2005
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| Beitrag No.1404, vom Themenstarter, eingetragen 2018-09-17 05:25
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2018-09-17 04:55 - StefanVogel in Beitrag No. 1403 schreibt:
Hallo Slash, wie hast du geschafft, dass im #1400 der Winkel zwischen den Vektoren P33-P5 und P89-P62 gleich 13.33333333333...° ist, so dass sich der Kreis schließt?
Da habe ich etwas improvisiert, da ich es mit der Kopierfunktion "A(...,"gespiegelt")" nicht geschafft habe genau 27 Teilgraphen aneinander zu kopieren. Ich habe dann einen Ring mit 32 Teilgraphen erstellt, indem ich immer den vorhandenen Teil verdoppelt habe. Das ergab natürlich einen Ring mit Überschneidungen. Dann habe ich in ca. 20 Minuten händisch den grünen und orangenen Winkel bis zur vierten Nachkommastelle so eingestellt bis die Kanten fast deckungsgleich waren. Optisch mit starker Vergrößerung waren nur einzelne Kanten zu erkennen, aber es gab eben keine Punktüberlagerungen. Dann habe ich die dritte Messkannte RA(57,85) durch RA(57,x) ersetzt, wobei x der Punkt tausend irgendwas war, und feinjustiert. Die Kontrolle der alten Kante RA(57,85) ergab dann immer noch 1. Ob das jetzt geometrisch ganz "koscher" ist, kann ich nicht sagen.  Die händische Feinjustierung wäre wohl auch nicht unbedingt nötig gewesen, aber wegen der (nur) drei einstellbaren Winkel und feinjustierbaren Kanten wollte ich auf Nummer sicher gehen.
Der Teilgraph ist auf jeden Fall beweglich. Ob es der Kreis auch noch ist, weiß ich nicht, glaube aber er ist starr.
Es sind also auch Ringe aus 24-26 Teilgraphen möglich?
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StefanVogel
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| Beitrag No.1405, eingetragen 2018-09-17 05:59
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Ja, Ringe aus 24 und mehr sind möglich, falls ich nicht noch eine andere Überschneidung übersehen habe. Diese sind starr, weil die eine Bewegungsmöglichkeit des Teilgraphen durch das genaue Einstellen des Winkels 360°/27 aufgebraucht wird. Die Teilgraphen unterschiedlich einstellen geht auch nicht, weil sie dann nicht mehr zusammenpassen.
2018-09-17 05:25 - Slash in Beitrag No. 1404 schreibt:
2018-09-17 04:55 - StefanVogel in Beitrag No. 1403 schreibt:
Hallo Slash, wie hast du geschafft, dass im #1400 der Winkel zwischen den Vektoren P33-P5 und P89-P62 gleich 13.33333333333...° ist, so dass sich der Kreis schließt?
Da habe ich etwas improvisiert, da ich es mit der Kopierfunktion "A(...,"gespiegelt")" nicht geschafft habe genau 27 Teilgraphen aneinander zu kopieren. Ich habe dann einen Ring mit 32 Teilgraphen erstellt, indem ich immer den vorhandenen Teil verdoppelt habe. Das ergab natürlich einen Ring mit Überschneidungen. Dann habe ich in ca. 20 Minuten händisch den grünen und orangenen Winkel bis zur vierten Nachkommastelle so eingestellt bis die Kanten fast deckungsgleich waren. Optisch mit starker Vergrößerung waren nur einzelne Kanten zu erkennen, aber es gab eben keine Punktüberlagerungen.
Das kenne ich, habe ich auch schon oft versucht. Wenn es damit gelingt, einmal eine geringe Überlappung und einmal einen etwas zu großen Zwischenraum einzustellen, sollte das meiner Meinung nach Beweis genug sein. Doch damit 11 Nachkommastellen in 13.33333333333...° einzustellen wäre schon extrem, aber
Dann habe ich die dritte Messkannte RA(57,85) durch RA(57,x) ersetzt, wobei x der Punkt tausend irgendwas war, und feinjustiert. Die Kontrolle der alten Kante RA(57,85) ergab dann immer noch 1. Ob das jetzt geometrisch ganz "koscher" ist, kann ich nicht sagen. ;-)
genau, das wollte ich wissen, das ist die perfekte Lösung. Bei soviel Punkten macht mein Browser den fedgeo und zeichnet nichts mehr, deshalb bin ich auf das RW(...) ausgewichen. So richtig streichholzgraphenmäßig ist das nicht, da werden Kanten eingestellt. Ich bin für deine Lösung mit dem RA(57,x).
Die händische Feinjustierung wäre wohl auch nicht unbedingt nötig gewesen, aber wegen der (nur) drei einstellbaren Winkel und feinjustierbaren Kanten wollte ich auf Nummer sicher gehen.
Ja, geht mir auch so.
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| Beitrag No.1406, vom Themenstarter, eingetragen 2018-09-17 07:14
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Hier ein Ring mit 22 großen Dreiecken.
68 Knoten, 4×Grad 2, 64×Grad 4
132 Kanten, minimal 0.99999999999998323563, maximal 1.00000000000000310862
einstellbare Kanten R(j,k):
|P30-P16|=1.00000000000000044409
|P31-P32|=0.99999999999999933387
|P33-P34|=1.00000000000000177636
\geo ebene(483.18,244.47) x(2.39,13.83) y(12.48,18.26) form(.) #//Eingabe war: #<Streichholzgraph> #<Bildtext>#1373 Fig.2 blauerWinkel=70,nach Feinjustieren(2)</Bildtext> #<Winkel size=''18'' color=''green'' id=''gruenerWinkel'' value=''6.642483684209693''/> #<Winkel size=''18'' color=''orange'' id=''orangerWinkel'' value=''146.47834422411853''/> #<Winkel size=''18'' color=''blue'' id=''blauerWinkel'' value=''10.328908426063999''/> #<Winkel size=''18'' color=''violet'' id=''vierterWinkel'' value=''42.55314061271968''/> #<Feinjustieren Anzahl=''4''/> #<Rechenweg> #P[1]=[-245.7108031423992,107.16408353468191]; #P[2]=[-209.66390939893165,129.22427949387458]; D=ab(1,2); A(2,1,Bew(1)); #N(3,1,2); #M(4,1,3,blauerWinkel); N(5,1,4); A(3,4,ab(4,3,[1,5])); #A(2,8,ab(5,7,[1,8])); N(15,14,10); N(16,14,15); N(17,15,10); #M(18,7,6,gruenerWinkel); N(19,7,18); #M(20,19,18,orangerWinkel); N(21,20,19); #A(18,21,ab(21,18,7,[18,21])); #A(24,22,ab(7,20,[18,24])); RA(30,16); N(31,30,16); #M(32,28,29,vierterWinkel); N(33,28,32); N(34,32,31); RA(31,32); RA(33,34); #N(35,33,34); #A(17,35,ab(17,35,[1,35],''gespiegelt'')); #</Rechenweg> #</Streichholzgraph> #//Ende der Eingabe, weiter mit fedgeo: p(4.19,12.54,P1) p(5.04,13.06,P2) p(4.16,13.54,P3) p(3.98,13.51,P4) p(3.24,12.85,P5) p(3.96,14.51,P6) p(3.10,13.99,P7) p(4.91,14.20,P8) p(5.99,12.75,P9) p(6.84,13.27,P10) p(5.96,13.74,P11) p(5.78,13.72,P12) p(5.76,14.72,P13) p(6.71,14.41,P14) p(7.59,13.93,P15) p(7.56,14.93,P16) p(7.79,12.95,P17) p(3.89,14.61,P18) p(2.96,14.98,P19) p(2.39,15.81,P20) p(3.39,15.89,P21) p(4.18,16.50,P22) p(4.32,15.51,P23) p(4.89,14.69,P24) p(5.67,15.31,P25) p(4.75,15.68,P26) p(5.17,16.58,P27) p(5.96,17.20,P28) p(6.10,16.21,P29) p(6.67,15.39,P30) p(7.51,15.93,P31) p(6.73,16.57,P32) p(6.90,17.55,P33) p(7.67,16.92,P34) p(7.83,17.91,P35) p(11.39,12.48,P36) p(10.55,13.01,P37) p(11.43,13.47,P38) p(11.61,13.45,P39) p(12.35,12.77,P40) p(11.65,14.45,P41) p(12.50,13.91,P42) p(10.70,14.15,P43) p(9.59,12.72,P44) p(8.75,13.25,P45) p(9.63,13.71,P46) p(9.81,13.69,P47) p(9.85,14.69,P48) p(8.90,14.39,P49) p(8.01,13.93,P50) p(8.05,14.93,P51) p(11.72,14.54,P52) p(12.65,14.90,P53) p(13.24,15.72,P54) p(12.24,15.81,P55) p(11.46,16.44,P56) p(11.31,15.45,P57) p(10.73,14.64,P58) p(9.95,15.27,P59) p(10.88,15.63,P60) p(10.47,16.54,P61) p(9.69,17.17,P62) p(9.53,16.18,P63) p(8.95,15.37,P64) p(8.12,15.93,P65) p(8.91,16.55,P66) p(8.76,17.54,P67) p(7.98,16.92,P68) nolabel() s(P1,P2) s(P9,P2) s(P12,P2) s(P1,P3) s(P2,P3) s(P6,P3) s(P1,P4) s(P6,P4) s(P7,P4) s(P1,P5) s(P4,P5) s(P6,P7) s(P6,P8) s(P3,P8) s(P13,P8) s(P9,P10) s(P9,P11) s(P10,P11) s(P13,P11) s(P9,P12) s(P13,P12) s(P8,P12) s(P11,P14) s(P13,P14) s(P14,P15) s(P10,P15) s(P14,P16) s(P15,P16) s(P15,P17) s(P10,P17) s(P45,P17) s(P50,P17) s(P7,P18) s(P23,P18) s(P24,P18) s(P7,P19) s(P18,P19) s(P19,P20) s(P20,P21) s(P19,P21) s(P22,P21) s(P26,P22) s(P22,P23) s(P21,P23) s(P23,P24) s(P24,P25) s(P29,P25) s(P30,P25) s(P24,P26) s(P25,P26) s(P26,P27) s(P22,P27) s(P28,P27) s(P27,P29) s(P28,P29) s(P29,P30) s(P16,P30) s(P30,P31) s(P16,P31) s(P32,P31) s(P28,P32) s(P28,P33) s(P32,P33) s(P34,P33) s(P32,P34) s(P31,P34) s(P33,P35) s(P34,P35) s(P67,P35) s(P68,P35) s(P36,P37) s(P44,P37) s(P47,P37) s(P36,P38) s(P37,P38) s(P41,P38) s(P36,P39) s(P41,P39) s(P42,P39) s(P36,P40) s(P39,P40) s(P41,P42) s(P38,P43) s(P41,P43) s(P48,P43) s(P44,P45) s(P44,P46) s(P45,P46) s(P48,P46) s(P43,P47) s(P44,P47) s(P48,P47) s(P46,P49) s(P48,P49) s(P45,P50) s(P49,P50) s(P49,P51) s(P50,P51) s(P42,P52) s(P57,P52) s(P58,P52) s(P42,P53) s(P52,P53) s(P53,P54) s(P53,P55) s(P54,P55) s(P56,P55) s(P60,P56) s(P55,P57) s(P56,P57) s(P57,P58) s(P58,P59) s(P63,P59) s(P64,P59) s(P58,P60) s(P59,P60) s(P56,P61) s(P60,P61) s(P62,P61) s(P61,P63) s(P62,P63) s(P51,P64) s(P63,P64) s(P51,P65) s(P64,P65) s(P66,P65) s(P62,P66) s(P62,P67) s(P66,P67) s(P68,P67) s(P65,P68) s(P66,P68) pen(2) color(#008000) m(P6,P7,MA10) m(P7,P18,MB10) f(P7,MA10,MB10) color(#FFA500) m(P18,P19,MA11) m(P19,P20,MB11) b(P19,MA11,MB11) color(#0000FF) m(P3,P1,MA12) m(P1,P4,MB12) f(P1,MA12,MB12) color(#EE82EE) m(P29,P28,MA13) m(P28,P32,MB13) b(P28,MA13,MB13) pen(2) color(#008000) s(P30,P16) color(#008000) s(P31,P32) color(#008000) s(P33,P34) color(blue) color(orange) color(red) \geooff \geoprint()
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haribo
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| Beitrag No.1407, eingetragen 2018-09-17 09:14
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sehr gut dass du sowas zeichnen kannst, slash
es reichen aber auch diese 14 entscheidenden grossen dreiecke im 7-eck, weiss nicht wann wir das schon hatten? suche ich später..
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| Beitrag No.1408, vom Themenstarter, eingetragen 2018-09-17 09:25
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Ja schon, aber da überwiegen ja die großen Dreiecke. Es ging mir auch mehr um den Winkel für die Girlanden. Gibt es einen Ring mit nur einem großen Dreieck im symmetrischen Teilgraph?
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| Beitrag No.1409, eingetragen 2018-09-17 11:22
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ja die grossen dreiecke überwiegen, da hast du recht, führst aber damit ne neue bedingung ein... "grosse dreiecke sollen nicht überwiegen", ich habs dargestellt weil es nur 14 sind und nicht 22, wohl wissend das u.A. der 126er nur 12 grosse dreiecke, also nochmals weniger, hätte
also wir hatten den 168er in #547(und dort behaupte ich auch schon das wir ihn noch früher schon hatten, dass hab ich aber jetzt nicht finden können bei händischem durchsuchen...)
dafür bin ich über #567 gestolpert eineeer den du evtl für deine fast-graphen-sammlung gebrauchen könntest?
und nochmals die frage wie füge ich einen link hier ein der direkt auf #567 führt??? (wie das geht vergess ich immer wieder...)
haribo
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| Beitrag No.1410, vom Themenstarter, eingetragen 2018-09-17 12:50
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#567 ist ein 4/6.
Was die Bedingungen mit den großen Dreiecken betrifft... Ich experimentiere mit diesen Girlanden. Mehr steckt nicht dahinter.
2018-09-17 11:22 - haribo in Beitrag No. 1409 schreibt:
und nochmals die frage wie füge ich einen link hier ein der direkt auf #345 führt??? (wie das geht vergess ich immer wieder...)
Ich mache es so: Mit der rechten Maustaste unter dem Beitrag auf "Link" klicken und "Link Adresse kopieren" wählen. Dann im neuen Beitrag "Link extern" (intern mag ich nicht so) anklicken und kopierten Link einfügen.
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| Beitrag No.1411, vom Themenstarter, eingetragen 2018-09-17 16:21
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4/4 Dreieck-Speichenrad mit 600 Knoten aber 30 Rauten.  Geht vielleicht auch noch kleiner. Eingabe ist vollständig im Code.
\geo ebene(183.99,308.91) x(11.86,18.23) y(12.34,23.04) form(.) #//Eingabe war: #<Streichholzgraph> #<Bildtext>#1373 Fig.2 blauerWinkel=70,nach Feinjustieren(2)</Bildtext> #<Winkel size=''18'' color=''green'' id=''gruenerWinkel'' value=''-333.06143960169146''/> #<Winkel size=''18'' color=''orange'' id=''orangerWinkel'' value=''62.93856039830859''/> #<Feinjustieren Anzahl=''2''/> #<Rechenweg> #P[1]=[79.02738208087105,319.9587593230809]; #P[2]=[53.667587779922265,306.17190399485537]; D=ab(1,2); A(2,1); #N(3,1,2); #M(4,1,3,gruenerWinkel); N(5,1,4); A(3,4,ab(4,3,[1,5])); N(9,5,7); #M(10,7,6,orangerWinkel); N(11,5,9); N(12,9,10); #A(11,12,ab(11,12,[1,12],''gespiegelt'')); #N(23,22,10); N(24,22,23); N(25,23,10); #A(25,24,ab(24,25,10,[22,25])); #A(27,26,ab(26,27,10,[22,28])); #A(30,29,ab(29,30,[26,28],[31,34])); N(42,36,37); #//A(2,8,ab(2,8,[1,42],''gespiegelt'')); N(83,35,75); RA(37,83); A(77,83); #//A(54,60,ab(54,60,[1,83],''gespiegelt'')); #//A(103,97,ab(103,97,[1,164],''gespiegelt'')); #//A(184,178,ab(184,178,[1,326],''gespiegelt'')); R(1,343); #</Rechenweg> #</Streichholzgraph> #//Ende der Eingabe, weiter mit fedgeo: p(12.737813525852884,21.084606321558454,P1) p(11.85925237373305,20.606976441854652,P2) p(12.712172559222964,20.08493510519265,P3) p(13.167840629171335,20.18179034340369,P4) p(13.734688649536631,21.00561272827069,P5) p(13.142199662541415,19.182119127037886,P6) p(14.020760814661251,19.65974900674169,P7) p(12.145324538857668,19.261112720325656,P8) p(14.587608835026547,20.483571391608685,P9) p(14.046401781291165,18.660077790375887,P10) p(14.613249801656467,21.48324260797449,P11) p(14.613249801656458,19.483900175242887,P12) p(16.48868607746005,21.08460632155844,P13) p(17.367247229579878,20.60697644185463,P14) p(16.51432704408996,20.084935105192635,P15) p(16.05865897414159,20.181790343403677,P16) p(15.491810953776298,21.005612728270684,P17) p(16.0842999407715,19.18211912703788,P18) p(15.205738788651669,19.659749006741684,P19) p(17.08117506445525,19.261112720325634,P20) p(14.63889076828638,20.483571391608685,P21) p(15.180097822021747,18.660077790375883,P22) p(14.613249801656455,17.836255405508886,P23) p(15.610124925340202,17.757261812221124,P24) p(13.616374677972706,17.757261812221127,P25) p(15.180097822021743,16.85444583406636,P26) p(14.046401781291161,16.854445834066365,P27) p(14.613249801656455,17.67826821893336,P28) p(15.18009782202174,15.048813877756839,P29) p(14.046401781291157,15.048813877756842,P30) p(14.613249801656451,15.87263626262384,P31) p(13.6163746779727,15.951629855911605,P32) p(15.610124925340198,15.9516298559116,P33) p(14.61324980165645,16.030623449199364,P34) p(14.046401781291154,13.243181921447322,P35) p(15.180097822021738,13.243181921447317,P36) p(14.61324980165644,12.419359536580322,P37) p(14.613249801656448,14.224991492889842,P38) p(15.610124925340195,14.145997899602078,P39) p(13.616374677972699,14.145997899602083,P40) p(14.613249801656448,14.067004306314319,P41) p(15.61012492534019,12.340365943292555,P42) nolabel() s(P1,P2) s(P1,P3) s(P2,P3) s(P6,P3) s(P1,P4) s(P6,P4) s(P7,P4) s(P1,P5) s(P4,P5) s(P6,P7) s(P6,P8) s(P3,P8) s(P5,P9) s(P7,P9) s(P7,P10) s(P5,P11) s(P9,P11) s(P17,P11) s(P21,P11) s(P9,P12) s(P10,P12) s(P21,P12) s(P22,P12) s(P13,P14) s(P13,P15) s(P14,P15) s(P18,P15) s(P13,P16) s(P18,P16) s(P19,P16) s(P13,P17) s(P16,P17) s(P18,P19) s(P15,P20) s(P18,P20) s(P17,P21) s(P19,P21) s(P19,P22) s(P22,P23) s(P10,P23) s(P22,P24) s(P23,P24) s(P26,P24) s(P28,P24) s(P23,P25) s(P10,P25) s(P27,P25) s(P28,P25) s(P26,P28) s(P27,P28) s(P29,P31) s(P30,P31) s(P30,P32) s(P31,P32) s(P27,P32) s(P34,P32) s(P29,P33) s(P31,P33) s(P26,P33) s(P34,P33) s(P27,P34) s(P26,P34) s(P35,P37) s(P36,P37) s(P30,P38) s(P29,P38) s(P36,P39) s(P29,P39) s(P38,P39) s(P41,P39) s(P35,P40) s(P30,P40) s(P38,P40) s(P41,P40) s(P35,P41) s(P36,P41) s(P36,P42) s(P37,P42) pen(2) color(#008000) m(P3,P1,MA10) m(P1,P4,MB10) b(P1,MA10,MB10) color(#FFA500) m(P6,P7,MA11) m(P7,P10,MB11) b(P7,MA11,MB11) pen(2) print(min=0.9999999999999984,11.86,23.042) print(max=1.000000000000003,11.86,22.523) \geooff \geoprint()
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haribo
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| Beitrag No.1412, eingetragen 2018-09-17 17:11
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2018-09-16 12:43 - Slash in Beitrag No. 1402 schreibt:
Vielleicht ist ein Beweis, dass so ein Ring-Graph bzw. ein 4/4 mit den geforderten Eigenschaften überhaupt nicht möglich ist, gar nicht mal so schwer. Es geht nur zwingend mit diesen "Girlanden", da sich die Dreiecke nicht anders verbinden lassen. Und man muss irgendwie eine Keilform für den Teilgraph erhalten. Das geht aber nicht ohen Rauten oder größere Dreiecke, da die Winkel der Girlanden begrenzt sind. Ein Beweis wäre bestimmt ähnlich dem Beweis, dass kein regulärer SHG mit Grad > 4 existiert.
habe einen ansatz der evtl deine these widerlegt:
-ich nehme den harborth ansatz mit den berührenden, drehe aber das letzte dreieck innen (weis) marginal nach oben bis die berührpunkte frei sind,
-das geht da ja harborths ansatz soweit elastisch ist
-dann füge ich innen einige, hier zwei, dreiecke an (blau;gelb) bis einer die tortenwand in geeigneter weise berührt,
-den gelben kann ich dann ewig hin und herspiegeln, bis er irgendwo innen beide tortenwände berührt
-dann kann man die torte, wie gehabt, schliessen
ok, es ist momentan die frage offen, ob der rechteste gelbe exakt berührt und gleichzeitig die torte geschlossen werden kann, darüber muss man nochmal nachdenken, ich vermute aber dass links ausreichende elastizität gegeben ist
[Die Antwort wurde nach Beitrag No.1410 begonnen.]
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| Beitrag No.1413, eingetragen 2018-09-17 17:20
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sehr spassig, wir haben mal wieder gleichzeitig, die gleiche speichen-rad konstruktion avisiert...
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| Beitrag No.1414, vom Themenstarter, eingetragen 2018-09-17 17:31
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Geht noch kleiner mit 176 Knoten und 22 Rauten.
176 Knoten, 176×Grad 4
352 Kanten, minimal 0.99999999999999200639, maximal 1.00000000000035815795
einstellbare Kanten R(j,k):
|P10-P41|=1.00000000000001176836
|P13-P279|=1.00000000000035815795
\geo ebene(561.23,545.77) x(3.38,17.99) y(4.45,18.65) form(.) #//Eingabe war: #<Streichholzgraph> #<Bildtext>#1373 Fig.2 blauerWinkel=70,nach Feinjustieren(2)</Bildtext> #<Winkel size=''18'' color=''green'' id=''gruenerWinkel'' value=''-313.41503942543915''/> #<Winkel size=''18'' color=''orange'' id=''orangerWinkel'' value=''73.85768784728818''/> #<Feinjustieren Anzahl=''2''/> #<Rechenweg> #P[1]=[-59.29281384833949,295.8838027559203]; #P[2]=[-94.63948597219365,280.8281965753754]; D=ab(1,2); A(2,1); #N(3,1,2); #M(4,1,3,gruenerWinkel); N(5,1,4); A(3,4,ab(4,3,[1,5])); N(9,5,7); #M(10,7,6,orangerWinkel); N(11,5,9); N(12,9,10); #A(11,12,ab(11,12,1,[4,7],[9,12],''gespiegelt'')); #N(20,19,10); N(21,19,20); #A(1,6,ab(1,6,[1,21],''gespiegelt'')); N(41,29,39); RA(10,41); A(41,20); #A(32,35,ab(32,35,[1,60],''gespiegelt'')); #A(54,57,ab(54,57,[1,138],''gespiegelt'')); #A(93,96,ab(93,96,[1,216],''gespiegelt'')); #R(13,279); # #//ergänzt von Button ''Knoten zusammenfassen'': #C(1,212); C(2,25,214); C(3,24,213); C(4,23,290); C(5,22,291); C(6,215); #C(7,27,292); C(8,26,216); C(9,293); C(10,294); C(11,288); C(12,289); C(13,278); #C(14,281,298); C(15,282,297); C(16,283); C(17,284,302); C(18,286); C(19,287); #C(20,295); C(21,314); C(28,217); C(29,218); C(30,210); C(31,211); C(32,200); #C(33,203,222); C(34,204,221); C(35,205); C(36,206,226); C(37,208); C(38,209); #C(39,219); C(40,79,238); C(41,220,296); C(42,190); C(43,66,232); C(44,65,231); #C(45,64,191); C(46,63,192); C(47,193); C(48,68,194); C(49,67,233); C(50,195); #C(51,196); C(52,188); C(53,189); C(54,159); C(55,161,182); C(56,160,183); #C(57,164); C(58,166,184); C(59,186); C(60,187); C(61,197); C(62,140,199); #C(69,234); C(70,235); C(71,229); C(72,230); C(73,202,223); C(74,201,224); #C(75,207,225); C(76,227); C(77,228); C(78,236); C(80,198,237); C(82,105); #C(83,104); C(84,103); C(85,102); C(87,107); C(88,106); C(101,257); C(120,157); #C(122,171); C(123,144); C(124,143); C(125,142,172); C(126,141,173); C(127,174); #C(128,146,175); C(129,145); C(130,176); C(131,177); C(132,169); C(133,170); #C(134,162,181); C(135,163,180); C(136,165,185); C(137,167); C(138,168); #C(139,178); C(158,179); C(240,261); C(241,260); C(242,259); C(243,258); #C(245,263); C(246,262); C(276,313); C(279,300); C(280,299); C(285,301); #</Rechenweg> #</Streichholzgraph> #//Ende der Eingabe, weiter mit fedgeo: p(8.46,17.70,P1) p(7.54,17.31,P2) p(8.34,16.71,P3) p(9.09,16.93,P4) p(9.44,17.87,P5) p(8.97,15.94,P6) p(9.89,16.33,P7) p(7.99,15.77,P8) p(10.24,17.27,P9) p(10.01,15.34,P10) p(10.36,18.26,P11) p(10.36,16.28,P12) p(12.27,17.70,P13) p(11.63,16.93,P14) p(11.28,17.87,P15) p(11.75,15.94,P16) p(10.83,16.33,P17) p(10.48,17.27,P18) p(10.71,15.34,P19) p(10.36,14.40,P20) p(11.35,14.57,P21) p(7.19,16.37,P28) p(8.42,14.87,P29) p(6.55,17.14,P30) p(7.62,15.47,P31) p(5.25,15.64,P32) p(6.20,15.34,P33) p(5.99,16.31,P34) p(6.64,14.44,P35) p(7.20,15.26,P36) p(6.99,16.24,P37) p(7.84,14.49,P38) p(8.64,13.89,P39) p(7.72,13.50,P40) p(9.38,14.57,P41) p(3.67,12.17,P42) p(3.92,13.14,P43) p(4.63,12.43,P44) p(4.52,11.65,P45) p(3.64,11.17,P46) p(5.48,11.91,P47) p(5.23,10.95,P48) p(5.51,12.91,P49) p(4.35,10.47,P50) p(6.23,10.97,P51) p(3.38,10.21,P52) p(5.35,10.49,P53) p(4.21,8.40,P54) p(4.88,9.14,P55) p(3.90,9.35,P56) p(5.88,9.16,P57) p(5.36,10.02,P58) p(4.38,10.23,P59) p(6.33,10.28,P60) p(7.21,10.76,P61) p(7.18,9.76,P62) p(4.80,13.62,P69) p(6.46,12.61,P70) p(3.95,14.14,P71) p(5.76,13.31,P72) p(5.69,14.74,P73) p(4.69,14.81,P74) p(5.90,13.76,P75) p(4.90,13.84,P76) p(6.75,13.24,P77) p(7.46,12.54,P78) p(6.90,11.71,P80) p(14.02,5.52,P81) p(13.12,5.08,P82) p(13.19,6.08,P83) p(13.86,6.51,P84) p(14.79,6.15,P85) p(13.03,7.07,P86) p(13.93,7.50,P87) p(12.25,6.43,P88) p(14.86,7.15,P89) p(13.25,8.25,P90) p(15.69,6.59,P91) p(14.19,7.89,P92) p(16.52,8.40,P93) p(15.52,8.42,P94) p(16.00,7.55,P95) p(14.84,9.16,P96) p(14.54,8.21,P97) p(15.02,7.33,P98) p(13.71,8.77,P99) p(12.77,9.12,P100) p(13.55,9.76,P101) p(12.18,5.43,P108) p(11.86,7.35,P109) p(12.35,4.45,P110) p(11.79,6.35,P111) p(10.36,4.45,P112) p(10.76,5.36,P113) p(11.36,4.56,P114) p(10.36,6.28,P115) p(11.36,6.17,P116) p(11.95,5.36,P117) p(11.19,7.15,P118) p(11.26,8.15,P119) p(10.36,7.71,P120) p(12.25,8.27,P121) p(6.71,5.52,P122) p(7.60,5.08,P123) p(7.53,6.08,P124) p(6.87,6.51,P125) p(5.93,6.15,P126) p(7.70,7.07,P127) p(6.80,7.50,P128) p(8.47,6.43,P129) p(5.86,7.15,P130) p(7.47,8.25,P131) p(5.03,6.59,P132) p(6.53,7.89,P133) p(5.21,8.42,P134) p(4.73,7.55,P135) p(6.19,8.21,P136) p(5.71,7.33,P137) p(7.02,8.77,P138) p(7.95,9.12,P139) p(8.54,5.43,P147) p(8.87,7.35,P148) p(8.38,4.45,P149) p(8.94,6.35,P150) p(9.97,5.36,P151) p(9.37,4.56,P152) p(9.37,6.17,P153) p(8.77,5.36,P154) p(9.53,7.15,P155) p(9.46,8.15,P156) p(8.47,8.27,P158) p(17.06,12.17,P239) p(16.80,13.14,P240) p(16.09,12.43,P241) p(16.21,11.65,P242) p(17.08,11.17,P243) p(15.24,11.91,P244) p(15.50,10.95,P245) p(15.21,12.91,P246) p(16.38,10.47,P247) p(14.50,10.97,P248) p(17.34,10.21,P249) p(15.38,10.49,P250) p(15.84,9.14,P251) p(16.82,9.35,P252) p(15.36,10.02,P253) p(16.34,10.23,P254) p(14.40,10.28,P255) p(13.52,10.76,P256) p(15.92,13.62,P264) p(14.26,12.61,P265) p(16.78,14.14,P266) p(14.97,13.31,P267) p(15.48,15.64,P268) p(15.04,14.74,P269) p(16.04,14.81,P270) p(14.09,14.44,P271) p(14.83,13.76,P272) p(15.82,13.84,P273) p(13.97,13.24,P274) p(13.26,12.54,P275) p(13.01,13.50,P276) p(13.83,11.71,P277) p(13.19,17.31,P279) p(12.39,16.71,P280) p(12.74,15.77,P285) p(13.54,16.37,P303) p(12.30,14.87,P304) p(14.17,17.14,P305) p(13.10,15.47,P306) p(14.52,15.34,P307) p(14.74,16.31,P308) p(13.52,15.26,P309) p(13.74,16.24,P310) p(12.89,14.49,P311) p(12.09,13.89,P312) nolabel() s(P3,P1) s(P2,P1) s(P4,P1) s(P5,P1) s(P3,P2) s(P28,P2) s(P30,P2) s(P6,P3) s(P8,P3) s(P6,P4) s(P7,P4) s(P5,P4) s(P9,P5) s(P11,P5) s(P7,P6) s(P8,P6) s(P9,P7) s(P10,P7) s(P28,P8) s(P29,P8) s(P11,P9) s(P12,P9) s(P41,P10) s(P12,P10) s(P20,P10) s(P15,P11) s(P18,P11) s(P18,P12) s(P19,P12) s(P14,P13) s(P15,P13) s(P279,P13) s(P280,P13) s(P16,P14) s(P17,P14) s(P15,P14) s(P18,P15) s(P17,P16) s(P280,P16) s(P285,P16) s(P18,P17) s(P19,P17) s(P20,P19) s(P21,P19) s(P21,P20) s(P41,P20) s(P304,P21) s(P312,P21) s(P30,P28) s(P31,P28) s(P31,P29) s(P39,P29) s(P41,P29) s(P34,P30) s(P37,P30) s(P37,P31) s(P38,P31) s(P33,P32) s(P34,P32) s(P73,P32) s(P74,P32) s(P35,P33) s(P36,P33) s(P34,P33) s(P37,P34) s(P36,P35) s(P73,P35) s(P75,P35) s(P37,P36) s(P38,P36) s(P39,P38) s(P40,P38) s(P40,P39) s(P41,P39) s(P77,P40) s(P78,P40) s(P43,P42) s(P44,P42) s(P45,P42) s(P46,P42) s(P44,P43) s(P69,P43) s(P71,P43) s(P47,P44) s(P49,P44) s(P47,P45) s(P48,P45) s(P46,P45) s(P50,P46) s(P52,P46) s(P48,P47) s(P49,P47) s(P50,P48) s(P51,P48) s(P69,P49) s(P70,P49) s(P52,P50) s(P53,P50) s(P80,P51) s(P53,P51) s(P61,P51) s(P56,P52) s(P59,P52) s(P59,P53) s(P60,P53) s(P55,P54) s(P56,P54) s(P134,P54) s(P135,P54) s(P57,P55) s(P58,P55) s(P56,P55) s(P59,P56) s(P58,P57) s(P134,P57) s(P136,P57) s(P59,P58) s(P60,P58) s(P61,P60) s(P62,P60) s(P62,P61) s(P80,P61) s(P138,P62) s(P139,P62) s(P71,P69) s(P72,P69) s(P72,P70) s(P78,P70) s(P80,P70) s(P74,P71) s(P76,P71) s(P76,P72) s(P77,P72) s(P75,P73) s(P74,P73) s(P76,P74) s(P76,P75) s(P77,P75) s(P78,P77) s(P80,P78) s(P82,P81) s(P83,P81) s(P84,P81) s(P85,P81) s(P83,P82) s(P108,P82) s(P110,P82) s(P86,P83) s(P88,P83) s(P86,P84) s(P87,P84) s(P85,P84) s(P89,P85) s(P91,P85) s(P87,P86) s(P88,P86) s(P89,P87) s(P90,P87) s(P108,P88) s(P109,P88) s(P91,P89) s(P92,P89) s(P121,P90) s(P92,P90) s(P100,P90) s(P95,P91) s(P98,P91) s(P98,P92) s(P99,P92) s(P94,P93) s(P95,P93) s(P251,P93) s(P252,P93) s(P96,P94) s(P97,P94) s(P95,P94) s(P98,P95) s(P97,P96) s(P251,P96) s(P253,P96) s(P98,P97) s(P99,P97) s(P100,P99) s(P101,P99) s(P101,P100) s(P121,P100) s(P255,P101) s(P256,P101) s(P110,P108) s(P111,P108) s(P111,P109) s(P119,P109) s(P121,P109) s(P114,P110) s(P117,P110) s(P117,P111) s(P118,P111) s(P113,P112) s(P114,P112) s(P151,P112) s(P152,P112) s(P115,P113) s(P116,P113) s(P114,P113) s(P117,P114) s(P116,P115) s(P151,P115) s(P153,P115) s(P117,P116) s(P118,P116) s(P119,P118) s(P120,P118) s(P120,P119) s(P121,P119) s(P155,P120) s(P156,P120) s(P123,P122) s(P124,P122) s(P125,P122) s(P126,P122) s(P124,P123) s(P147,P123) s(P149,P123) s(P127,P124) s(P129,P124) s(P127,P125) s(P128,P125) s(P126,P125) s(P130,P126) s(P132,P126) s(P128,P127) s(P129,P127) s(P130,P128) s(P131,P128) s(P147,P129) s(P148,P129) s(P132,P130) s(P133,P130) s(P158,P131) s(P133,P131) s(P139,P131) s(P135,P132) s(P137,P132) s(P137,P133) s(P138,P133) s(P136,P134) s(P135,P134) s(P137,P135) s(P137,P136) s(P138,P136) s(P139,P138) s(P158,P139) s(P149,P147) s(P150,P147) s(P150,P148) s(P156,P148) s(P158,P148) s(P152,P149) s(P154,P149) s(P154,P150) s(P155,P150) s(P153,P151) s(P152,P151) s(P154,P152) s(P154,P153) s(P155,P153) s(P156,P155) s(P158,P156) s(P240,P239) s(P241,P239) s(P242,P239) s(P243,P239) s(P241,P240) s(P264,P240) s(P266,P240) s(P244,P241) s(P246,P241) s(P244,P242) s(P245,P242) s(P243,P242) s(P247,P243) s(P249,P243) s(P245,P244) s(P246,P244) s(P247,P245) s(P248,P245) s(P264,P246) s(P265,P246) s(P249,P247) s(P250,P247) s(P277,P248) s(P250,P248) s(P256,P248) s(P252,P249) s(P254,P249) s(P254,P250) s(P255,P250) s(P253,P251) s(P252,P251) s(P254,P252) s(P254,P253) s(P255,P253) s(P256,P255) s(P277,P256) s(P266,P264) s(P267,P264) s(P267,P265) s(P275,P265) s(P277,P265) s(P270,P266) s(P273,P266) s(P273,P267) s(P274,P267) s(P269,P268) s(P270,P268) s(P307,P268) s(P308,P268) s(P271,P269) s(P272,P269) s(P270,P269) s(P273,P270) s(P272,P271) s(P307,P271) s(P309,P271) s(P273,P272) s(P274,P272) s(P275,P274) s(P276,P274) s(P276,P275) s(P277,P275) s(P311,P276) s(P312,P276) s(P280,P279) s(P303,P279) s(P305,P279) s(P285,P280) s(P303,P285) s(P304,P285) s(P305,P303) s(P306,P303) s(P306,P304) s(P312,P304) s(P308,P305) s(P310,P305) s(P310,P306) s(P311,P306) s(P309,P307) s(P308,P307) s(P310,P308) s(P310,P309) s(P311,P309) s(P312,P311) pen(2) color(#008000) m(P3,P1,MA10) m(P1,P4,MB10) b(P1,MA10,MB10) color(#FFA500) m(P6,P7,MA11) m(P7,P10,MB11) b(P7,MA11,MB11) pen(2) color(#008000) s(P10,P41) color(#008000) s(P13,P279) color(blue) color(orange) color(red) \geooff \geoprint()
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| Beitrag No.1415, vom Themenstarter, eingetragen 2018-09-17 17:37
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2018-09-17 17:11 - haribo in Beitrag No. 1412 schreibt:
und gleichzeitig die torte geschlossen werden kann
Tja, das ist Streichholzgraphen-Jargon. 
Also wenn du mit deinem Ansatz rechts hast, dann hat sich das hier ja mal wieder gelohnt und kein Graph war umsonst.
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| Beitrag No.1416, vom Themenstarter, eingetragen 2018-09-17 17:53
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Ob auch Doppelspeichen möglich sind? Hier gibt es minimale Überschneidungen im inneren Kreis. Der Graph ist noch nicht getestet worden.
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haribo
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| Beitrag No.1417, eingetragen 2018-09-17 18:03
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klar sind speichen-seiten-wechsel möglich, das erhöht die variantenmöglichkeit bis es innen passt sogar nochmal enorm
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| Beitrag No.1418, vom Themenstarter, eingetragen 2018-09-17 18:25
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Spiegel dein letztes Tortenstück mal auf jeder Seite, dann kann ich mir das besser vorstellen. Ich versuche es gerade zu konstruieren. Bis hier hin richtig?
66 Knoten, 6×Grad 2, 60×Grad 4
126 Kanten, minimal 0.99999999999999633626, maximal 1.00000000000002997602
einstellbare Kanten R(j,k):
|P55-P28|=1.00000000000002997602
\geo ebene(585.13,232.96) x(4.78,16.48) y(10.77,15.43) form(.) #//Eingabe war: #<Streichholzgraph> #<Bildtext>#1373 Fig.2 RA(55,28); RA(59,28); RW(8,7,36,7,1.8); dann #Feinjustieren(3)</Bildtext> #<Winkel size=''18'' color=''green'' id=''gruenerWinkel'' value=''43.206788004551434''/> #<Winkel size=''18'' color=''orange'' id=''orangerWinkel'' value=''89.1''/> #<Winkel size=''18'' color=''blue'' id=''blauerWinkel'' value=''116.59''/> #<Winkel size=''18'' color=''violet'' id=''vierterWinkel'' value=''-40''/> #<Feinjustieren Anzahl=''1''/> #<Rechenweg> #P[1]=[-216.7626818452764,64.74181068041395]; #P[2]=[-172.94433547447844,40.65960726526153]; D=ab(1,2); A(2,1,Bew(1)); #L(3,1,2); M(4,1,3,blauerWinkel); L(5,1,4); A(3,4,ab(4,3,[1,5])); #A(2,8,ab(5,7,[1,8])); A(10,14,ab(5,7,[1,14])); N(27,26,22); L(28,26,27); #L(29,27,22); M(30,7,6,gruenerWinkel); L(31,7,30); M(32,31,30,orangerWinkel); #L(33,31,32); A(30,32,ab(32,30,7,[30,33])); A(36,34,ab(7,33,[30,36])); #A(42,40,ab(7,33,[30,42])); A(54,52,ab(7,33,[30,33])); RA(55,28); N(58,55,28); #M(59,58,55,vierterWinkel); N(60,59,58); #N(61,57,59); N(62,61,59); N(63,57,61); #A(62,63,ab(63,62,57,59,[61,63])); # #</Rechenweg> #</Streichholzgraph> #//Ende der Eingabe, weiter mit fedgeo: p(5.66,11.29,P1) p(6.54,10.81,P2) p(6.52,11.81,P3) p(4.82,11.83,P4) p(4.78,10.83,P5) p(5.67,12.35,P6) p(4.80,12.83,P7) p(6.56,12.81,P8) p(7.43,11.28,P9) p(8.30,10.80,P10) p(8.28,11.80,P11) p(6.58,11.81,P12) p(7.43,12.33,P13) p(8.32,12.80,P14) p(9.19,11.26,P15) p(10.06,10.78,P16) p(10.04,11.78,P17) p(8.34,11.80,P18) p(9.20,12.32,P19) p(10.08,12.78,P20) p(10.95,11.25,P21) p(11.82,10.77,P22) p(11.80,11.77,P23) p(10.10,11.78,P24) p(10.96,12.30,P25) p(11.84,12.77,P26) p(11.86,11.77,P27) p(12.72,12.28,P28) p(12.71,11.23,P29) p(5.77,13.08,P30) p(5.07,13.79,P31) p(5.79,14.48,P32) p(4.83,14.76,P33) p(6.76,14.73,P34) p(6.49,13.76,P35) p(6.72,12.79,P36) p(7.69,13.04,P37) p(6.99,13.76,P38) p(7.72,14.44,P39) p(8.69,14.69,P40) p(8.42,13.73,P41) p(8.65,12.76,P42) p(9.62,13.01,P43) p(8.92,13.72,P44) p(9.65,14.41,P45) p(10.61,14.66,P46) p(10.35,13.70,P47) p(10.58,12.72,P48) p(11.55,12.97,P49) p(10.85,13.69,P50) p(11.57,14.37,P51) p(12.54,14.62,P52) p(12.27,13.66,P53) p(12.51,12.69,P54) p(13.48,12.94,P55) p(12.78,13.65,P56) p(13.50,14.34,P57) p(13.66,11.95,P58) p(14.15,12.83,P59) p(14.66,11.97,P60) p(14.35,13.81,P61) p(15.10,13.15,P62) p(14.39,14.81,P63) p(15.98,13.61,P64) p(15.33,15.13,P65) p(15.14,14.15,P66) nolabel() s(P1,P2) s(P9,P2) s(P12,P2) s(P1,P3) s(P2,P3) s(P6,P3) s(P1,P4) s(P6,P4) s(P7,P4) s(P1,P5) s(P4,P5) s(P6,P7) s(P6,P8) s(P3,P8) s(P13,P8) s(P9,P10) s(P15,P10) s(P18,P10) s(P9,P11) s(P10,P11) s(P13,P11) s(P9,P12) s(P13,P12) s(P8,P12) s(P11,P14) s(P13,P14) s(P19,P14) s(P15,P16) s(P21,P16) s(P24,P16) s(P15,P17) s(P16,P17) s(P19,P17) s(P15,P18) s(P19,P18) s(P14,P18) s(P17,P20) s(P19,P20) s(P25,P20) s(P21,P22) s(P21,P23) s(P22,P23) s(P25,P23) s(P20,P24) s(P21,P24) s(P25,P24) s(P23,P26) s(P25,P26) s(P26,P27) s(P22,P27) s(P26,P28) s(P27,P28) s(P27,P29) s(P22,P29) s(P7,P30) s(P35,P30) s(P7,P31) s(P30,P31) s(P31,P32) s(P34,P32) s(P31,P33) s(P32,P33) s(P38,P34) s(P39,P34) s(P34,P35) s(P32,P35) s(P35,P36) s(P30,P36) s(P36,P37) s(P41,P37) s(P36,P38) s(P37,P38) s(P38,P39) s(P40,P39) s(P44,P40) s(P45,P40) s(P39,P41) s(P40,P41) s(P37,P42) s(P41,P42) s(P42,P43) s(P47,P43) s(P42,P44) s(P43,P44) s(P44,P45) s(P46,P45) s(P50,P46) s(P51,P46) s(P45,P47) s(P46,P47) s(P43,P48) s(P47,P48) s(P48,P49) s(P53,P49) s(P48,P50) s(P49,P50) s(P50,P51) s(P52,P51) s(P56,P52) s(P57,P52) s(P51,P53) s(P52,P53) s(P49,P54) s(P53,P54) s(P54,P55) s(P28,P55) s(P54,P56) s(P55,P56) s(P56,P57) s(P55,P58) s(P28,P58) s(P58,P59) s(P59,P60) s(P58,P60) s(P57,P61) s(P59,P61) s(P61,P62) s(P59,P62) s(P64,P62) s(P66,P62) s(P57,P63) s(P61,P63) s(P65,P63) s(P66,P63) s(P64,P66) s(P65,P66) pen(2) color(#008000) m(P6,P7,MA10) m(P7,P30,MB10) b(P7,MA10,MB10) color(#FFA500) m(P30,P31,MA11) m(P31,P32,MB11) b(P31,MA11,MB11) color(#0000FF) m(P3,P1,MA12) m(P1,P4,MB12) b(P1,MA12,MB12) color(#EE82EE) m(P55,P58,MA13) m(P58,P59,MB13) b(P58,MA13,MB13) pen(2) color(#008000) s(P55,P28) color(blue) color(orange) color(red) \geooff \geoprint()
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haribo
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| Beitrag No.1419, eingetragen 2018-09-17 18:43
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die rechte ecke vom blauen muss auf der unteren tortenkante liegen
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| Beitrag No.1420, vom Themenstarter, eingetragen 2018-09-17 21:08
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Ok, das geht. Ich kann aber nicht sagen, ob die langen Linien genau durch die Punkte gehen.
62 Knoten, 5×Grad 2, 2×Grad 3, 53×Grad 4, 2×Grad 5
119 Kanten, minimal 0.99999999999999833467, maximal 9.82401540009238516404
einstellbare Kanten R(j,k):
|P55-P28|=1.00000000000000133227
nicht passende Kanten:
|P4-P60|=9.82401540009238516404
|P31-P62|=9.60297407278868675462
\geo ebene(550.62,212.33) x(4.79,15.8) y(8.82,13.06) form(.) #//Eingabe war: #<Streichholzgraph> #<Bildtext>#1373 Fig.2 RA(55,28); RA(59,28); RW(8,7,36,7,1.8); dann #Feinjustieren(3)</Bildtext> #<Winkel size=''18'' color=''green'' id=''gruenerWinkel'' value=''43.206788004551434''/> #<Winkel size=''18'' color=''orange'' id=''orangerWinkel'' value=''89.1''/> #<Winkel size=''18'' color=''blue'' id=''blauerWinkel'' value=''116.59''/> #<Winkel size=''18'' color=''violet'' id=''vierterWinkel'' value=''-52''/> #<Winkel size=''18'' color=''aqua'' id=''fuenfterWinkel'' value=''81''/> #<Feinjustieren Anzahl=''1''/> #<Rechenweg> #P[1]=[-216.5768659929221,-34.96084416443349]; #P[2]=[-172.59071903159037,-58.73517644729951]; D=ab(1,2); A(2,1,Bew(1)); #L(3,1,2); M(4,1,3,blauerWinkel); L(5,1,4); A(3,4,ab(4,3,[1,5])); #A(2,8,ab(5,7,[1,8])); A(10,14,ab(5,7,[1,14])); N(27,26,22); L(28,26,27); #L(29,27,22); M(30,7,6,gruenerWinkel); L(31,7,30); M(32,31,30,orangerWinkel); #L(33,31,32); A(30,32,ab(32,30,7,[30,33])); A(36,34,ab(7,33,[30,36])); #A(42,40,ab(7,33,[30,42])); A(54,52,ab(7,33,[30,33])); RA(55,28); N(58,55,28); #M(59,58,55,vierterWinkel); N(60,59,58); #M(61,59,60,fuenfterWinkel); N(62,59,61); #A(31,62); #A(4,60); #</Rechenweg> #</Streichholzgraph> #//Ende der Eingabe, weiter mit fedgeo: p(5.67,9.30,P1) p(6.55,8.83,P2) p(6.52,9.82,P3) p(4.82,9.83,P4) p(4.79,8.83,P5) p(5.67,10.35,P6) p(4.79,10.83,P7) p(6.55,10.82,P8) p(7.43,9.30,P9) p(8.31,8.82,P10) p(8.28,9.82,P11) p(6.58,9.82,P12) p(7.43,10.35,P13) p(8.31,10.82,P14) p(9.19,9.29,P15) p(10.07,8.82,P16) p(10.04,9.82,P17) p(8.34,9.82,P18) p(9.19,10.35,P19) p(10.07,10.82,P20) p(10.95,9.29,P21) p(11.83,8.82,P22) p(11.80,9.82,P23) p(10.10,9.82,P24) p(10.95,10.34,P25) p(11.83,10.82,P26) p(11.86,9.82,P27) p(12.71,10.34,P28) p(12.71,9.29,P29) p(5.76,11.08,P30) p(5.05,11.79,P31) p(5.77,12.49,P32) p(4.81,12.76,P33) p(6.74,12.74,P34) p(6.48,11.78,P35) p(6.72,10.81,P36) p(7.68,11.06,P37) p(6.98,11.77,P38) p(7.70,12.46,P39) p(8.67,12.72,P40) p(8.41,11.76,P41) p(8.65,10.78,P42) p(9.61,11.04,P43) p(8.91,11.75,P44) p(9.63,12.44,P45) p(10.59,12.70,P46) p(10.33,11.73,P47) p(10.57,10.76,P48) p(11.54,11.02,P49) p(10.84,11.73,P50) p(11.56,12.42,P51) p(12.52,12.68,P52) p(12.26,11.71,P53) p(12.50,10.74,P54) p(13.47,11.00,P55) p(12.76,11.71,P56) p(13.48,12.40,P57) p(13.66,10.02,P58) p(14.32,10.77,P59) p(14.64,9.83,P60) p(15.30,10.95,P61) p(14.66,11.71,P62) nolabel() s(P1,P2) s(P9,P2) s(P12,P2) s(P1,P3) s(P2,P3) s(P6,P3) s(P1,P4) s(P6,P4) s(P7,P4) s(P60,P4) s(P1,P5) s(P4,P5) s(P6,P7) s(P6,P8) s(P3,P8) s(P13,P8) s(P9,P10) s(P15,P10) s(P18,P10) s(P9,P11) s(P10,P11) s(P13,P11) s(P9,P12) s(P13,P12) s(P8,P12) s(P11,P14) s(P13,P14) s(P19,P14) s(P15,P16) s(P21,P16) s(P24,P16) s(P15,P17) s(P16,P17) s(P19,P17) s(P15,P18) s(P19,P18) s(P14,P18) s(P17,P20) s(P19,P20) s(P25,P20) s(P21,P22) s(P21,P23) s(P22,P23) s(P25,P23) s(P20,P24) s(P21,P24) s(P25,P24) s(P23,P26) s(P25,P26) s(P26,P27) s(P22,P27) s(P26,P28) s(P27,P28) s(P27,P29) s(P22,P29) s(P7,P30) s(P35,P30) s(P7,P31) s(P30,P31) s(P62,P31) s(P31,P32) s(P34,P32) s(P31,P33) s(P32,P33) s(P38,P34) s(P39,P34) s(P34,P35) s(P32,P35) s(P35,P36) s(P30,P36) s(P36,P37) s(P41,P37) s(P36,P38) s(P37,P38) s(P38,P39) s(P40,P39) s(P44,P40) s(P45,P40) s(P39,P41) s(P40,P41) s(P37,P42) s(P41,P42) s(P42,P43) s(P47,P43) s(P42,P44) s(P43,P44) s(P44,P45) s(P46,P45) s(P50,P46) s(P51,P46) s(P45,P47) s(P46,P47) s(P43,P48) s(P47,P48) s(P48,P49) s(P53,P49) s(P48,P50) s(P49,P50) s(P50,P51) s(P52,P51) s(P56,P52) s(P57,P52) s(P51,P53) s(P52,P53) s(P49,P54) s(P53,P54) s(P54,P55) s(P28,P55) s(P54,P56) s(P55,P56) s(P56,P57) s(P55,P58) s(P28,P58) s(P58,P59) s(P59,P60) s(P58,P60) s(P59,P61) s(P59,P62) s(P61,P62) pen(2) color(#008000) m(P6,P7,MA10) m(P7,P30,MB10) b(P7,MA10,MB10) color(#FFA500) m(P30,P31,MA11) m(P31,P32,MB11) b(P31,MA11,MB11) color(#0000FF) m(P3,P1,MA12) m(P1,P4,MB12) b(P1,MA12,MB12) color(#EE82EE) m(P55,P58,MA13) m(P58,P59,MB13) b(P58,MA13,MB13) color(#00FFFF) m(P60,P59,MA14) m(P59,P61,MB14) b(P59,MA14,MB14) pen(2) color(#008000) s(P55,P28) color(blue) color(orange) color(red) \geooff \geoprint()
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| Beitrag No.1421, vom Themenstarter, eingetragen 2018-09-18 09:24
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Ich denke, deine Idee könnte wirklich funktionieren. Nicht an den Stacheln stören, das sind nur Kopierfehler, so war es aber einfacher. Es sind 44 Girlandenelemente. Hut ab, haribo! 
Tortenstück zweigeteilt. Blaues Dreick ist identisch. Der Teilgraph besteht aus 108 Dreiecken.
Der Ring schließt schon fast genau. Die Überschneidung ist minimal.
MGC <Streichholzgraph>
<Bildtext>#1373 Fig.2 RA(55,28); RA(59,28); RW(8,7,36,7,1.8); dann
Feinjustieren(3)</Bildtext>
<Winkel size="18" color="green" id="gruenerWinkel" value="42.26669754754279"/>
<Winkel size="18" color="orange" id="orangerWinkel" value="90.60021230933455"/>
<Winkel size="18" color="blue" id="blauerWinkel" value="116.3667049506522"/>
<Winkel size="18" color="violet" id="vierterWinkel" value="-49.15745373964623"/>
<Winkel size="18" color="aqua" id="fuenfterWinkel" value="76.6"/>
<Feinjustieren Anzahl="4"/>
<Rechenweg>
P[1]=[-251.94378616620986,-42.0055401352237];
P[2]=[-218.45767233361585,-59.03096246552255]; D=ab(1,2); A(2,1,Bew(1));
N(3,1,2); M(4,1,3,blauerWinkel); N(5,1,4); A(3,4,ab(4,3,[1,5]));
A(2,8,ab(5,7,[1,8])); A(10,14,ab(5,7,[1,14])); N(27,26,22); N(28,26,27); N(29,27,22);
M(30,7,6,gruenerWinkel); N(31,7,30);
M(32,31,30,orangerWinkel);
N(33,31,32); A(30,32,ab(32,30,7,[30,33])); A(36,34,ab(7,33,[30,36]));
A(42,40,ab(7,33,[30,42])); A(54,52,ab(7,33,[30,33])); RA(55,28); N(58,55,28);
A(31,56,ab(31,56,[1,59],"gespiegelt"));
M(115,58,55,vierterWinkel); N(116,115,58);
M(117,115,116,fuenfterWinkel); N(118,115,117);
A(56,118,ab(56,118,[115,118],"gespiegelt")); RA(114,119); A(114,120);
A(117,121,ab(121,117,115,118,119));
A(122,124,ab(124,122,115,[117,123]));
A(125,128,ab(128,125,115,[117,131]));
A(135,132,ab(132,135,115,[117,159]));
A(146,149,ab(149,146,115,[117,186]));
A(174,177,ab(177,174,115,[117,242]));
A(230,233,ab(233,230,115,[117,342]));
A(62,120,ab(62,120,[1,565],"gespiegelt"));
R(529,1118);
//ergänzt von Button "Knoten zusammenfassen":
C(7,90); C(30,89); C(32,88); C(33,65); C(34,93); C(35,92); C(36,91); C(37,96); C(38,95); C(39,94); C(40,99); C(41,98); C(42,97); C(43,102); C(44,101); C(45,100); C(46,105); C(47,104); C(48,103); C(49,108); C(50,107); C(51,106); C(52,111); C(53,110); C(54,109); C(55,113); C(57,112);
//A(4,58); A(31,118);
//ergänzt von Button "Knoten zusammenfassen":
C(33,627); C(59,628); C(60,630); C(61,626); C(63,598,629); C(64,624); C(66,625); C(67,635); C(68,636); C(69,633); C(70,634); C(71,631); C(72,632); C(73,641); C(74,642); C(75,639); C(76,640); C(77,637); C(78,638); C(79,647); C(80,648); C(81,645); C(82,646); C(83,643); C(84,644); C(85,649); C(86,651); C(87,650); C(529,1092); C(572,654); C(595,653); C(597,652); C(599,657); C(600,656); C(601,655); C(602,660); C(603,659); C(604,658); C(605,663); C(606,662); C(607,661); C(608,666); C(609,665); C(610,664); C(611,669); C(612,668); C(613,667); C(614,672); C(615,671); C(616,670); C(617,675); C(618,674); C(619,673); C(620,677); C(622,676);
</Rechenweg>
</Streichholzgraph> |
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haribo
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| Beitrag No.1422, eingetragen 2018-09-18 12:41
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möglicherweise, zum zeichnen brauch ich aber drei itterationen hintereinander, das is sehr sehr schwierig
evtl kannst du es nochmals mit folgenden startwerten versuchen
leider hast du den für mich entscheidenden winkel(wie weit das weisse dreieck hochgedreht werden muss) nicht als konstruktion benutzt... ich drehe es nur 0.08° !!!
#<Winkel size=''18'' color=''green'' id=''gruenerWinkel'' value=''43.8526''/>
#<Winkel size=''18'' color=''orange'' id=''orangerWinkel'' value=''88.5478''/>
#<Winkel size=''18'' color=''blue'' id=''blauerWinkel'' value=''119.821''/>
#<Winkel size=''18'' color=''violet'' id=''vierterWinkel'' value=''-30.0596''/>
#<Winkel size=''18'' color=''aqua'' id=''fuenfterWinkel'' value=''53.0719''/>
dann 25 gelbe angesetzt mit nem winkel (analog angeordnet wie der blaue) 49.5734°
es besteht dann noch ein abstands fehler von 0,03...
als funktionsnachweis könnte ich evtl nach mehreren versuchen einen positiven und einen negativen abstand argumentieren
ob 25 gelbe die endmenge ist weiss ich noch nicht,
du oder stefan bekommen das evtl schneller hin???
nachtrag: du hast es ja schon versucht inzwischen... toll!!!
ich versuche natürlich die 100 speichen des harborth ansatzes nicht zu erhöhen... ziele also 1,8° zwischen meinen blauen langen geraden an, das ist offenbar erheblich mehr als in deinem versuch?? daher kommt der grosse unterschied in der gelben speichen länge(42 girlanden nennst du es?) dann brauche ich nur 12,5??
dieser punkt ist aber ganz egal für den gesuchten nachweis ob es überhaupts einen streichholzgraphen mit den gewünschten eigenschaften gibt
da spielt die grösse ja keinerlei rolle
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| Beitrag No.1423, vom Themenstarter, eingetragen 2018-09-18 14:40
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keine überschneidungen
376 Knoten, 8×Grad 2, 368×Grad 4
744 Kanten, minimal 0.99999999929334770776, maximal 1.00000000008176992417
einstellbare Kanten R(j,k):
|P55-P28|=0.99999999999954691798
|P29-P163|=0.99999999999957001062
|P5-P139|=0.99999999999957567276
|P59-P303|= nicht mehr vorhanden
\geo ebene(605.84,181.1) x(-6.54,29.21) y(14.11,24.79) form(.) #//Eingabe war: #<Streichholzgraph> #<Bildtext>#1373 Fig.2 RA(55,28); RA(59,28); RW(8,7,36,7,1.8); dann #Feinjustieren(3)</Bildtext> #<Winkel size=''18'' color=''green'' id=''gruenerWinkel'' value=''43.89948121158556''/> #<Winkel size=''18'' color=''orange'' id=''orangerWinkel'' value=''88.4790492807313''/> #<Winkel size=''18'' color=''blue'' id=''blauerWinkel'' value=''119.84850364640812''/> #<Winkel size=''18'' color=''violet'' id=''vierterWinkel'' #value=''-30.127259345359786''/> #<Winkel size=''18'' color=''aqua'' id=''fuenfterWinkel'' value=''53.07''/> #<Feinjustieren Anzahl=''4''/> #<Rechenweg> #P[1]=[-265.6033541159036,110.8558214993576]; #P[2]=[-250.91603340522488,102.4020302553788]; D=ab(1,2); A(2,1,Bew(1)); #N(3,1,2); M(4,1,3,blauerWinkel); N(5,1,4); A(3,4,ab(4,3,[1,5])); #A(2,8,ab(5,7,[1,8])); A(10,14,ab(5,7,[1,14])); N(27,26,22); N(28,26,27); #N(29,27,22); #M(30,7,6,gruenerWinkel); N(31,7,30); #M(32,31,30,orangerWinkel); #N(33,31,32); A(30,32,ab(32,30,7,[30,33])); A(36,34,ab(7,33,[30,36])); #A(42,40,ab(7,33,[30,42])); A(54,52,ab(7,33,[30,33])); RA(55,28); N(58,55,28); #M(59,58,55,vierterWinkel); N(60,59,58); #M(61,59,60,fuenfterWinkel); N(62,59,61); #A(56,62,ab(56,62,59,61,''gespiegelt'')); #A(61,64,ab(64,61,59,[62,63])); #A(67,65,ab(59,63,[61,67])); #A(73,71,ab(59,63,59,[61,73])); #A(85,83,ab(59,63,59,[61,85])); #A(109,107,ab(59,63,59,[61,88])); #A(60,134,ab(60,134,[29,136],''gespiegelt'')); #RA(29,163); RA(5,139); A(29,166); A(5,138); #A(135,31,ab(135,31,[1,242],''gespiegelt'')); R(59,303); # #//ergänzt von Button ''Knoten zusammenfassen'': #C(7,274); C(28,137); C(30,273); C(32,272); C(33,249); C(34,277); C(35,276); #C(36,275); C(37,280); C(38,279); C(39,278); C(40,283); C(41,282); C(42,281); #C(43,286); C(44,285); C(45,284); C(46,289); C(47,288); C(48,287); C(49,292); #C(50,291); C(51,290); C(52,295); C(53,294); C(54,293); C(55,298); C(56,297); #C(57,296); C(59,304); C(61,305); C(62,303); C(63,300); C(64,302); C(65,308); #C(66,307); C(67,306); C(68,311); C(69,310); C(70,309); C(71,314); C(72,313); #C(73,312); C(74,317); C(75,316); C(76,315); C(77,320); C(78,319); C(79,318); #C(80,323); C(81,322); C(82,321); C(83,326); C(84,325); C(85,324); C(86,329); #C(87,328); C(88,327); C(89,332); C(90,331); C(91,330); C(92,335); C(93,334); #C(94,333); C(95,338); C(96,337); C(97,336); C(98,341); C(99,340); C(100,339); #C(101,344); C(102,343); C(103,342); C(104,347); C(105,346); C(106,345); #C(107,350); C(108,349); C(109,348); C(110,353); C(111,352); C(112,351); #C(113,356); C(114,355); C(115,354); C(116,359); C(117,358); C(118,357); #C(119,362); C(120,361); C(121,360); C(122,365); C(123,364); C(124,363); #C(125,368); C(126,367); C(127,366); C(128,371); C(129,370); C(130,369); #C(131,374); C(132,373); C(133,372); C(134,376); C(136,375); C(270,377); #</Rechenweg> #</Streichholzgraph> #//Ende der Eingabe, weiter mit fedgeo: p(-5.67,16.54,P1) p(-4.81,16.04,P2) p(-4.81,17.04,P3) p(-6.54,17.04,P4) p(-6.54,16.04,P5) p(-5.67,17.54,P6) p(-6.54,18.04,P7) p(-4.81,18.04,P8) p(-3.94,16.54,P9) p(-3.07,16.04,P10) p(-3.07,17.04,P11) p(-4.81,17.04,P12) p(-3.94,17.54,P13) p(-3.07,18.04,P14) p(-2.21,16.54,P15) p(-1.34,16.04,P16) p(-1.34,17.04,P17) p(-3.07,17.04,P18) p(-2.21,17.54,P19) p(-1.34,18.04,P20) p(-0.47,16.54,P21) p(0.39,16.04,P22) p(0.39,17.04,P23) p(-1.34,17.04,P24) p(-0.47,17.54,P25) p(0.39,18.04,P26) p(0.40,17.04,P27) p(1.26,17.54,P28) p(1.26,16.54,P29) p(-5.57,18.28,P30) p(-6.26,19.00,P31) p(-5.53,19.68,P32) p(-6.48,19.98,P33) p(-4.56,19.92,P34) p(-4.83,18.96,P35) p(-4.62,17.98,P36) p(-3.65,18.22,P37) p(-4.34,18.94,P38) p(-3.60,19.62,P39) p(-2.63,19.86,P40) p(-2.91,18.90,P41) p(-2.69,17.92,P42) p(-1.72,18.16,P43) p(-2.42,18.88,P44) p(-1.68,19.56,P45) p(-0.71,19.80,P46) p(-0.98,18.84,P47) p(-0.77,17.86,P48) p(0.20,18.10,P49) p(-0.49,18.82,P50) p(0.25,19.50,P51) p(1.22,19.74,P52) p(0.94,18.78,P53) p(1.16,17.80,P54) p(2.13,18.04,P55) p(1.43,18.76,P56) p(2.17,19.44,P57) p(2.13,17.04,P58) p(2.63,17.91,P59) p(3.13,17.04,P60) p(3.62,17.79,P61) p(3.23,18.71,P62) p(2.68,19.54,P63) p(3.68,19.60,P64) p(4.67,19.48,P65) p(4.07,18.68,P66) p(4.62,17.85,P67) p(5.61,17.73,P68) p(5.22,18.65,P69) p(5.67,19.54,P70) p(6.66,19.42,P71) p(6.06,18.62,P72) p(6.61,17.79,P73) p(7.60,17.66,P74) p(7.21,18.58,P75) p(7.66,19.48,P76) p(8.65,19.36,P77) p(8.05,18.56,P78) p(8.60,17.72,P79) p(9.59,17.60,P80) p(9.20,18.52,P81) p(9.65,19.42,P82) p(10.64,19.29,P83) p(10.04,18.50,P84) p(10.59,17.66,P85) p(11.58,17.54,P86) p(11.19,18.46,P87) p(11.64,19.35,P88) p(12.63,19.23,P89) p(12.03,18.43,P90) p(12.58,17.60,P91) p(13.57,17.48,P92) p(13.18,18.40,P93) p(13.63,19.29,P94) p(14.62,19.17,P95) p(14.02,18.37,P96) p(14.57,17.54,P97) p(15.56,17.42,P98) p(15.17,18.34,P99) p(15.62,19.23,P100) p(16.61,19.11,P101) p(16.01,18.31,P102) p(16.56,17.48,P103) p(17.56,17.35,P104) p(17.17,18.27,P105) p(17.61,19.17,P106) p(18.60,19.05,P107) p(18.00,18.25,P108) p(18.55,17.41,P109) p(19.55,17.29,P110) p(19.16,18.21,P111) p(19.60,19.11,P112) p(20.60,18.98,P113) p(19.99,18.19,P114) p(20.54,17.35,P115) p(21.54,17.23,P116) p(21.15,18.15,P117) p(21.59,19.04,P118) p(22.59,18.92,P119) p(21.98,18.12,P120) p(22.53,17.29,P121) p(23.53,17.17,P122) p(23.14,18.09,P123) p(23.58,18.98,P124) p(24.58,18.86,P125) p(23.97,18.06,P126) p(24.53,17.23,P127) p(25.52,17.10,P128) p(25.13,18.03,P129) p(25.57,18.92,P130) p(26.57,18.80,P131) p(25.97,18.00,P132) p(26.52,17.17,P133) p(27.51,17.04,P134) p(27.12,17.96,P135) p(27.57,18.86,P136) p(-5.57,15.80,P138) p(-6.26,15.08,P139) p(-5.53,14.41,P140) p(-6.48,14.11,P141) p(-4.56,14.17,P142) p(-4.83,15.13,P143) p(-4.62,16.10,P144) p(-3.65,15.86,P145) p(-4.34,15.14,P146) p(-3.60,14.47,P147) p(-2.63,14.22,P148) p(-2.91,15.19,P149) p(-2.69,16.16,P150) p(-1.72,15.92,P151) p(-2.42,15.20,P152) p(-1.68,14.53,P153) p(-0.71,14.28,P154) p(-0.98,15.25,P155) p(-0.77,16.22,P156) p(0.20,15.98,P157) p(-0.49,15.26,P158) p(0.25,14.59,P159) p(1.22,14.34,P160) p(0.94,15.31,P161) p(1.16,16.28,P162) p(2.13,16.04,P163) p(1.43,15.32,P164) p(2.17,14.65,P165) p(2.13,17.04,P166) p(2.63,16.18,P167) p(3.62,16.30,P168) p(3.23,15.38,P169) p(2.68,14.54,P170) p(3.68,14.48,P171) p(4.67,14.61,P172) p(4.07,15.40,P173) p(4.62,16.24,P174) p(5.61,16.36,P175) p(5.22,15.44,P176) p(5.67,14.54,P177) p(6.66,14.67,P178) p(6.06,15.47,P179) p(6.61,16.30,P180) p(7.60,16.42,P181) p(7.21,15.50,P182) p(7.66,14.61,P183) p(8.65,14.73,P184) p(8.05,15.53,P185) p(8.60,16.36,P186) p(9.59,16.48,P187) p(9.20,15.56,P188) p(9.65,14.67,P189) p(10.64,14.79,P190) p(10.04,15.59,P191) p(10.59,16.42,P192) p(11.58,16.55,P193) p(11.19,15.63,P194) p(11.64,14.73,P195) p(12.63,14.85,P196) p(12.03,15.65,P197) p(12.58,16.49,P198) p(13.57,16.61,P199) p(13.18,15.69,P200) p(13.63,14.79,P201) p(14.62,14.92,P202) p(14.02,15.71,P203) p(14.57,16.55,P204) p(15.56,16.67,P205) p(15.17,15.75,P206) p(15.62,14.86,P207) p(16.61,14.98,P208) p(16.01,15.78,P209) p(16.56,16.61,P210) p(17.56,16.73,P211) p(17.17,15.81,P212) p(17.61,14.92,P213) p(18.60,15.04,P214) p(18.00,15.84,P215) p(18.55,16.67,P216) p(19.55,16.79,P217) p(19.16,15.87,P218) p(19.60,14.98,P219) p(20.60,15.10,P220) p(19.99,15.90,P221) p(20.54,16.73,P222) p(21.54,16.86,P223) p(21.15,15.94,P224) p(21.59,15.04,P225) p(22.59,15.16,P226) p(21.98,15.96,P227) p(22.53,16.80,P228) p(23.53,16.92,P229) p(23.14,16.00,P230) p(23.58,15.10,P231) p(24.58,15.23,P232) p(23.97,16.02,P233) p(24.53,16.86,P234) p(25.52,16.98,P235) p(25.13,16.06,P236) p(25.57,15.17,P237) p(26.57,15.29,P238) p(25.97,16.09,P239) p(26.52,16.92,P240) p(27.12,16.12,P241) p(27.57,15.23,P242) p(-5.52,21.42,P243) p(-4.62,21.87,P244) p(-4.69,20.87,P245) p(-6.42,20.98,P246) p(-6.35,21.98,P247) p(-5.58,20.42,P248) p(-4.75,19.87,P250) p(-3.79,21.32,P251) p(-2.89,21.76,P252) p(-2.96,20.76,P253) p(-4.69,20.87,P254) p(-3.85,20.32,P255) p(-3.02,19.76,P256) p(-2.06,21.21,P257) p(-1.16,21.65,P258) p(-1.23,20.65,P259) p(-2.96,20.76,P260) p(-2.12,20.21,P261) p(-1.29,19.66,P262) p(-0.33,21.10,P263) p(0.57,21.54,P264) p(0.50,20.55,P265) p(-1.23,20.65,P266) p(-0.39,20.10,P267) p(0.44,19.55,P268) p(0.50,20.55,P269) p(1.34,19.99,P270) p(1.40,20.99,P271) p(2.23,20.44,P299) p(3.23,20.38,P301) p(-5.37,22.16,P378) p(-6.02,22.92,P379) p(-5.24,23.55,P380) p(-6.17,23.91,P381) p(-4.26,23.73,P382) p(-4.59,22.78,P383) p(-4.44,21.80,P384) p(-3.45,21.98,P385) p(-4.10,22.74,P386) p(-3.32,23.37,P387) p(-2.34,23.55,P388) p(-2.68,22.61,P389) p(-2.52,21.62,P390) p(-1.54,21.80,P391) p(-2.19,22.56,P392) p(-1.41,23.19,P393) p(-0.42,23.37,P394) p(-0.76,22.43,P395) p(-0.61,21.44,P396) p(0.38,21.62,P397) p(-0.27,22.38,P398) p(0.51,23.01,P399) p(1.49,23.19,P400) p(1.16,22.25,P401) p(1.31,21.26,P402) p(2.29,21.44,P403) p(1.65,22.20,P404) p(2.42,22.83,P405) p(2.23,20.44,P406) p(2.79,21.27,P407) p(3.77,21.09,P408) p(3.44,22.03,P409) p(2.94,22.90,P410) p(3.94,22.90,P411) p(4.92,22.71,P412) p(4.27,21.95,P413) p(4.77,21.09,P414) p(5.75,20.90,P415) p(5.42,21.85,P416) p(5.92,22.71,P417) p(6.91,22.53,P418) p(6.25,21.77,P419) p(6.75,20.90,P420) p(7.74,20.72,P421) p(7.40,21.66,P422) p(7.91,22.53,P423) p(8.89,22.34,P424) p(8.24,21.58,P425) p(8.74,20.71,P426) p(9.72,20.53,P427) p(9.39,21.47,P428) p(9.89,22.34,P429) p(10.87,22.16,P430) p(10.22,21.40,P431) p(10.72,20.53,P432) p(11.70,20.35,P433) p(11.37,21.29,P434) p(11.87,22.15,P435) p(12.85,21.97,P436) p(12.20,21.21,P437) p(12.70,20.34,P438) p(13.68,20.16,P439) p(13.35,21.10,P440) p(13.85,21.97,P441) p(14.84,21.78,P442) p(14.19,21.02,P443) p(14.68,20.16,P444) p(15.67,19.97,P445) p(15.34,20.92,P446) p(15.84,21.78,P447) p(16.82,21.60,P448) p(16.17,20.84,P449) p(16.67,19.97,P450) p(17.65,19.79,P451) p(17.32,20.73,P452) p(17.82,21.60,P453) p(18.80,21.41,P454) p(18.15,20.65,P455) p(18.65,19.79,P456) p(19.63,19.60,P457) p(19.30,20.54,P458) p(19.80,21.41,P459) p(20.79,21.23,P460) p(20.14,20.47,P461) p(20.63,19.60,P462) p(21.62,19.42,P463) p(21.28,20.36,P464) p(21.79,21.22,P465) p(22.77,21.04,P466) p(22.12,20.28,P467) p(22.62,19.41,P468) p(23.60,19.23,P469) p(23.27,20.17,P470) p(23.77,21.04,P471) p(24.75,20.85,P472) p(24.10,20.09,P473) p(24.60,19.23,P474) p(25.58,19.04,P475) p(25.25,19.99,P476) p(25.75,20.85,P477) p(26.73,20.67,P478) p(26.08,19.91,P479) p(26.58,19.04,P480) p(27.23,19.80,P481) p(27.73,20.67,P482) nolabel() s(P2,P1) s(P3,P1) s(P4,P1) s(P5,P1) s(P9,P2) s(P12,P2) s(P3,P2) s(P6,P3) s(P8,P3) s(P6,P4) s(P7,P4) s(P5,P4) s(P139,P5) s(P138,P5) s(P7,P6) s(P8,P6) s(P31,P7) s(P30,P7) s(P13,P8) s(P12,P8) s(P10,P9) s(P11,P9) s(P12,P9) s(P15,P10) s(P18,P10) s(P11,P10) s(P13,P11) s(P14,P11) s(P13,P12) s(P14,P13) s(P19,P14) s(P18,P14) s(P16,P15) s(P17,P15) s(P18,P15) s(P21,P16) s(P24,P16) s(P17,P16) s(P19,P17) s(P20,P17) s(P19,P18) s(P20,P19) s(P25,P20) s(P24,P20) s(P22,P21) s(P23,P21) s(P24,P21) s(P23,P22) s(P27,P22) s(P29,P22) s(P25,P23) s(P26,P23) s(P25,P24) s(P26,P25) s(P27,P26) s(P28,P26) s(P28,P27) s(P29,P27) s(P55,P28) s(P58,P28) s(P163,P29) s(P166,P29) s(P35,P30) s(P31,P30) s(P36,P30) s(P33,P31) s(P32,P31) s(P34,P32) s(P33,P32) s(P35,P32) s(P246,P33) s(P248,P33) s(P38,P34) s(P39,P34) s(P35,P34) s(P36,P35) s(P37,P36) s(P38,P36) s(P41,P37) s(P38,P37) s(P42,P37) s(P39,P38) s(P40,P39) s(P41,P39) s(P44,P40) s(P45,P40) s(P41,P40) s(P42,P41) s(P43,P42) s(P44,P42) s(P47,P43) s(P44,P43) s(P48,P43) s(P45,P44) s(P46,P45) s(P47,P45) s(P50,P46) s(P51,P46) s(P47,P46) s(P48,P47) s(P49,P48) s(P50,P48) s(P53,P49) s(P50,P49) s(P54,P49) s(P51,P50) s(P52,P51) s(P53,P51) s(P56,P52) s(P57,P52) s(P53,P52) s(P54,P53) s(P55,P54) s(P56,P54) s(P56,P55) s(P58,P55) s(P57,P56) s(P270,P57) s(P299,P57) s(P59,P58) s(P60,P58) s(P60,P59) s(P61,P59) s(P62,P59) s(P166,P60) s(P167,P60) s(P67,P61) s(P62,P61) s(P66,P61) s(P63,P62) s(P64,P62) s(P64,P63) s(P299,P63) s(P301,P63) s(P65,P64) s(P66,P64) s(P66,P65) s(P69,P65) s(P70,P65) s(P67,P66) s(P68,P67) s(P69,P67) s(P73,P68) s(P69,P68) s(P72,P68) s(P70,P69) s(P71,P70) s(P72,P70) s(P72,P71) s(P75,P71) s(P76,P71) s(P73,P72) s(P74,P73) s(P75,P73) s(P79,P74) s(P75,P74) s(P78,P74) s(P76,P75) s(P77,P76) s(P78,P76) s(P78,P77) s(P81,P77) s(P82,P77) s(P79,P78) s(P80,P79) s(P81,P79) s(P85,P80) s(P81,P80) s(P84,P80) s(P82,P81) s(P83,P82) s(P84,P82) s(P84,P83) s(P87,P83) s(P88,P83) s(P85,P84) s(P86,P85) s(P87,P85) s(P91,P86) s(P87,P86) s(P90,P86) s(P88,P87) s(P89,P88) s(P90,P88) s(P90,P89) s(P93,P89) s(P94,P89) s(P91,P90) s(P92,P91) s(P93,P91) s(P97,P92) s(P93,P92) s(P96,P92) s(P94,P93) s(P95,P94) s(P96,P94) s(P96,P95) s(P99,P95) s(P100,P95) s(P97,P96) s(P98,P97) s(P99,P97) s(P103,P98) s(P99,P98) s(P102,P98) s(P100,P99) s(P101,P100) s(P102,P100) s(P102,P101) s(P105,P101) s(P106,P101) s(P103,P102) s(P104,P103) s(P105,P103) s(P109,P104) s(P105,P104) s(P108,P104) s(P106,P105) s(P107,P106) s(P108,P106) s(P108,P107) s(P111,P107) s(P112,P107) s(P109,P108) s(P110,P109) s(P111,P109) s(P115,P110) s(P111,P110) s(P114,P110) s(P112,P111) s(P113,P112) s(P114,P112) s(P114,P113) s(P117,P113) s(P118,P113) s(P115,P114) s(P116,P115) s(P117,P115) s(P121,P116) s(P117,P116) s(P120,P116) s(P118,P117) s(P119,P118) s(P120,P118) s(P120,P119) s(P123,P119) s(P124,P119) s(P121,P120) s(P122,P121) s(P123,P121) s(P127,P122) s(P123,P122) s(P126,P122) s(P124,P123) s(P125,P124) s(P126,P124) s(P126,P125) s(P129,P125) s(P130,P125) s(P127,P126) s(P128,P127) s(P129,P127) s(P133,P128) s(P129,P128) s(P132,P128) s(P130,P129) s(P131,P130) s(P132,P130) s(P132,P131) s(P135,P131) s(P136,P131) s(P133,P132) s(P134,P133) s(P135,P133) s(P240,P134) s(P135,P134) s(P241,P134) s(P136,P135) s(P480,P136) s(P481,P136) s(P143,P138) s(P139,P138) s(P144,P138) s(P140,P139) s(P141,P139) s(P142,P140) s(P141,P140) s(P143,P140) s(P146,P142) s(P147,P142) s(P143,P142) s(P144,P143) s(P145,P144) s(P146,P144) s(P149,P145) s(P146,P145) s(P150,P145) s(P147,P146) s(P148,P147) s(P149,P147) s(P152,P148) s(P153,P148) s(P149,P148) s(P150,P149) s(P151,P150) s(P152,P150) s(P155,P151) s(P152,P151) s(P156,P151) s(P153,P152) s(P154,P153) s(P155,P153) s(P158,P154) s(P159,P154) s(P155,P154) s(P156,P155) s(P157,P156) s(P158,P156) s(P161,P157) s(P158,P157) s(P162,P157) s(P159,P158) s(P160,P159) s(P161,P159) s(P164,P160) s(P165,P160) s(P161,P160) s(P162,P161) s(P163,P162) s(P164,P162) s(P164,P163) s(P166,P163) s(P165,P164) s(P167,P166) s(P168,P167) s(P169,P167) s(P174,P168) s(P169,P168) s(P173,P168) s(P170,P169) s(P171,P169) s(P171,P170) s(P172,P171) s(P173,P171) s(P173,P172) s(P176,P172) s(P177,P172) s(P174,P173) s(P175,P174) s(P176,P174) s(P180,P175) s(P176,P175) s(P179,P175) s(P177,P176) s(P178,P177) s(P179,P177) s(P179,P178) s(P182,P178) s(P183,P178) s(P180,P179) s(P181,P180) s(P182,P180) s(P186,P181) s(P182,P181) s(P185,P181) s(P183,P182) s(P184,P183) s(P185,P183) s(P185,P184) s(P188,P184) s(P189,P184) s(P186,P185) s(P187,P186) s(P188,P186) s(P192,P187) s(P188,P187) s(P191,P187) s(P189,P188) s(P190,P189) s(P191,P189) s(P191,P190) s(P194,P190) s(P195,P190) s(P192,P191) s(P193,P192) s(P194,P192) s(P198,P193) s(P194,P193) s(P197,P193) s(P195,P194) s(P196,P195) s(P197,P195) s(P197,P196) s(P200,P196) s(P201,P196) s(P198,P197) s(P199,P198) s(P200,P198) s(P204,P199) s(P200,P199) s(P203,P199) s(P201,P200) s(P202,P201) s(P203,P201) s(P203,P202) s(P206,P202) s(P207,P202) s(P204,P203) s(P205,P204) s(P206,P204) s(P210,P205) s(P206,P205) s(P209,P205) s(P207,P206) s(P208,P207) s(P209,P207) s(P209,P208) s(P212,P208) s(P213,P208) s(P210,P209) s(P211,P210) s(P212,P210) s(P216,P211) s(P212,P211) s(P215,P211) s(P213,P212) s(P214,P213) s(P215,P213) s(P215,P214) s(P218,P214) s(P219,P214) s(P216,P215) s(P217,P216) s(P218,P216) s(P222,P217) s(P218,P217) s(P221,P217) s(P219,P218) s(P220,P219) s(P221,P219) s(P221,P220) s(P224,P220) s(P225,P220) s(P222,P221) s(P223,P222) s(P224,P222) s(P228,P223) s(P224,P223) s(P227,P223) s(P225,P224) s(P226,P225) s(P227,P225) s(P227,P226) s(P230,P226) s(P231,P226) s(P228,P227) s(P229,P228) s(P230,P228) s(P234,P229) s(P230,P229) s(P233,P229) s(P231,P230) s(P232,P231) s(P233,P231) s(P233,P232) s(P236,P232) s(P237,P232) s(P234,P233) s(P235,P234) s(P236,P234) s(P240,P235) s(P236,P235) s(P239,P235) s(P237,P236) s(P238,P237) s(P239,P237) s(P239,P238) s(P241,P238) s(P242,P238) s(P240,P239) s(P241,P240) s(P242,P241) s(P244,P243) s(P245,P243) s(P246,P243) s(P247,P243) s(P251,P244) s(P254,P244) s(P245,P244) s(P248,P245) s(P250,P245) s(P248,P246) s(P247,P246) s(P378,P247) s(P379,P247) s(P250,P248) s(P255,P250) s(P254,P250) s(P252,P251) s(P253,P251) s(P254,P251) s(P257,P252) s(P260,P252) s(P253,P252) s(P255,P253) s(P256,P253) s(P255,P254) s(P256,P255) s(P261,P256) s(P260,P256) s(P258,P257) s(P259,P257) s(P260,P257) s(P263,P258) s(P266,P258) s(P259,P258) s(P261,P259) s(P262,P259) s(P261,P260) s(P262,P261) s(P267,P262) s(P266,P262) s(P264,P263) s(P265,P263) s(P266,P263) s(P265,P264) s(P269,P264) s(P271,P264) s(P267,P265) s(P268,P265) s(P267,P266) s(P268,P267) s(P269,P268) s(P270,P268) s(P270,P269) s(P271,P269) s(P299,P270) s(P403,P271) s(P406,P271) s(P301,P299) s(P406,P301) s(P407,P301) s(P383,P378) s(P379,P378) s(P384,P378) s(P380,P379) s(P381,P379) s(P382,P380) s(P381,P380) s(P383,P380) s(P386,P382) s(P387,P382) s(P383,P382) s(P384,P383) s(P385,P384) s(P386,P384) s(P389,P385) s(P386,P385) s(P390,P385) s(P387,P386) s(P388,P387) s(P389,P387) s(P392,P388) s(P393,P388) s(P389,P388) s(P390,P389) s(P391,P390) s(P392,P390) s(P395,P391) s(P392,P391) s(P396,P391) s(P393,P392) s(P394,P393) s(P395,P393) s(P398,P394) s(P399,P394) s(P395,P394) s(P396,P395) s(P397,P396) s(P398,P396) s(P401,P397) s(P398,P397) s(P402,P397) s(P399,P398) s(P400,P399) s(P401,P399) s(P404,P400) s(P405,P400) s(P401,P400) s(P402,P401) s(P403,P402) s(P404,P402) s(P404,P403) s(P406,P403) s(P405,P404) s(P407,P406) s(P408,P407) s(P409,P407) s(P414,P408) s(P409,P408) s(P413,P408) s(P410,P409) s(P411,P409) s(P411,P410) s(P412,P411) s(P413,P411) s(P413,P412) s(P416,P412) s(P417,P412) s(P414,P413) s(P415,P414) s(P416,P414) s(P420,P415) s(P416,P415) s(P419,P415) s(P417,P416) s(P418,P417) s(P419,P417) s(P419,P418) s(P422,P418) s(P423,P418) s(P420,P419) s(P421,P420) s(P422,P420) s(P426,P421) s(P422,P421) s(P425,P421) s(P423,P422) s(P424,P423) s(P425,P423) s(P425,P424) s(P428,P424) s(P429,P424) s(P426,P425) s(P427,P426) s(P428,P426) s(P432,P427) s(P428,P427) s(P431,P427) s(P429,P428) s(P430,P429) s(P431,P429) s(P431,P430) s(P434,P430) s(P435,P430) s(P432,P431) s(P433,P432) s(P434,P432) s(P438,P433) s(P434,P433) s(P437,P433) s(P435,P434) s(P436,P435) s(P437,P435) s(P437,P436) s(P440,P436) s(P441,P436) s(P438,P437) s(P439,P438) s(P440,P438) s(P444,P439) s(P440,P439) s(P443,P439) s(P441,P440) s(P442,P441) s(P443,P441) s(P443,P442) s(P446,P442) s(P447,P442) s(P444,P443) s(P445,P444) s(P446,P444) s(P450,P445) s(P446,P445) s(P449,P445) s(P447,P446) s(P448,P447) s(P449,P447) s(P449,P448) s(P452,P448) s(P453,P448) s(P450,P449) s(P451,P450) s(P452,P450) s(P456,P451) s(P452,P451) s(P455,P451) s(P453,P452) s(P454,P453) s(P455,P453) s(P455,P454) s(P458,P454) s(P459,P454) s(P456,P455) s(P457,P456) s(P458,P456) s(P462,P457) s(P458,P457) s(P461,P457) s(P459,P458) s(P460,P459) s(P461,P459) s(P461,P460) s(P464,P460) s(P465,P460) s(P462,P461) s(P463,P462) s(P464,P462) s(P468,P463) s(P464,P463) s(P467,P463) s(P465,P464) s(P466,P465) s(P467,P465) s(P467,P466) s(P470,P466) s(P471,P466) s(P468,P467) s(P469,P468) s(P470,P468) s(P474,P469) s(P470,P469) s(P473,P469) s(P471,P470) s(P472,P471) s(P473,P471) s(P473,P472) s(P476,P472) s(P477,P472) s(P474,P473) s(P475,P474) s(P476,P474) s(P480,P475) s(P476,P475) s(P479,P475) s(P477,P476) s(P478,P477) s(P479,P477) s(P479,P478) s(P481,P478) s(P482,P478) s(P480,P479) s(P481,P480) s(P482,P481) pen(2) color(#008000) m(P6,P7,MA10) m(P7,P30,MB10) b(P7,MA10,MB10) color(#FFA500) m(P30,P31,MA11) m(P31,P32,MB11) b(P31,MA11,MB11) color(#0000FF) m(P3,P1,MA12) m(P1,P4,MB12) b(P1,MA12,MB12) color(#EE82EE) m(P55,P58,MA13) m(P58,P59,MB13) b(P58,MA13,MB13) color(#00FFFF) m(P60,P59,MA14) m(P59,P61,MB14) b(P59,MA14,MB14) pen(2) color(#008000) s(P55,P28) color(#008000) s(P29,P163) color(#008000) s(P5,P139) color(#008000) s(P59,P303) color(blue) color(orange) color(red) \geooff \geoprint()
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| Beitrag No.1424, eingetragen 2018-09-18 21:42
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also ich bekomme es jetzt mit einem übertritt von 0,01 hin
und bin dabei im genauigkeitsbereich meiner möglichkeiten...
evtl. sollte man doch mal paar gleichungen auflösen, denn ansich geometrisch braucht es wohl nur zwei variable winkel zum ausprobieren und nicht fünf
in #1420 hast du die beiden langen linien eingezeichnet, kannst du den winkel dazwischen errechnen/darstellen?
[ nicht passende Kanten:
|P4-P60|=9.82401540009238516404
|P31-P62|=9.60297407278868675462 ]
haribo
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| Beitrag No.1425, eingetragen 2018-09-18 23:02
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wenn du keine überschneidung gefunden hast, und ich bei ansich gleicher anordnung, aber marginal anderen winkeln eine finde, dann könnte man ja argumentieren: dann gibt es auch eine dazwischenliegende exakte lösung...
allerdings gleiche zeichengenaueigkeit angenommen
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| Beitrag No.1426, vom Themenstarter, eingetragen 2018-09-18 23:52
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Es gibt bestimmt eine Lösung. Die Frage nach der kleinsten wird allerdings knifflig werden, da vielleicht andere Speichen andere Möglichkeiten bieten.
Den Winkel kann ich nur mit CAD bestimmen, ist 1,79. Genauer geht bei mir nicht. Den Graphen kann ich leider nicht konstruieren, da das Programm an seine Grenzen kommt bei 10000 Punkten oder sogar weniger. Stefan kann vielleicht Teile durch größere Teilgraphen ersetzen, dann sind es nur ein paar hundert Punkte. Ich weiß leider nicht wie das geht.
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| Beitrag No.1427, vom Themenstarter, eingetragen 2018-09-19 02:32
|
Der Beweis ist erbracht. Ich kann jetzt mit dem Programm die Winkel messen und habe einen Ring-Graph aus meinem ersten langen Tortenstück konstruiert. Er besteht aus 584 Speichensegmenten. Der Tortenwinkel P31,P118,P62,P120 beträgt 0,61643835616456865711 und 360/584=0,61643835616438356164. Übereinstimmung bis zur 12. Nachkommastelle und der Teilgraph besitzt noch sehr viel Spiel. Dabei stellt allein der fünte/türkise Winkel den Tortenwinkel ein. Es ist also totale Genauigkeit möglich.
MGC <Streichholzgraph>
<Bildtext>#1373 Fig.2 RA(55,28); RA(59,28); RW(8,7,36,7,1.8); dann
Feinjustieren(3)</Bildtext>
<Winkel size="18" color="green" id="gruenerWinkel" value="42.23238929683882"/>
<Winkel size="18" color="orange" id="orangerWinkel" value="90.65316029965142"/>
<Winkel size="18" color="blue" id="blauerWinkel" value="116.35081560565838"/>
<Winkel size="18" color="violet" id="vierterWinkel" value="-49.08306933905506"/>
<Winkel size="18" color="aqua" id="fuenfterWinkel" value="76.580621330451"/>
<Feinjustieren Anzahl="4"/>
<Rechenweg>
P[1]=[-245.05471013690757,-173.12164286983693];
P[2]=[-200.72785239338685,-196.25451304596675]; D=ab(1,2); A(2,1,Bew(1));
N(3,1,2); M(4,1,3,blauerWinkel); N(5,1,4); A(3,4,ab(4,3,[1,5]));
A(2,8,ab(5,7,[1,8])); A(10,14,ab(5,7,[1,14])); N(27,26,22); N(28,26,27); N(29,27,22);
M(30,7,6,gruenerWinkel); N(31,7,30);
M(32,31,30,orangerWinkel);
N(33,31,32); A(30,32,ab(32,30,7,[30,33])); A(36,34,ab(7,33,[30,36]));
A(42,40,ab(7,33,[30,42])); A(54,52,ab(7,33,[30,33])); RA(55,28); N(58,55,28);
A(31,56,ab(31,56,[1,59],"gespiegelt"));
M(115,58,55,vierterWinkel); N(116,115,58);
M(117,115,116,fuenfterWinkel); N(118,115,117);
A(56,118,ab(56,118,[115,118],"gespiegelt")); RA(114,119); A(114,120);
A(117,121,ab(121,117,115,118,119));
A(122,124,ab(124,122,115,[117,123]));
A(125,128,ab(128,125,115,[117,131]));
A(135,132,ab(132,135,115,[117,159]));
A(146,149,ab(149,146,115,[117,186]));
A(174,177,ab(177,174,115,[117,242]));
A(230,233,ab(233,230,115,[117,342]));
A(62,120,ab(62,120,[1,565],"gespiegelt"));
R(529,1118);
R(63,596);
//ergänzt von Button "Knoten zusammenfassen":
C(7,90); C(30,89); C(32,88); C(33,65); C(34,93); C(35,92); C(36,91); C(37,96); C(38,95); C(39,94); C(40,99); C(41,98); C(42,97); C(43,102); C(44,101); C(45,100); C(46,105); C(47,104); C(48,103); C(49,108); C(50,107); C(51,106); C(52,111); C(53,110); C(54,109); C(55,113); C(57,112);
//ergänzt von Button "Knoten zusammenfassen":
C(33,627); C(59,628); C(60,630); C(61,626); C(63,598,629); C(64,624); C(66,625); C(67,635); C(68,636); C(69,633); C(70,634); C(71,631); C(72,632); C(73,641); C(74,642); C(75,639); C(76,640); C(77,637); C(78,638); C(79,647); C(80,648); C(81,645); C(82,646); C(83,643); C(84,644); C(85,649); C(86,651); C(87,650); C(529,1092); C(572,654); C(595,653); C(597,652); C(599,657); C(600,656); C(601,655); C(602,660); C(603,659); C(604,658); C(605,663); C(606,662); C(607,661); C(608,666); C(609,665); C(610,664); C(611,669); C(612,668); C(613,667); C(614,672); C(615,671); C(616,670); C(617,675); C(618,674); C(619,673); C(620,677); C(622,676);
</Rechenweg>
</Streichholzgraph> |
Hier ist das gute Stück aus 126144 Dreiecken.
1,8 Grad bekomme ich noch nicht ohne Überschneidungen im kurzen Tortenstück hin. Aber klar, sehr viele kleinere Ringe sind möglich. Ein Dreifachhoch auf haribo, den Tortenspezialist!
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haribo
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Dabei seit: 25.10.2012
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| Beitrag No.1428, eingetragen 2018-09-19 06:40
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ich hab es in den daten gefunden:
dein rechenweg war PANAMA!
Passt Alles Nachdem Allerlei Material Angepasstwurde
klar dass man da über kanäle stolpert
und klar dass es noch kürzer geht...
aber als beweisfahrschein soll es gelten !!! hurra
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| Beitrag No.1429, vom Themenstarter, eingetragen 2018-09-19 19:27
|
Hier ein Vergleich der Teilgraphen. Ich bin immer noch baff, wie simpel die Lösung eigentlich ist. Doch es brauchte schon eine Portion haribo, um diese zu finden.
Herr Harborth beglückwünscht uns zu dieser Konstruktion und dem damit erbrachten Beweis der Existenz "echter" vertex-to-vertex unit triangle Graphen und lobt die gute Idee des Teilgraphen (haribo!!!).
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| Beitrag No.1430, eingetragen 2018-09-19 23:09
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THX
Ich zerleg dir das die Tage nochmal in drei teilschritte , schätze dann kanst du auch kleinere Versionen darstellen...
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| Beitrag No.1431, vom Themenstarter, eingetragen 2018-09-20 04:24
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Torten-Teilgraph mit 49 Dreiecken und Ring aus 224 Speichensegmenten. Also 21952 Dreiecke insgesamt. 360/224 = 1,60714285714285714285 und Tortenwinkel = 1,60714282020611554103, also bis zur 7. Nachkommastelle stimmt es schon und der Graph hat noch Luft.
412 Knoten, 8×Grad 2, 404×Grad 4
816 Kanten, minimal 0.99999999999796163053, maximal 1.00000000000041189274
einstellbare Kanten R(j,k):
|P55-P28|=0.99999999999998856470
|P29-P175|=0.99999999999999056310
|P5-P151|=1.00000000000039435122
|P33-P270|=1.00000000000001798561
\geo ebene(748.55,199.84) x(-6.34,33.25) y(6.54,17.11) form(.) #//Eingabe war: #<Streichholzgraph> #// 360/222 = 1,6071428571428571428571428571429 #// Tortenwinkel = 1,60714204772194579895 #<Bildtext>Ring-Graph </Bildtext> #<Winkel size=''18'' color=''green'' id=''gruenerWinkel'' value=''42.309771176187404''/> #<Winkel size=''18'' color=''orange'' id=''orangerWinkel'' value=''90.83233475794268''/> #<Winkel size=''18'' color=''blue'' id=''blauerWinkel'' value=''118.66616275072778''/> #<Winkel size=''18'' color=''violet'' id=''vierterWinkel'' value=''-30.24267917090016''/> #<Winkel size=''18'' color=''aqua'' id=''fuenfterWinkel'' value=''55.5054''/> #<Feinjustieren Anzahl=''4''/> #<Rechenweg> #P[1]=[-291.62280919351116,-19.28095593689927]; #P[2]=[-274.8865405732622,-28.07736085997911]; D=ab(1,2); A(2,1,Bew(1)); #N(3,1,2); M(4,1,3,blauerWinkel); N(5,1,4); A(3,4,ab(4,3,[1,5])); #A(2,8,ab(5,7,[1,8])); A(10,14,ab(5,7,[1,14])); N(27,26,22); N(28,26,27); #N(29,27,22); #M(30,7,6,gruenerWinkel); N(31,7,30); #M(32,31,30,orangerWinkel); #N(33,31,32); A(30,32,ab(32,30,7,[30,33])); A(36,34,ab(7,33,[30,36])); #A(42,40,ab(7,33,[30,42])); A(54,52,ab(7,33,[30,33])); RA(55,28); N(58,55,28); #M(59,58,55,vierterWinkel); N(60,59,58); #M(61,59,60,fuenfterWinkel); N(62,59,61); #A(56,62,ab(56,62,59,61,''gespiegelt'')); #A(61,64,ab(64,61,59,[62,63])); #A(67,65,ab(59,63,[61,67])); #A(73,71,ab(59,63,59,[61,73])); #A(85,83,ab(59,63,59,[61,85])); #A(109,107,ab(59,63,59,[61,100])); #A(60,146,ab(60,146,[29,148],''gespiegelt'')); #RA(29,175); RA(5,151); A(29,178); A(5,150); #A(147,31,ab(147,31,[1,266],''gespiegelt'')); R(33,270); # #//ergänzt von Button ''Knoten zusammenfassen'': #C(7,298); C(28,149); C(30,297); C(32,296); C(33,273); C(34,301); C(35,300); #C(36,299); C(37,304); C(38,303); C(39,302); C(40,307); C(41,306); C(42,305); #C(43,310); C(44,309); C(45,308); C(46,313); C(47,312); C(48,311); C(49,316); #C(50,315); C(51,314); C(52,319); C(53,318); C(54,317); C(55,322); C(56,321); #C(57,320); C(59,328); C(61,329); C(62,327); C(63,324); C(64,326); C(65,332); #C(66,331); C(67,330); C(68,335); C(69,334); C(70,333); C(71,338); C(72,337); #C(73,336); C(74,341); C(75,340); C(76,339); C(77,344); C(78,343); C(79,342); #C(80,347); C(81,346); C(82,345); C(83,350); C(84,349); C(85,348); C(86,353); #C(87,352); C(88,351); C(89,356); C(90,355); C(91,354); C(92,359); C(93,358); #C(94,357); C(95,362); C(96,361); C(97,360); C(98,365); C(99,364); C(100,363); #C(101,368); C(102,367); C(103,366); C(104,371); C(105,370); C(106,369); #C(107,374); C(108,373); C(109,372); C(110,377); C(111,376); C(112,375); #C(113,380); C(114,379); C(115,378); C(116,383); C(117,382); C(118,381); #C(119,386); C(120,385); C(121,384); C(122,389); C(123,388); C(124,387); #C(125,392); C(126,391); C(127,390); C(128,395); C(129,394); C(130,393); #C(131,398); C(132,397); C(133,396); C(134,401); C(135,400); C(136,399); #C(137,404); C(138,403); C(139,402); C(140,407); C(141,406); C(142,405); #C(143,410); C(144,409); C(145,408); C(146,412); C(148,411); C(294,413); #</Rechenweg> #</Streichholzgraph> #//Ende der Eingabe, weiter mit fedgeo: p(-5.42,8.98,P1) p(-4.54,8.51,P2) p(-4.58,9.51,P3) p(-6.30,9.47,P4) p(-6.28,8.47,P5) p(-5.45,10.00,P6) p(-6.34,10.47,P7) p(-4.59,10.51,P8) p(-3.68,9.03,P9) p(-2.80,8.56,P10) p(-2.84,9.56,P11) p(-4.56,9.51,P12) p(-3.71,10.05,P13) p(-2.85,10.56,P14) p(-1.94,9.08,P15) p(-1.05,8.61,P16) p(-1.09,9.61,P17) p(-2.81,9.56,P18) p(-1.97,10.10,P19) p(-1.11,10.61,P20) p(-0.20,9.13,P21) p(0.69,8.66,P22) p(0.65,9.66,P23) p(-1.07,9.61,P24) p(-0.22,10.15,P25) p(0.63,10.66,P26) p(0.67,9.66,P27) p(1.52,10.20,P28) p(1.55,9.18,P29) p(-5.37,10.72,P30) p(-6.07,11.43,P31) p(-5.37,12.14,P32) p(-6.34,12.39,P33) p(-4.40,12.39,P34) p(-4.67,11.43,P35) p(-4.40,10.47,P36) p(-3.43,10.72,P37) p(-4.14,11.43,P38) p(-3.43,12.14,P39) p(-2.47,12.39,P40) p(-2.73,11.43,P41) p(-2.47,10.47,P42) p(-1.50,10.72,P43) p(-2.20,11.43,P44) p(-1.50,12.14,P45) p(-0.53,12.39,P46) p(-0.80,11.43,P47) p(-0.53,10.47,P48) p(0.44,10.72,P49) p(-0.27,11.43,P50) p(0.44,12.14,P51) p(1.40,12.39,P52) p(1.14,11.43,P53) p(1.40,10.47,P54) p(2.37,10.72,P55) p(1.67,11.43,P56) p(2.37,12.14,P57) p(2.40,9.72,P58) p(2.88,10.59,P59) p(3.40,9.74,P60) p(3.88,10.54,P61) p(3.43,11.43,P62) p(2.88,12.26,P63) p(3.88,12.32,P64) p(4.88,12.26,P65) p(4.33,11.43,P66) p(4.88,10.59,P67) p(5.87,10.54,P68) p(5.42,11.43,P69) p(5.87,12.32,P70) p(6.87,12.26,P71) p(6.32,11.43,P72) p(6.87,10.59,P73) p(7.87,10.54,P74) p(7.42,11.43,P75) p(7.87,12.32,P76) p(8.87,12.26,P77) p(8.32,11.43,P78) p(8.87,10.59,P79) p(9.87,10.54,P80) p(9.42,11.43,P81) p(9.87,12.32,P82) p(10.87,12.26,P83) p(10.32,11.43,P84) p(10.87,10.59,P85) p(11.86,10.54,P86) p(11.41,11.43,P87) p(11.86,12.32,P88) p(12.86,12.26,P89) p(12.31,11.43,P90) p(12.86,10.59,P91) p(13.86,10.54,P92) p(13.41,11.43,P93) p(13.86,12.32,P94) p(14.86,12.26,P95) p(14.31,11.43,P96) p(14.86,10.59,P97) p(15.86,10.54,P98) p(15.41,11.43,P99) p(15.86,12.32,P100) p(16.86,12.26,P101) p(16.31,11.43,P102) p(16.86,10.59,P103) p(17.85,10.54,P104) p(17.40,11.43,P105) p(17.85,12.32,P106) p(18.85,12.26,P107) p(18.30,11.43,P108) p(18.85,10.59,P109) p(19.85,10.54,P110) p(19.40,11.43,P111) p(19.85,12.32,P112) p(20.85,12.26,P113) p(20.30,11.43,P114) p(20.85,10.59,P115) p(21.85,10.54,P116) p(21.40,11.43,P117) p(21.85,12.32,P118) p(22.85,12.26,P119) p(22.30,11.43,P120) p(22.85,10.59,P121) p(23.84,10.54,P122) p(23.39,11.43,P123) p(23.84,12.32,P124) p(24.84,12.26,P125) p(24.29,11.43,P126) p(24.84,10.59,P127) p(25.84,10.54,P128) p(25.39,11.43,P129) p(25.84,12.32,P130) p(26.84,12.26,P131) p(26.29,11.43,P132) p(26.84,10.59,P133) p(27.84,10.54,P134) p(27.39,11.43,P135) p(27.84,12.32,P136) p(28.84,12.26,P137) p(28.29,11.43,P138) p(28.84,10.59,P139) p(29.83,10.54,P140) p(29.38,11.43,P141) p(29.83,12.32,P142) p(30.83,12.26,P143) p(30.28,11.43,P144) p(30.83,10.59,P145) p(31.83,10.54,P146) p(31.38,11.43,P147) p(31.83,12.32,P148) p(-5.30,8.27,P150) p(-5.96,7.52,P151) p(-5.22,6.85,P152) p(-6.17,6.54,P153) p(-4.24,6.65,P154) p(-4.56,7.60,P155) p(-4.35,8.57,P156) p(-3.37,8.38,P157) p(-4.03,7.63,P158) p(-3.29,6.96,P159) p(-2.31,6.76,P160) p(-2.63,7.71,P161) p(-2.42,8.68,P162) p(-1.44,8.49,P163) p(-2.10,7.74,P164) p(-1.36,7.06,P165) p(-0.38,6.87,P166) p(-0.70,7.81,P167) p(-0.48,8.79,P168) p(0.50,8.59,P169) p(-0.16,7.84,P170) p(0.58,7.17,P171) p(1.56,6.98,P172) p(1.24,7.92,P173) p(1.45,8.90,P174) p(2.43,8.70,P175) p(1.77,7.95,P176) p(2.51,7.28,P177) p(2.40,9.70,P178) p(2.93,8.85,P179) p(3.92,8.97,P180) p(3.52,8.05,P181) p(3.02,7.19,P182) p(4.02,7.18,P183) p(5.02,7.30,P184) p(4.42,8.10,P185) p(4.92,8.97,P186) p(5.92,9.08,P187) p(5.52,8.16,P188) p(6.02,7.30,P189) p(7.01,7.41,P190) p(6.41,8.21,P191) p(6.91,9.08,P192) p(7.91,9.19,P193) p(7.51,8.28,P194) p(8.01,7.41,P195) p(9.00,7.52,P196) p(8.41,8.33,P197) p(8.91,9.19,P198) p(9.90,9.30,P199) p(9.50,8.39,P200) p(10.00,7.52,P201) p(11.00,7.63,P202) p(10.40,8.44,P203) p(10.90,9.30,P204) p(11.90,9.42,P205) p(11.50,8.50,P206) p(12.00,7.63,P207) p(12.99,7.75,P208) p(12.39,8.55,P209) p(12.90,9.41,P210) p(13.89,9.53,P211) p(13.49,8.61,P212) p(13.99,7.74,P213) p(14.98,7.86,P214) p(14.39,8.66,P215) p(14.89,9.53,P216) p(15.88,9.64,P217) p(15.48,8.72,P218) p(15.98,7.86,P219) p(16.98,7.97,P220) p(16.38,8.77,P221) p(16.88,9.64,P222) p(17.88,9.75,P223) p(17.48,8.83,P224) p(17.98,7.97,P225) p(18.97,8.08,P226) p(18.37,8.89,P227) p(18.88,9.75,P228) p(19.87,9.86,P229) p(19.47,8.95,P230) p(19.97,8.08,P231) p(20.96,8.19,P232) p(20.37,9.00,P233) p(20.87,9.86,P234) p(21.86,9.98,P235) p(21.46,9.06,P236) p(21.96,8.19,P237) p(22.96,8.31,P238) p(22.36,9.11,P239) p(22.86,9.97,P240) p(23.86,10.09,P241) p(23.46,9.17,P242) p(23.96,8.30,P243) p(24.95,8.42,P244) p(24.36,9.22,P245) p(24.86,10.09,P246) p(25.85,10.20,P247) p(25.45,9.28,P248) p(25.95,8.42,P249) p(26.94,8.53,P250) p(26.35,9.33,P251) p(26.85,10.20,P252) p(27.84,10.31,P253) p(27.45,9.39,P254) p(27.94,8.53,P255) p(28.94,8.64,P256) p(28.34,9.44,P257) p(28.84,10.31,P258) p(29.84,10.42,P259) p(29.44,9.51,P260) p(29.94,8.64,P261) p(30.93,8.75,P262) p(30.34,9.56,P263) p(30.84,10.42,P264) p(31.43,9.62,P265) p(31.93,8.75,P266) p(-5.42,13.88,P267) p(-4.54,14.34,P268) p(-4.58,13.34,P269) p(-6.30,13.39,P270) p(-6.28,14.39,P271) p(-5.45,12.86,P272) p(-4.59,12.34,P274) p(-3.68,13.83,P275) p(-2.80,14.29,P276) p(-2.84,13.30,P277) p(-4.56,13.34,P278) p(-3.71,12.81,P279) p(-2.85,12.30,P280) p(-1.94,13.78,P281) p(-1.05,14.25,P282) p(-1.09,13.25,P283) p(-2.81,13.29,P284) p(-1.97,12.76,P285) p(-1.11,12.25,P286) p(-0.20,13.73,P287) p(0.69,14.20,P288) p(0.65,13.20,P289) p(-1.07,13.25,P290) p(-0.22,12.71,P291) p(0.63,12.20,P292) p(0.67,13.20,P293) p(1.52,12.66,P294) p(1.55,13.68,P295) p(2.40,13.14,P323) p(3.40,13.12,P325) p(-5.30,14.59,P414) p(-5.96,15.34,P415) p(-5.22,16.01,P416) p(-6.17,16.32,P417) p(-4.24,16.21,P418) p(-4.56,15.26,P419) p(-4.35,14.28,P420) p(-3.37,14.48,P421) p(-4.03,15.23,P422) p(-3.29,15.90,P423) p(-2.31,16.10,P424) p(-2.63,15.15,P425) p(-2.42,14.18,P426) p(-1.44,14.37,P427) p(-2.10,15.12,P428) p(-1.36,15.79,P429) p(-0.38,15.99,P430) p(-0.70,15.04,P431) p(-0.48,14.07,P432) p(0.50,14.26,P433) p(-0.16,15.01,P434) p(0.58,15.69,P435) p(1.56,15.88,P436) p(1.24,14.94,P437) p(1.45,13.96,P438) p(2.43,14.16,P439) p(1.77,14.91,P440) p(2.51,15.58,P441) p(2.40,13.16,P442) p(2.93,14.00,P443) p(3.92,13.89,P444) p(3.52,14.81,P445) p(3.02,15.67,P446) p(4.02,15.67,P447) p(5.02,15.56,P448) p(4.42,14.76,P449) p(4.92,13.89,P450) p(5.92,13.78,P451) p(5.52,14.70,P452) p(6.02,15.56,P453) p(7.01,15.45,P454) p(6.41,14.64,P455) p(6.91,13.78,P456) p(7.91,13.67,P457) p(7.51,14.58,P458) p(8.01,15.45,P459) p(9.00,15.34,P460) p(8.41,14.53,P461) p(8.91,13.67,P462) p(9.90,13.55,P463) p(9.50,14.47,P464) p(10.00,15.34,P465) p(11.00,15.22,P466) p(10.40,14.42,P467) p(10.90,13.56,P468) p(11.90,13.44,P469) p(11.50,14.36,P470) p(12.00,15.23,P471) p(12.99,15.11,P472) p(12.39,14.31,P473) p(12.90,13.44,P474) p(13.89,13.33,P475) p(13.49,14.25,P476) p(13.99,15.11,P477) p(14.98,15.00,P478) p(14.39,14.20,P479) p(14.89,13.33,P480) p(15.88,13.22,P481) p(15.48,14.14,P482) p(15.98,15.00,P483) p(16.98,14.89,P484) p(16.38,14.09,P485) p(16.88,13.22,P486) p(17.88,13.11,P487) p(17.48,14.02,P488) p(17.98,14.89,P489) p(18.97,14.78,P490) p(18.37,13.97,P491) p(18.88,13.11,P492) p(19.87,12.99,P493) p(19.47,13.91,P494) p(19.97,14.78,P495) p(20.96,14.66,P496) p(20.37,13.86,P497) p(20.87,13.00,P498) p(21.86,12.88,P499) p(21.46,13.80,P500) p(21.96,14.67,P501) p(22.96,14.55,P502) p(22.36,13.75,P503) p(22.86,12.88,P504) p(23.86,12.77,P505) p(23.46,13.69,P506) p(23.96,14.55,P507) p(24.95,14.44,P508) p(24.36,13.64,P509) p(24.86,12.77,P510) p(25.85,12.66,P511) p(25.45,13.58,P512) p(25.95,14.44,P513) p(26.94,14.33,P514) p(26.35,13.53,P515) p(26.85,12.66,P516) p(27.84,12.55,P517) p(27.45,13.46,P518) p(27.94,14.33,P519) p(28.94,14.22,P520) p(28.34,13.41,P521) p(28.84,12.55,P522) p(29.84,12.43,P523) p(29.44,13.35,P524) p(29.94,14.22,P525) p(30.93,14.11,P526) p(30.34,13.30,P527) p(30.84,12.44,P528) p(31.43,13.24,P529) p(31.93,14.11,P530) nolabel() s(P2,P1) s(P3,P1) s(P4,P1) s(P5,P1) s(P9,P2) s(P12,P2) s(P3,P2) s(P6,P3) s(P8,P3) s(P6,P4) s(P7,P4) s(P5,P4) s(P151,P5) s(P150,P5) s(P7,P6) s(P8,P6) s(P31,P7) s(P30,P7) s(P13,P8) s(P12,P8) s(P10,P9) s(P11,P9) s(P12,P9) s(P15,P10) s(P18,P10) s(P11,P10) s(P13,P11) s(P14,P11) s(P13,P12) s(P14,P13) s(P19,P14) s(P18,P14) s(P16,P15) s(P17,P15) s(P18,P15) s(P21,P16) s(P24,P16) s(P17,P16) s(P19,P17) s(P20,P17) s(P19,P18) s(P20,P19) s(P25,P20) s(P24,P20) s(P22,P21) s(P23,P21) s(P24,P21) s(P23,P22) s(P27,P22) s(P29,P22) s(P25,P23) s(P26,P23) s(P25,P24) s(P26,P25) s(P27,P26) s(P28,P26) s(P28,P27) s(P29,P27) s(P55,P28) s(P58,P28) s(P175,P29) s(P178,P29) s(P35,P30) s(P31,P30) s(P36,P30) s(P33,P31) s(P32,P31) s(P34,P32) s(P33,P32) s(P35,P32) s(P270,P33) s(P272,P33) s(P38,P34) s(P39,P34) s(P35,P34) s(P36,P35) s(P37,P36) s(P38,P36) s(P41,P37) s(P38,P37) s(P42,P37) s(P39,P38) s(P40,P39) s(P41,P39) s(P44,P40) s(P45,P40) s(P41,P40) s(P42,P41) s(P43,P42) s(P44,P42) s(P47,P43) s(P44,P43) s(P48,P43) s(P45,P44) s(P46,P45) s(P47,P45) s(P50,P46) s(P51,P46) s(P47,P46) s(P48,P47) s(P49,P48) s(P50,P48) s(P53,P49) s(P50,P49) s(P54,P49) s(P51,P50) s(P52,P51) s(P53,P51) s(P56,P52) s(P57,P52) s(P53,P52) s(P54,P53) s(P55,P54) s(P56,P54) s(P56,P55) s(P58,P55) s(P57,P56) s(P294,P57) s(P323,P57) s(P59,P58) s(P60,P58) s(P60,P59) s(P61,P59) s(P62,P59) s(P178,P60) s(P179,P60) s(P67,P61) s(P62,P61) s(P66,P61) s(P63,P62) s(P64,P62) s(P64,P63) s(P323,P63) s(P325,P63) s(P65,P64) s(P66,P64) s(P66,P65) s(P69,P65) s(P70,P65) s(P67,P66) s(P68,P67) s(P69,P67) s(P73,P68) s(P69,P68) s(P72,P68) s(P70,P69) s(P71,P70) s(P72,P70) s(P72,P71) s(P75,P71) s(P76,P71) s(P73,P72) s(P74,P73) s(P75,P73) s(P79,P74) s(P75,P74) s(P78,P74) s(P76,P75) s(P77,P76) s(P78,P76) s(P78,P77) s(P81,P77) s(P82,P77) s(P79,P78) s(P80,P79) s(P81,P79) s(P85,P80) s(P81,P80) s(P84,P80) s(P82,P81) s(P83,P82) s(P84,P82) s(P84,P83) s(P87,P83) s(P88,P83) s(P85,P84) s(P86,P85) s(P87,P85) s(P91,P86) s(P87,P86) s(P90,P86) s(P88,P87) s(P89,P88) s(P90,P88) s(P90,P89) s(P93,P89) s(P94,P89) s(P91,P90) s(P92,P91) s(P93,P91) s(P97,P92) s(P93,P92) s(P96,P92) s(P94,P93) s(P95,P94) s(P96,P94) s(P96,P95) s(P99,P95) s(P100,P95) s(P97,P96) s(P98,P97) s(P99,P97) s(P103,P98) s(P99,P98) s(P102,P98) s(P100,P99) s(P101,P100) s(P102,P100) s(P102,P101) s(P105,P101) s(P106,P101) s(P103,P102) s(P104,P103) s(P105,P103) s(P109,P104) s(P105,P104) s(P108,P104) s(P106,P105) s(P107,P106) s(P108,P106) s(P108,P107) s(P111,P107) s(P112,P107) s(P109,P108) s(P110,P109) s(P111,P109) s(P115,P110) s(P111,P110) s(P114,P110) s(P112,P111) s(P113,P112) s(P114,P112) s(P114,P113) s(P117,P113) s(P118,P113) s(P115,P114) s(P116,P115) s(P117,P115) s(P121,P116) s(P117,P116) s(P120,P116) s(P118,P117) s(P119,P118) s(P120,P118) s(P120,P119) s(P123,P119) s(P124,P119) s(P121,P120) s(P122,P121) s(P123,P121) s(P127,P122) s(P123,P122) s(P126,P122) s(P124,P123) s(P125,P124) s(P126,P124) s(P126,P125) s(P129,P125) s(P130,P125) s(P127,P126) s(P128,P127) s(P129,P127) s(P133,P128) s(P129,P128) s(P132,P128) s(P130,P129) s(P131,P130) s(P132,P130) s(P132,P131) s(P135,P131) s(P136,P131) s(P133,P132) s(P134,P133) s(P135,P133) s(P139,P134) s(P135,P134) s(P138,P134) s(P136,P135) s(P137,P136) s(P138,P136) s(P138,P137) s(P141,P137) s(P142,P137) s(P139,P138) s(P140,P139) s(P141,P139) s(P145,P140) s(P141,P140) s(P144,P140) s(P142,P141) s(P143,P142) s(P144,P142) s(P144,P143) s(P147,P143) s(P148,P143) s(P145,P144) s(P146,P145) s(P147,P145) s(P264,P146) s(P147,P146) s(P265,P146) s(P148,P147) s(P528,P148) s(P529,P148) s(P155,P150) s(P151,P150) s(P156,P150) s(P152,P151) s(P153,P151) s(P154,P152) s(P153,P152) s(P155,P152) s(P158,P154) s(P159,P154) s(P155,P154) s(P156,P155) s(P157,P156) s(P158,P156) s(P161,P157) s(P158,P157) s(P162,P157) s(P159,P158) s(P160,P159) s(P161,P159) s(P164,P160) s(P165,P160) s(P161,P160) s(P162,P161) s(P163,P162) s(P164,P162) s(P167,P163) s(P164,P163) s(P168,P163) s(P165,P164) s(P166,P165) s(P167,P165) s(P170,P166) s(P171,P166) s(P167,P166) s(P168,P167) s(P169,P168) s(P170,P168) s(P173,P169) s(P170,P169) s(P174,P169) s(P171,P170) s(P172,P171) s(P173,P171) s(P176,P172) s(P177,P172) s(P173,P172) s(P174,P173) s(P175,P174) s(P176,P174) s(P176,P175) s(P178,P175) s(P177,P176) s(P179,P178) s(P180,P179) s(P181,P179) s(P186,P180) s(P181,P180) s(P185,P180) s(P182,P181) s(P183,P181) s(P183,P182) s(P184,P183) s(P185,P183) s(P185,P184) s(P188,P184) s(P189,P184) s(P186,P185) s(P187,P186) s(P188,P186) s(P192,P187) s(P188,P187) s(P191,P187) s(P189,P188) s(P190,P189) s(P191,P189) s(P191,P190) s(P194,P190) s(P195,P190) s(P192,P191) s(P193,P192) s(P194,P192) s(P198,P193) s(P194,P193) s(P197,P193) s(P195,P194) s(P196,P195) s(P197,P195) s(P197,P196) s(P200,P196) s(P201,P196) s(P198,P197) s(P199,P198) s(P200,P198) s(P204,P199) s(P200,P199) s(P203,P199) s(P201,P200) s(P202,P201) s(P203,P201) s(P203,P202) s(P206,P202) s(P207,P202) s(P204,P203) s(P205,P204) s(P206,P204) s(P210,P205) s(P206,P205) s(P209,P205) s(P207,P206) s(P208,P207) s(P209,P207) s(P209,P208) s(P212,P208) s(P213,P208) s(P210,P209) s(P211,P210) s(P212,P210) s(P216,P211) s(P212,P211) s(P215,P211) s(P213,P212) s(P214,P213) s(P215,P213) s(P215,P214) s(P218,P214) s(P219,P214) s(P216,P215) s(P217,P216) s(P218,P216) s(P222,P217) s(P218,P217) s(P221,P217) s(P219,P218) s(P220,P219) s(P221,P219) s(P221,P220) s(P224,P220) s(P225,P220) s(P222,P221) s(P223,P222) s(P224,P222) s(P228,P223) s(P224,P223) s(P227,P223) s(P225,P224) s(P226,P225) s(P227,P225) s(P227,P226) s(P230,P226) s(P231,P226) s(P228,P227) s(P229,P228) s(P230,P228) s(P234,P229) s(P230,P229) s(P233,P229) s(P231,P230) s(P232,P231) s(P233,P231) s(P233,P232) s(P236,P232) s(P237,P232) s(P234,P233) s(P235,P234) s(P236,P234) s(P240,P235) s(P236,P235) s(P239,P235) s(P237,P236) s(P238,P237) s(P239,P237) s(P239,P238) s(P242,P238) s(P243,P238) s(P240,P239) s(P241,P240) s(P242,P240) s(P246,P241) s(P242,P241) s(P245,P241) s(P243,P242) s(P244,P243) s(P245,P243) s(P245,P244) s(P248,P244) s(P249,P244) s(P246,P245) s(P247,P246) s(P248,P246) s(P252,P247) s(P248,P247) s(P251,P247) s(P249,P248) s(P250,P249) s(P251,P249) s(P251,P250) s(P254,P250) s(P255,P250) s(P252,P251) s(P253,P252) s(P254,P252) s(P258,P253) s(P254,P253) s(P257,P253) s(P255,P254) s(P256,P255) s(P257,P255) s(P257,P256) s(P260,P256) s(P261,P256) s(P258,P257) s(P259,P258) s(P260,P258) s(P264,P259) s(P260,P259) s(P263,P259) s(P261,P260) s(P262,P261) s(P263,P261) s(P263,P262) s(P265,P262) s(P266,P262) s(P264,P263) s(P265,P264) s(P266,P265) s(P268,P267) s(P269,P267) s(P270,P267) s(P271,P267) s(P275,P268) s(P278,P268) s(P269,P268) s(P272,P269) s(P274,P269) s(P272,P270) s(P271,P270) s(P414,P271) s(P415,P271) s(P274,P272) s(P279,P274) s(P278,P274) s(P276,P275) s(P277,P275) s(P278,P275) s(P281,P276) s(P284,P276) s(P277,P276) s(P279,P277) s(P280,P277) s(P279,P278) s(P280,P279) s(P285,P280) s(P284,P280) s(P282,P281) s(P283,P281) s(P284,P281) s(P287,P282) s(P290,P282) s(P283,P282) s(P285,P283) s(P286,P283) s(P285,P284) s(P286,P285) s(P291,P286) s(P290,P286) s(P288,P287) s(P289,P287) s(P290,P287) s(P289,P288) s(P293,P288) s(P295,P288) s(P291,P289) s(P292,P289) s(P291,P290) s(P292,P291) s(P293,P292) s(P294,P292) s(P294,P293) s(P295,P293) s(P323,P294) s(P439,P295) s(P442,P295) s(P325,P323) s(P442,P325) s(P443,P325) s(P419,P414) s(P415,P414) s(P420,P414) s(P416,P415) s(P417,P415) s(P418,P416) s(P417,P416) s(P419,P416) s(P422,P418) s(P423,P418) s(P419,P418) s(P420,P419) s(P421,P420) s(P422,P420) s(P425,P421) s(P422,P421) s(P426,P421) s(P423,P422) s(P424,P423) s(P425,P423) s(P428,P424) s(P429,P424) s(P425,P424) s(P426,P425) s(P427,P426) s(P428,P426) s(P431,P427) s(P428,P427) s(P432,P427) s(P429,P428) s(P430,P429) s(P431,P429) s(P434,P430) s(P435,P430) s(P431,P430) s(P432,P431) s(P433,P432) s(P434,P432) s(P437,P433) s(P434,P433) s(P438,P433) s(P435,P434) s(P436,P435) s(P437,P435) s(P440,P436) s(P441,P436) s(P437,P436) s(P438,P437) s(P439,P438) s(P440,P438) s(P440,P439) s(P442,P439) s(P441,P440) s(P443,P442) s(P444,P443) s(P445,P443) s(P450,P444) s(P445,P444) s(P449,P444) s(P446,P445) s(P447,P445) s(P447,P446) s(P448,P447) s(P449,P447) s(P449,P448) s(P452,P448) s(P453,P448) s(P450,P449) s(P451,P450) s(P452,P450) s(P456,P451) s(P452,P451) s(P455,P451) s(P453,P452) s(P454,P453) s(P455,P453) s(P455,P454) s(P458,P454) s(P459,P454) s(P456,P455) s(P457,P456) s(P458,P456) s(P462,P457) s(P458,P457) s(P461,P457) s(P459,P458) s(P460,P459) s(P461,P459) s(P461,P460) s(P464,P460) s(P465,P460) s(P462,P461) s(P463,P462) s(P464,P462) s(P468,P463) s(P464,P463) s(P467,P463) s(P465,P464) s(P466,P465) s(P467,P465) s(P467,P466) s(P470,P466) s(P471,P466) s(P468,P467) s(P469,P468) s(P470,P468) s(P474,P469) s(P470,P469) s(P473,P469) s(P471,P470) s(P472,P471) s(P473,P471) s(P473,P472) s(P476,P472) s(P477,P472) s(P474,P473) s(P475,P474) s(P476,P474) s(P480,P475) s(P476,P475) s(P479,P475) s(P477,P476) s(P478,P477) s(P479,P477) s(P479,P478) s(P482,P478) s(P483,P478) s(P480,P479) s(P481,P480) s(P482,P480) s(P486,P481) s(P482,P481) s(P485,P481) s(P483,P482) s(P484,P483) s(P485,P483) s(P485,P484) s(P488,P484) s(P489,P484) s(P486,P485) s(P487,P486) s(P488,P486) s(P492,P487) s(P488,P487) s(P491,P487) s(P489,P488) s(P490,P489) s(P491,P489) s(P491,P490) s(P494,P490) s(P495,P490) s(P492,P491) s(P493,P492) s(P494,P492) s(P498,P493) s(P494,P493) s(P497,P493) s(P495,P494) s(P496,P495) s(P497,P495) s(P497,P496) s(P500,P496) s(P501,P496) s(P498,P497) s(P499,P498) s(P500,P498) s(P504,P499) s(P500,P499) s(P503,P499) s(P501,P500) s(P502,P501) s(P503,P501) s(P503,P502) s(P506,P502) s(P507,P502) s(P504,P503) s(P505,P504) s(P506,P504) s(P510,P505) s(P506,P505) s(P509,P505) s(P507,P506) s(P508,P507) s(P509,P507) s(P509,P508) s(P512,P508) s(P513,P508) s(P510,P509) s(P511,P510) s(P512,P510) s(P516,P511) s(P512,P511) s(P515,P511) s(P513,P512) s(P514,P513) s(P515,P513) s(P515,P514) s(P518,P514) s(P519,P514) s(P516,P515) s(P517,P516) s(P518,P516) s(P522,P517) s(P518,P517) s(P521,P517) s(P519,P518) s(P520,P519) s(P521,P519) s(P521,P520) s(P524,P520) s(P525,P520) s(P522,P521) s(P523,P522) s(P524,P522) s(P528,P523) s(P524,P523) s(P527,P523) s(P525,P524) s(P526,P525) s(P527,P525) s(P527,P526) s(P529,P526) s(P530,P526) s(P528,P527) s(P529,P528) s(P530,P529) pen(2) color(#008000) m(P6,P7,MA10) m(P7,P30,MB10) b(P7,MA10,MB10) color(#FFA500) m(P30,P31,MA11) m(P31,P32,MB11) b(P31,MA11,MB11) color(#0000FF) m(P3,P1,MA12) m(P1,P4,MB12) b(P1,MA12,MB12) color(#EE82EE) m(P55,P58,MA13) m(P58,P59,MB13) b(P58,MA13,MB13) color(#00FFFF) m(P60,P59,MA14) m(P59,P61,MB14) b(P59,MA14,MB14) pen(2) color(#008000) s(P55,P28) color(#008000) s(P29,P175) color(#008000) s(P5,P151) color(#008000) s(P33,P270) color(blue) color(orange) color(red) \geooff \geoprint()
Ich sehe zwar keinen Fehler, aber Stefan sollte das auf jeden Fall noch überprüfen. An der Existenz gibt es aber keine Zweifel mehr.
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haribo
Senior
Dabei seit: 25.10.2012
Mitteilungen: 1687
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| Beitrag No.1432, eingetragen 2018-09-20 07:36
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zeichnest du nochmal deine aktuellen winkel farbig ein? bitte
und fals möglich die grauen punktbezeichnungen weitgehend aus
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