| |
| Autor |
 Streichholzgraphen 4-regulär und 4/n-regulär (n>4) und 2/5 |
|
Slash
Aktiv 
Dabei seit: 23.03.2005
Mitteilungen: 9108
 |  Beitrag No.1400, vom Themenstarter, eingetragen 2018-09-16
|
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:
#
#Teilgraph für 4/4 Ring aus 27 Stück.
#
#
#
#
#
#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);
#
#
#//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()
https://www.matheplanet.de/matheplanet/nuke/html/uploads/b/8038_slash_27er_ring.png
|
 Profil
|
haribo
Senior 
Dabei seit: 25.10.2012
Mitteilungen: 4376
 | Beitrag No.1401, eingetragen 2018-09-16
|
4/6er mit überschneidung
https://www.matheplanet.com/matheplanet/nuke/html/uploads/b/35059_st-4-6-210er.PNG
|
Profil
|
Slash
Aktiv
Dabei seit: 23.03.2005
Mitteilungen: 9108
| Beitrag No.1402, vom Themenstarter, eingetragen 2018-09-16
|
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.
|
Profil
|
StefanVogel
Senior
Dabei seit: 26.11.2005
Mitteilungen: 4248
Wohnort: Raun
| Beitrag No.1403, eingetragen 2018-09-17
|
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:
#
##1400 mit RW(...)
#
#
#
#
#
#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);
#
#
#//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()
|
Profil
|
Slash
Aktiv
Dabei seit: 23.03.2005
Mitteilungen: 9108
| Beitrag No.1404, vom Themenstarter, eingetragen 2018-09-17
|
\quoteon(2018-09-17 04:55 - StefanVogel in Beitrag No. 1403)
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?
\quoteoff
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?
|
Profil
|
StefanVogel
Senior
Dabei seit: 26.11.2005
Mitteilungen: 4248
Wohnort: Raun
| Beitrag No.1405, eingetragen 2018-09-17
|
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.
\quoteon(2018-09-17 05:25 - Slash in Beitrag No. 1404)
\quoteon(2018-09-17 04:55 - StefanVogel in Beitrag No. 1403)
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?
\quoteoff
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.
\quoteoff
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
\quoteon
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. ;-)
\quoteoff
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).
\quoteon
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.
\quoteoff
Ja, geht mir auch so.
|
Profil
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Slash
Aktiv
Dabei seit: 23.03.2005
Mitteilungen: 9108
| Beitrag No.1406, vom Themenstarter, eingetragen 2018-09-17
|
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:
#
##1373 Fig.2 blauerWinkel=70,nach Feinjustieren(2)
#
#
#
#
#
#
#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"));
#
#
#//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()
https://www.matheplanet.de/matheplanet/nuke/html/uploads/b/8038_slash_ring_2_gr._dreiecke.png
|
Profil
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haribo
Senior
Dabei seit: 25.10.2012
Mitteilungen: 4376
| Beitrag No.1407, eingetragen 2018-09-17
|
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..
https://www.matheplanet.com/matheplanet/nuke/html/uploads/b/35059_st-14x12b.PNG
|
Profil
|
Slash
Aktiv
Dabei seit: 23.03.2005
Mitteilungen: 9108
| Beitrag No.1408, vom Themenstarter, eingetragen 2018-09-17
|
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?
|
Profil
|
haribo
Senior
Dabei seit: 25.10.2012
Mitteilungen: 4376
| Beitrag No.1409, eingetragen 2018-09-17
|
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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Slash
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Dabei seit: 23.03.2005
Mitteilungen: 9108
| Beitrag No.1410, vom Themenstarter, eingetragen 2018-09-17
|
#567 ist ein 4/6.
Was die Bedingungen mit den großen Dreiecken betrifft... Ich experimentiere mit diesen Girlanden. Mehr steckt nicht dahinter.
\quoteon(2018-09-17 11:22 - haribo in Beitrag No. 1409)
und nochmals die frage wie füge ich einen link hier ein der direkt auf #345 führt??? (wie das geht vergess ich immer wieder...)
\quoteoff
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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Slash
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Dabei seit: 23.03.2005
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| Beitrag No.1411, vom Themenstarter, eingetragen 2018-09-17
|
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:
#
##1373 Fig.2 blauerWinkel=70,nach Feinjustieren(2)
#
#
#
#
#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);
#
#
#//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()
https://www.matheplanet.de/matheplanet/nuke/html/uploads/b/8038_slash_speichenrad.png
|
Profil
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haribo
Senior
Dabei seit: 25.10.2012
Mitteilungen: 4376
| Beitrag No.1412, eingetragen 2018-09-17
|
\quoteon(2018-09-16 12:43 - Slash in Beitrag No. 1402)
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.
\quoteoff
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
https://www.matheplanet.com/matheplanet/nuke/html/uploads/b/35059_st-harborth-torte-ansatz.PNG
[Die Antwort wurde nach Beitrag No.1410 begonnen.]
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haribo
Senior
Dabei seit: 25.10.2012
Mitteilungen: 4376
| Beitrag No.1413, eingetragen 2018-09-17
|
sehr spassig, wir haben mal wieder gleichzeitig, die gleiche speichen-rad konstruktion avisiert...
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Dabei seit: 23.03.2005
Mitteilungen: 9108
| Beitrag No.1414, vom Themenstarter, eingetragen 2018-09-17
|
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:
#
##1373 Fig.2 blauerWinkel=70,nach Feinjustieren(2)
#
#
#
#
#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);
#
#
#//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()
|
Profil
|
Slash
Aktiv
Dabei seit: 23.03.2005
Mitteilungen: 9108
| Beitrag No.1415, vom Themenstarter, eingetragen 2018-09-17
|
\quoteon(2018-09-17 17:11 - haribo in Beitrag No. 1412)
und gleichzeitig die torte geschlossen werden kann
\quoteoff
Tja, das ist Streichholzgraphen-Jargon. :-D
Also wenn du mit deinem Ansatz rechts hast, dann hat sich das hier ja mal wieder gelohnt und kein Graph war umsonst. :-)
|
Profil
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Slash
Aktiv
Dabei seit: 23.03.2005
Mitteilungen: 9108
| Beitrag No.1416, vom Themenstarter, eingetragen 2018-09-17
|
Ob auch Doppelspeichen möglich sind? Hier gibt es minimale Überschneidungen im inneren Kreis. Der Graph ist noch nicht getestet worden.
https://www.matheplanet.de/matheplanet/nuke/html/uploads/b/8038_slash_doppelspeiche.png
|
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haribo
Senior
Dabei seit: 25.10.2012
Mitteilungen: 4376
| Beitrag No.1417, eingetragen 2018-09-17
|
klar sind speichen-seiten-wechsel möglich, das erhöht die variantenmöglichkeit bis es innen passt sogar nochmal enorm
https://www.matheplanet.com/matheplanet/nuke/html/uploads/b/35059_st-harborth-torte-ansatz2.PNG
|
Profil
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Slash
Aktiv
Dabei seit: 23.03.2005
Mitteilungen: 9108
| Beitrag No.1418, vom Themenstarter, eingetragen 2018-09-17
|
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:
#
##1373 Fig.2 RA(55,28); RA(59,28); RW(8,7,36,7,1.8); dann
#Feinjustieren(3)
#
#
#
#
#
#
#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]));
#
#
#
#//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()
|
Profil
|
haribo
Senior
Dabei seit: 25.10.2012
Mitteilungen: 4376
| Beitrag No.1419, eingetragen 2018-09-17
|
https://www.matheplanet.com/matheplanet/nuke/html/uploads/b/35059_slash-hilfe1.png
die rechte ecke vom blauen muss auf der unteren tortenkante liegen
|
Profil
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Slash
Aktiv
Dabei seit: 23.03.2005
Mitteilungen: 9108
| Beitrag No.1420, vom Themenstarter, eingetragen 2018-09-17
|
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:
#
##1373 Fig.2 RA(55,28); RA(59,28); RW(8,7,36,7,1.8); dann
#Feinjustieren(3)
#
#
#
#
#
#
#
#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);
#
#
#//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()
|
Profil
|
Slash
Aktiv
Dabei seit: 23.03.2005
Mitteilungen: 9108
| Beitrag No.1421, vom Themenstarter, eingetragen 2018-09-18
|
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! 8-)
https://www.matheplanet.de/matheplanet/nuke/html/uploads/b/8038_slash_haribo_ring_tg2.png
Tortenstück zweigeteilt. Blaues Dreick ist identisch. Der Teilgraph besteht aus 108 Dreiecken.
https://www.matheplanet.de/matheplanet/nuke/html/uploads/b/8038_tg_torte.png
Der Ring schließt schon fast genau. Die Überschneidung ist minimal.
https://www.matheplanet.de/matheplanet/nuke/html/uploads/b/8038_slash_haribo_ring.png
\sourceon MGC
#1373 Fig.2 RA(55,28); RA(59,28); RW(8,7,36,7,1.8); dann
Feinjustieren(3)
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);
\sourceoff
|
Profil
|
haribo
Senior
Dabei seit: 25.10.2012
Mitteilungen: 4376
| Beitrag No.1422, eingetragen 2018-09-18
|
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° !!!
#
#
#
#
#
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???
https://www.matheplanet.com/matheplanet/nuke/html/uploads/b/35059_st-harborth-torte-ansatz3.PNG
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
|
Profil
|
Slash
Aktiv
Dabei seit: 23.03.2005
Mitteilungen: 9108
| Beitrag No.1423, vom Themenstarter, eingetragen 2018-09-18
|
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:
#
##1373 Fig.2 RA(55,28); RA(59,28); RW(8,7,36,7,1.8); dann
#Feinjustieren(3)
#
#
#
#
#
#
#
#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);
#
#
#//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()
|
Profil
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haribo
Senior
Dabei seit: 25.10.2012
Mitteilungen: 4376
| Beitrag No.1424, eingetragen 2018-09-18
|
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
|
Profil
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haribo
Senior
Dabei seit: 25.10.2012
Mitteilungen: 4376
| Beitrag No.1425, eingetragen 2018-09-18
|
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
|
Profil
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Slash
Aktiv
Dabei seit: 23.03.2005
Mitteilungen: 9108
| Beitrag No.1426, vom Themenstarter, eingetragen 2018-09-18
|
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.
|
Profil
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Slash
Aktiv
Dabei seit: 23.03.2005
Mitteilungen: 9108
| Beitrag No.1427, vom Themenstarter, eingetragen 2018-09-19
|
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 Tortenstücken. 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.
\sourceon MGC
// 360/584 = 0,61643835616438356164
// Tortenwinkel P31,P118,P62,P120 = 0,61643835616456865711
Ring Graph mit 584 Speichen
P[1]=[-220.51898335931583,-147.11379166682062];
P[2]=[-176.1921256157948,-170.24666184295043]; 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);
\sourceoff
Hier ist das gute Stück aus 63072 Dreiecken.
https://www.matheplanet.de/matheplanet/nuke/html/uploads/b/8038_slash_ring_584.png
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! :-)
EDIT 1: Dreiecksanzahl korrigiert.
EDIT 2: Mit RW Funktion bekomme ich (nur) 11 Nachkommastellen Übereinstimmung.
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Profil
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haribo
Senior
Dabei seit: 25.10.2012
Mitteilungen: 4376
| Beitrag No.1428, eingetragen 2018-09-19
|
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
https://www.matheplanet.com/matheplanet/nuke/html/uploads/b/35059_st-panama.png
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Profil
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Slash
Aktiv
Dabei seit: 23.03.2005
Mitteilungen: 9108
| Beitrag No.1429, vom Themenstarter, eingetragen 2018-09-19
|
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.
https://www.matheplanet.de/matheplanet/nuke/html/uploads/b/8038_teilgraph_vergleich_3.png
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!!!). :-)
Wir waren auch recht schnell. Am 09.09.2018 Problem vorgestellt, 17.09.2018 erster Lösungsansatz und 19.09.2018 erste Lösung.
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Profil
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haribo
Senior
Dabei seit: 25.10.2012
Mitteilungen: 4376
| Beitrag No.1430, eingetragen 2018-09-19
|
THX
Ich zerleg dir das die Tage nochmal in drei teilschritte , schätze dann kanst du auch kleinere Versionen darstellen...
|
Profil
|
Slash
Aktiv
Dabei seit: 23.03.2005
Mitteilungen: 9108
| Beitrag No.1431, vom Themenstarter, eingetragen 2018-09-20
|
Torten-Teilgraph mit 49 Dreiecken und Ring aus 224 Teilgraphen. Also 10976 Dreiecke insgesamt. 360/224 = 1,60714285714285714285 und Tortenwinkel = 1,60714285714289850659, also korrekt bis zur 13. Nachkommastelle.
412 Knoten, 8×Grad 2, 404×Grad 4
816 Kanten, minimal 0.99999999999971000975, maximal 1.00000000000174904535
einstellbare Kanten R(j,k):
|P55-P28|=0.99999999999987754240
|P29-P175|=0.99999999999994282351
|P5-P151|=1.00000000000043232085
|P33-P270|=1.00000000000002220446
|P23-P60|=2.74786281795560816121
\geo
ebene(748.55,199.84)
x(10.73,50.32)
y(16.22,26.79)
form(.)
#//Eingabe war:
#
#// 360/224 = 1,60714285714285714285
#// Tortenwinkel = 1,60714285714289850659
#Ring-Graph
#
#
#
#
#
#
#
#P[1]=[31.020981113945098,163.79849485458618];
#P[2]=[47.757248836752986,155.00208822401208]; 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);
#RW(23,60,56,62,1.60714285714285714285);
#
#//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);
#
#
#//Ende der Eingabe, weiter mit fedgeo:
p(11.64,18.66,P1)
p(12.53,18.20,P2)
p(12.49,19.20,P3)
p(10.77,19.15,P4)
p(10.78,18.15,P5)
p(11.61,19.68,P6)
p(10.73,20.15,P7)
p(12.47,20.20,P8)
p(13.38,18.71,P9)
p(14.27,18.25,P10)
p(14.23,19.25,P11)
p(12.51,19.20,P12)
p(13.35,19.73,P13)
p(14.21,20.25,P14)
p(15.13,18.76,P15)
p(16.01,18.30,P16)
p(15.97,19.30,P17)
p(14.25,19.25,P18)
p(15.10,19.78,P19)
p(15.96,20.29,P20)
p(16.87,18.81,P21)
p(17.75,18.34,P22)
p(17.71,19.34,P23)
p(16.00,19.30,P24)
p(16.84,19.83,P25)
p(17.70,20.34,P26)
p(17.74,19.34,P27)
p(18.58,19.88,P28)
p(18.61,18.86,P29)
p(11.69,20.40,P30)
p(10.99,21.11,P31)
p(11.69,21.82,P32)
p(10.73,22.08,P33)
p(12.66,22.08,P34)
p(12.40,21.11,P35)
p(12.66,20.15,P36)
p(13.63,20.40,P37)
p(12.93,21.11,P38)
p(13.63,21.82,P39)
p(14.60,22.08,P40)
p(14.33,21.11,P41)
p(14.60,20.15,P42)
p(15.57,20.40,P43)
p(14.86,21.11,P44)
p(15.57,21.82,P45)
p(16.53,22.08,P46)
p(16.27,21.11,P47)
p(16.53,20.15,P48)
p(17.50,20.40,P49)
p(16.80,21.11,P50)
p(17.50,21.82,P51)
p(18.47,22.08,P52)
p(18.20,21.11,P53)
p(18.47,20.15,P54)
p(19.44,20.40,P55)
p(18.73,21.11,P56)
p(19.44,21.82,P57)
p(19.46,19.40,P58)
p(19.94,20.28,P59)
p(20.46,19.42,P60)
p(20.94,20.22,P61)
p(20.49,21.11,P62)
p(19.94,21.95,P63)
p(20.94,22.01,P64)
p(21.94,21.95,P65)
p(21.39,21.11,P66)
p(21.94,20.28,P67)
p(22.94,20.22,P68)
p(22.49,21.11,P69)
p(22.94,22.01,P70)
p(23.94,21.95,P71)
p(23.39,21.11,P72)
p(23.94,20.28,P73)
p(24.94,20.22,P74)
p(24.49,21.11,P75)
p(24.94,22.01,P76)
p(25.93,21.95,P77)
p(25.38,21.11,P78)
p(25.93,20.28,P79)
p(26.93,20.22,P80)
p(26.48,21.11,P81)
p(26.93,22.01,P82)
p(27.93,21.95,P83)
p(27.38,21.11,P84)
p(27.93,20.28,P85)
p(28.93,20.22,P86)
p(28.48,21.11,P87)
p(28.93,22.01,P88)
p(29.93,21.95,P89)
p(29.38,21.11,P90)
p(29.93,20.28,P91)
p(30.93,20.22,P92)
p(30.48,21.11,P93)
p(30.93,22.01,P94)
p(31.92,21.95,P95)
p(31.37,21.11,P96)
p(31.92,20.28,P97)
p(32.92,20.22,P98)
p(32.47,21.11,P99)
p(32.92,22.01,P100)
p(33.92,21.95,P101)
p(33.37,21.11,P102)
p(33.92,20.28,P103)
p(34.92,20.22,P104)
p(34.47,21.11,P105)
p(34.92,22.01,P106)
p(35.92,21.95,P107)
p(35.37,21.11,P108)
p(35.92,20.28,P109)
p(36.92,20.22,P110)
p(36.47,21.11,P111)
p(36.92,22.01,P112)
p(37.91,21.95,P113)
p(37.36,21.11,P114)
p(37.91,20.28,P115)
p(38.91,20.22,P116)
p(38.46,21.11,P117)
p(38.91,22.01,P118)
p(39.91,21.95,P119)
p(39.36,21.11,P120)
p(39.91,20.28,P121)
p(40.91,20.22,P122)
p(40.46,21.11,P123)
p(40.91,22.01,P124)
p(41.91,21.95,P125)
p(41.36,21.11,P126)
p(41.91,20.28,P127)
p(42.91,20.22,P128)
p(42.46,21.11,P129)
p(42.91,22.01,P130)
p(43.90,21.95,P131)
p(43.35,21.11,P132)
p(43.90,20.28,P133)
p(44.90,20.22,P134)
p(44.45,21.11,P135)
p(44.90,22.01,P136)
p(45.90,21.95,P137)
p(45.35,21.11,P138)
p(45.90,20.28,P139)
p(46.90,20.22,P140)
p(46.45,21.11,P141)
p(46.90,22.01,P142)
p(47.90,21.95,P143)
p(47.35,21.11,P144)
p(47.90,20.28,P145)
p(48.90,20.22,P146)
p(48.45,21.11,P147)
p(48.90,22.01,P148)
p(11.76,17.95,P150)
p(11.10,17.20,P151)
p(11.84,16.53,P152)
p(10.89,16.22,P153)
p(12.82,16.33,P154)
p(12.50,17.28,P155)
p(12.72,18.26,P156)
p(13.70,18.06,P157)
p(13.03,17.31,P158)
p(13.78,16.64,P159)
p(14.76,16.44,P160)
p(14.44,17.39,P161)
p(14.65,18.37,P162)
p(15.63,18.17,P163)
p(14.97,17.42,P164)
p(15.71,16.75,P165)
p(16.69,16.55,P166)
p(16.37,17.50,P167)
p(16.58,18.47,P168)
p(17.56,18.28,P169)
p(16.90,17.53,P170)
p(17.64,16.86,P171)
p(18.62,16.66,P172)
p(18.30,17.61,P173)
p(18.51,18.58,P174)
p(19.49,18.39,P175)
p(18.83,17.64,P176)
p(19.57,16.96,P177)
p(19.46,19.39,P178)
p(19.99,18.54,P179)
p(20.99,18.65,P180)
p(20.59,17.73,P181)
p(20.09,16.87,P182)
p(21.09,16.87,P183)
p(22.08,16.98,P184)
p(21.48,17.78,P185)
p(21.99,18.65,P186)
p(22.98,18.76,P187)
p(22.58,17.85,P188)
p(23.08,16.98,P189)
p(24.07,17.09,P190)
p(23.48,17.90,P191)
p(23.98,18.76,P192)
p(24.97,18.88,P193)
p(24.57,17.96,P194)
p(25.07,17.09,P195)
p(26.07,17.20,P196)
p(25.47,18.01,P197)
p(25.97,18.87,P198)
p(26.97,18.99,P199)
p(26.57,18.07,P200)
p(27.07,17.20,P201)
p(28.06,17.32,P202)
p(27.47,18.12,P203)
p(27.97,18.99,P204)
p(28.96,19.10,P205)
p(28.56,18.18,P206)
p(29.06,17.32,P207)
p(30.05,17.43,P208)
p(29.46,18.23,P209)
p(29.96,19.10,P210)
p(30.95,19.21,P211)
p(30.56,18.29,P212)
p(31.05,17.43,P213)
p(32.05,17.54,P214)
p(31.45,18.34,P215)
p(31.95,19.21,P216)
p(32.95,19.32,P217)
p(32.55,18.41,P218)
p(33.05,17.54,P219)
p(34.04,17.65,P220)
p(33.45,18.46,P221)
p(33.95,19.32,P222)
p(34.94,19.44,P223)
p(34.54,18.52,P224)
p(35.04,17.65,P225)
p(36.03,17.76,P226)
p(35.44,18.57,P227)
p(35.94,19.43,P228)
p(36.93,19.55,P229)
p(36.54,18.63,P230)
p(37.03,17.76,P231)
p(38.03,17.88,P232)
p(37.43,18.68,P233)
p(37.93,19.55,P234)
p(38.93,19.66,P235)
p(38.53,18.74,P236)
p(39.03,17.87,P237)
p(40.02,17.99,P238)
p(39.43,18.79,P239)
p(39.93,19.66,P240)
p(40.92,19.77,P241)
p(40.52,18.85,P242)
p(41.02,17.99,P243)
p(42.02,18.10,P244)
p(41.42,18.90,P245)
p(41.92,19.77,P246)
p(42.91,19.88,P247)
p(42.52,18.97,P248)
p(43.02,18.10,P249)
p(44.01,18.21,P250)
p(43.41,19.02,P251)
p(43.91,19.88,P252)
p(44.91,19.99,P253)
p(44.51,19.08,P254)
p(45.01,18.21,P255)
p(46.00,18.32,P256)
p(45.41,19.13,P257)
p(45.91,19.99,P258)
p(46.90,20.11,P259)
p(46.50,19.19,P260)
p(47.00,18.32,P261)
p(48.00,18.44,P262)
p(47.40,19.24,P263)
p(47.90,20.11,P264)
p(48.50,19.30,P265)
p(49.00,18.43,P266)
p(11.64,23.56,P267)
p(12.53,24.03,P268)
p(12.49,23.03,P269)
p(10.77,23.08,P270)
p(10.78,24.08,P271)
p(11.61,22.54,P272)
p(12.47,22.03,P274)
p(13.38,23.51,P275)
p(14.27,23.98,P276)
p(14.23,22.98,P277)
p(12.51,23.03,P278)
p(13.35,22.49,P279)
p(14.21,21.98,P280)
p(15.13,23.46,P281)
p(16.01,23.93,P282)
p(15.97,22.93,P283)
p(14.25,22.98,P284)
p(15.10,22.44,P285)
p(15.96,21.93,P286)
p(16.87,23.41,P287)
p(17.75,23.88,P288)
p(17.71,22.88,P289)
p(16.00,22.93,P290)
p(16.84,22.39,P291)
p(17.70,21.88,P292)
p(17.74,22.88,P293)
p(18.58,22.35,P294)
p(18.61,23.37,P295)
p(19.46,22.82,P323)
p(20.46,22.80,P325)
p(11.76,24.27,P414)
p(11.10,25.02,P415)
p(11.84,25.69,P416)
p(10.89,26.00,P417)
p(12.82,25.89,P418)
p(12.50,24.94,P419)
p(12.72,23.97,P420)
p(13.70,24.16,P421)
p(13.03,24.91,P422)
p(13.78,25.59,P423)
p(14.76,25.78,P424)
p(14.44,24.84,P425)
p(14.65,23.86,P426)
p(15.63,24.06,P427)
p(14.97,24.81,P428)
p(15.71,25.48,P429)
p(16.69,25.67,P430)
p(16.37,24.73,P431)
p(16.58,23.75,P432)
p(17.56,23.95,P433)
p(16.90,24.70,P434)
p(17.64,25.37,P435)
p(18.62,25.57,P436)
p(18.30,24.62,P437)
p(18.51,23.64,P438)
p(19.49,23.84,P439)
p(18.83,24.59,P440)
p(19.57,25.26,P441)
p(19.46,22.84,P442)
p(19.99,23.69,P443)
p(20.99,23.57,P444)
p(20.59,24.49,P445)
p(20.09,25.36,P446)
p(21.09,25.36,P447)
p(22.08,25.24,P448)
p(21.48,24.44,P449)
p(21.99,23.57,P450)
p(22.98,23.46,P451)
p(22.58,24.38,P452)
p(23.08,25.25,P453)
p(24.07,25.13,P454)
p(23.48,24.33,P455)
p(23.98,23.46,P456)
p(24.97,23.35,P457)
p(24.57,24.27,P458)
p(25.07,25.13,P459)
p(26.07,25.02,P460)
p(25.47,24.22,P461)
p(25.97,23.35,P462)
p(26.97,23.24,P463)
p(26.57,24.15,P464)
p(27.07,25.02,P465)
p(28.06,24.91,P466)
p(27.47,24.10,P467)
p(27.97,23.24,P468)
p(28.96,23.13,P469)
p(28.56,24.04,P470)
p(29.06,24.91,P471)
p(30.05,24.80,P472)
p(29.46,23.99,P473)
p(29.96,23.13,P474)
p(30.95,23.01,P475)
p(30.56,23.93,P476)
p(31.05,24.80,P477)
p(32.05,24.68,P478)
p(31.45,23.88,P479)
p(31.95,23.01,P480)
p(32.95,22.90,P481)
p(32.55,23.82,P482)
p(33.05,24.69,P483)
p(34.04,24.57,P484)
p(33.45,23.77,P485)
p(33.95,22.90,P486)
p(34.94,22.79,P487)
p(34.54,23.71,P488)
p(35.04,24.57,P489)
p(36.03,24.46,P490)
p(35.44,23.66,P491)
p(35.94,22.79,P492)
p(36.93,22.68,P493)
p(36.54,23.59,P494)
p(37.03,24.46,P495)
p(38.03,24.35,P496)
p(37.43,23.54,P497)
p(37.93,22.68,P498)
p(38.93,22.57,P499)
p(38.53,23.48,P500)
p(39.03,24.35,P501)
p(40.02,24.24,P502)
p(39.43,23.43,P503)
p(39.93,22.57,P504)
p(40.92,22.45,P505)
p(40.52,23.37,P506)
p(41.02,24.24,P507)
p(42.02,24.12,P508)
p(41.42,23.32,P509)
p(41.92,22.46,P510)
p(42.91,22.34,P511)
p(42.52,23.26,P512)
p(43.02,24.13,P513)
p(44.01,24.01,P514)
p(43.41,23.21,P515)
p(43.91,22.34,P516)
p(44.91,22.23,P517)
p(44.51,23.15,P518)
p(45.01,24.01,P519)
p(46.00,23.90,P520)
p(45.41,23.10,P521)
p(45.91,22.23,P522)
p(46.90,22.12,P523)
p(46.50,23.03,P524)
p(47.00,23.90,P525)
p(48.00,23.79,P526)
p(47.40,22.98,P527)
p(47.90,22.12,P528)
p(48.50,22.92,P529)
p(49.00,23.79,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(#EE82EE) s(P23,P60)
color(blue)
color(orange)
color(red)
\geooff
\geoprint()
Ich sehe zwar keinen Fehler, aber Stefan sollte das auf jeden Fall noch überprüfen.
EDIT 1: Neu mit RW Funktion.
EDIT 2: Dreiecksanzahl korrigiert
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haribo
Senior
Dabei seit: 25.10.2012
Mitteilungen: 4376
| Beitrag No.1432, eingetragen 2018-09-20
|
zeichnest du nochmal deine aktuellen winkel farbig ein? bitte
und fals möglich die grauen punktbezeichnungen weitgehend aus
in der 100er felge finde ich nachwievor keine lösung, aber dafür konstruktionen die einige der itterationen ersetzen...
teilweise verwende ich dort aber ellipsen, das taugt also füs matchstick program wohl eher noch nicht?
haribo
|
Profil
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Slash
Aktiv
Dabei seit: 23.03.2005
Mitteilungen: 9108
| Beitrag No.1433, vom Themenstarter, eingetragen 2018-09-20
|
Ich hoffe das hilft. Dass ich immer drei Speichen zeichnen muss, hat mit den Kopierfunktionen des Programms zu tun. Vielleicht kann Stefan das einfacher lösen mit weniger Punkten.
https://www.matheplanet.de/matheplanet/nuke/html/uploads/b/8038_nur_winkel_2.png
\sourceon MGC
// 360/224 = 1,60714285714285714285
// Tortenwinkel = 1,60714285714289850659
Ring-Graph
\sourceoff
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Profil
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Slash
Aktiv
Dabei seit: 23.03.2005
Mitteilungen: 9108
| Beitrag No.1434, vom Themenstarter, eingetragen 2018-09-21
|
@ Stefan
Bin mir nicht sicher, ob das ein Fehler meinerseits ist, aber ich kann mir das nicht erklären. Wenn ich in #1427 noch die Kante P120,P683 messe und dann alle 5 Winkel (vorher nur 4) feinjustieren lasse, dann reduziert sich die Genauigkeit des Tortenwinklels auf 8 Nachommastellen, obwohl die Kante vorher auch schon 1 war.
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Slash
Aktiv
Dabei seit: 23.03.2005
Mitteilungen: 9108
| Beitrag No.1435, vom Themenstarter, eingetragen 2018-09-21
|
Ich bin gerade erst auf den Trichter gekommen, dass ich ja Stefans RW Funktion benutzen kann um den Tortenwinkel einzustellen. Naja, besser spät als nie. ;-)
47 Dreiecke im Teilgraph macht bei 212 Teilgraphen 9964 Dreiecke. ABER leichte Überschneidung in den Rauten. Vielleicht kann man ihn retten.
392 Knoten, 8×Grad 2, 4×Grad 3, 378×Grad 4, 2×Grad 6
776 Kanten, minimal 0.99999999999835775810, maximal 1.00000000000026467717
einstellbare Kanten R(j,k):
|P55-P28|=0.99999999999989919175
|P5-P145|=1.00000000000001665335
|P29-P169|=0.99999999999990241140
|P33-P258|=0.99999999999999433786
|P23-P60|=2.74146065471743849429
\geo
ebene(776.64,220.03)
x(11.01,48.35)
y(12.19,22.77)
form(.)
#//Eingabe war:
#
#// 360/212 = 1,69811320754716981132
#// Tortenwinkel = 1,69811320754695782576
#Ring-Graph
#
#
#
#
#
#
#
#P[1]=[39.75019091701977,97.41664168175615];
#P[2]=[57.86460299987924,87.19812019177289]; 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,[61,94]));
#A(60,140,ab(60,140,[29,142],"gespiegelt"));
#RA(5,145); A(5,144); RA(29,169); A(29,172);
#A(141,31,ab(141,31,[1,254],"gespiegelt")); R(33,258);
#RW(23,60,56,62,1.69811320754716981132);
#
#//ergänzt von Button "Knoten zusammenfassen":
#C(7,286); C(23,27); C(28,143); C(30,285); C(32,284); C(33,261); C(34,289);
#C(35,288); C(36,287); C(37,292); C(38,291); C(39,290); C(40,295); C(41,294);
#C(42,293); C(43,298); C(44,297); C(45,296); C(46,301); C(47,300); C(48,299);
#C(49,304); C(50,303); C(51,302); C(52,307); C(53,306); C(54,305); C(55,310);
#C(56,309); C(57,308); C(59,316); C(61,317); C(62,315); C(63,312); C(64,314);
#C(65,320); C(66,319); C(67,318); C(68,323); C(69,322); C(70,321); C(71,326);
#C(72,325); C(73,324); C(74,329); C(75,328); C(76,327); C(77,332); C(78,331);
#C(79,330); C(80,335); C(81,334); C(82,333); C(83,338); C(84,337); C(85,336);
#C(86,341); C(87,340); C(88,339); C(89,344); C(90,343); C(91,342); C(92,347);
#C(93,346); C(94,345); C(95,350); C(96,349); C(97,348); C(98,353); C(99,352);
#C(100,351); C(101,356); C(102,355); C(103,354); C(104,359); C(105,358);
#C(106,357); C(107,362); C(108,361); C(109,360); C(110,365); C(111,364);
#C(112,363); C(113,368); C(114,367); C(115,366); C(116,371); C(117,370);
#C(118,369); C(119,374); C(120,373); C(121,372); C(122,377); C(123,376);
#C(124,375); C(125,380); C(126,379); C(127,378); C(128,383); C(129,382);
#C(130,381); C(131,386); C(132,385); C(133,384); C(134,389); C(135,388);
#C(136,387); C(137,392); C(138,391); C(139,390); C(140,394); C(142,393);
#C(277,281); C(282,395);
#
#
#//Ende der Eingabe, weiter mit fedgeo:
p(11.91,14.68,P1)
p(12.78,14.19,P2)
p(12.77,15.19,P3)
p(11.02,15.14,P4)
p(11.07,14.14,P5)
p(11.88,15.65,P6)
p(11.01,16.14,P7)
p(12.72,16.19,P8)
p(13.62,14.73,P9)
p(14.49,14.24,P10)
p(14.48,15.24,P11)
p(12.73,15.19,P12)
p(13.59,15.70,P13)
p(14.43,16.24,P14)
p(15.33,14.79,P15)
p(16.20,14.29,P16)
p(16.19,15.29,P17)
p(14.44,15.24,P18)
p(15.31,15.75,P19)
p(16.15,16.29,P20)
p(17.05,14.84,P21)
p(17.92,14.34,P22)
p(17.91,15.34,P23)
p(16.16,15.29,P24)
p(17.02,15.80,P25)
p(17.86,16.34,P26)
p(18.75,15.89,P28)
p(18.78,14.85,P29)
p(11.96,16.45,P30)
p(11.22,17.12,P31)
p(11.96,17.79,P32)
p(11.01,18.10,P33)
p(12.91,18.10,P34)
p(12.71,17.12,P35)
p(12.91,16.14,P36)
p(13.87,16.45,P37)
p(13.12,17.12,P38)
p(13.87,17.79,P39)
p(14.82,18.10,P40)
p(14.61,17.12,P41)
p(14.82,16.14,P42)
p(15.77,16.45,P43)
p(15.03,17.12,P44)
p(15.77,17.79,P45)
p(16.72,18.10,P46)
p(16.51,17.12,P47)
p(16.72,16.14,P48)
p(17.67,16.45,P49)
p(16.93,17.12,P50)
p(17.67,17.79,P51)
p(18.62,18.10,P52)
p(18.41,17.12,P53)
p(18.62,16.14,P54)
p(19.57,16.45,P55)
p(18.83,17.12,P56)
p(19.57,17.79,P57)
p(19.65,15.45,P58)
p(20.17,16.30,P59)
p(20.65,15.43,P60)
p(21.16,16.21,P61)
p(20.75,17.12,P62)
p(20.17,17.93,P63)
p(21.16,18.03,P64)
p(22.16,17.93,P65)
p(21.58,17.12,P66)
p(22.16,16.30,P67)
p(23.15,16.21,P68)
p(22.74,17.12,P69)
p(23.15,18.03,P70)
p(24.15,17.93,P71)
p(23.57,17.12,P72)
p(24.15,16.30,P73)
p(25.15,16.21,P74)
p(24.73,17.12,P75)
p(25.15,18.03,P76)
p(26.14,17.93,P77)
p(25.56,17.12,P78)
p(26.14,16.30,P79)
p(27.14,16.21,P80)
p(26.72,17.12,P81)
p(27.14,18.03,P82)
p(28.13,17.93,P83)
p(27.55,17.12,P84)
p(28.13,16.30,P85)
p(29.13,16.21,P86)
p(28.71,17.12,P87)
p(29.13,18.03,P88)
p(30.12,17.93,P89)
p(29.54,17.12,P90)
p(30.12,16.30,P91)
p(31.12,16.21,P92)
p(30.70,17.12,P93)
p(31.12,18.03,P94)
p(32.11,17.93,P95)
p(31.53,17.12,P96)
p(32.11,16.30,P97)
p(33.11,16.21,P98)
p(32.69,17.12,P99)
p(33.11,18.03,P100)
p(34.10,17.93,P101)
p(33.52,17.12,P102)
p(34.10,16.30,P103)
p(35.10,16.21,P104)
p(34.68,17.12,P105)
p(35.10,18.03,P106)
p(36.09,17.93,P107)
p(35.51,17.12,P108)
p(36.09,16.30,P109)
p(37.09,16.21,P110)
p(36.68,17.12,P111)
p(37.09,18.03,P112)
p(38.09,17.93,P113)
p(37.51,17.12,P114)
p(38.09,16.30,P115)
p(39.08,16.21,P116)
p(38.67,17.12,P117)
p(39.08,18.03,P118)
p(40.08,17.93,P119)
p(39.50,17.12,P120)
p(40.08,16.30,P121)
p(41.07,16.21,P122)
p(40.66,17.12,P123)
p(41.07,18.03,P124)
p(42.07,17.93,P125)
p(41.49,17.12,P126)
p(42.07,16.30,P127)
p(43.06,16.21,P128)
p(42.65,17.12,P129)
p(43.06,18.03,P130)
p(44.06,17.93,P131)
p(43.48,17.12,P132)
p(44.06,16.30,P133)
p(45.05,16.21,P134)
p(44.64,17.12,P135)
p(45.05,18.03,P136)
p(46.05,17.93,P137)
p(45.47,17.12,P138)
p(46.05,16.30,P139)
p(47.04,16.21,P140)
p(46.63,17.12,P141)
p(47.04,18.03,P142)
p(12.04,13.89,P144)
p(11.34,13.18,P145)
p(12.12,12.55,P146)
p(11.19,12.19,P147)
p(13.09,12.30,P148)
p(12.82,13.27,P149)
p(12.97,14.25,P150)
p(13.94,14.00,P151)
p(13.24,13.29,P152)
p(14.02,12.67,P153)
p(14.99,12.41,P154)
p(14.72,13.38,P155)
p(14.87,14.37,P156)
p(15.84,14.12,P157)
p(15.14,13.40,P158)
p(15.92,12.78,P159)
p(16.88,12.53,P160)
p(16.62,13.49,P161)
p(16.77,14.48,P162)
p(17.74,14.23,P163)
p(17.04,13.52,P164)
p(17.82,12.89,P165)
p(18.78,12.64,P166)
p(18.52,13.60,P167)
p(18.67,14.59,P168)
p(19.64,14.34,P169)
p(18.93,13.63,P170)
p(19.72,13.00,P171)
p(19.65,15.34,P172)
p(20.22,14.52,P173)
p(21.21,14.68,P174)
p(20.85,13.74,P175)
p(20.32,12.90,P176)
p(21.32,12.86,P177)
p(22.31,13.01,P178)
p(21.68,13.79,P179)
p(22.21,14.64,P180)
p(23.20,14.79,P181)
p(22.84,13.86,P182)
p(23.30,12.98,P183)
p(24.29,13.13,P184)
p(23.66,13.91,P185)
p(24.20,14.76,P186)
p(25.18,14.91,P187)
p(24.82,13.98,P188)
p(25.29,13.09,P189)
p(26.28,13.25,P190)
p(25.65,14.03,P191)
p(26.18,14.87,P192)
p(27.17,15.03,P193)
p(26.81,14.10,P194)
p(27.28,13.21,P195)
p(28.27,13.37,P196)
p(27.64,14.15,P197)
p(28.17,14.99,P198)
p(29.16,15.15,P199)
p(28.80,14.21,P200)
p(29.27,13.33,P201)
p(30.25,13.49,P202)
p(29.63,14.26,P203)
p(30.16,15.11,P204)
p(31.15,15.27,P205)
p(30.79,14.33,P206)
p(31.25,13.45,P207)
p(32.24,13.60,P208)
p(31.61,14.38,P209)
p(32.15,15.23,P210)
p(33.13,15.38,P211)
p(32.77,14.45,P212)
p(33.24,13.57,P213)
p(34.23,13.72,P214)
p(33.60,14.50,P215)
p(34.13,15.35,P216)
p(35.12,15.50,P217)
p(34.76,14.57,P218)
p(35.23,13.68,P219)
p(36.22,13.84,P220)
p(35.59,14.62,P221)
p(36.12,15.46,P222)
p(37.11,15.62,P223)
p(36.75,14.69,P224)
p(37.22,13.80,P225)
p(38.20,13.96,P226)
p(37.58,14.74,P227)
p(38.11,15.58,P228)
p(39.10,15.74,P229)
p(38.74,14.80,P230)
p(39.20,13.92,P231)
p(40.19,14.07,P232)
p(39.56,14.85,P233)
p(40.09,15.70,P234)
p(41.08,15.85,P235)
p(40.72,14.92,P236)
p(41.19,14.04,P237)
p(42.18,14.19,P238)
p(41.55,14.97,P239)
p(42.08,15.82,P240)
p(43.07,15.97,P241)
p(42.71,15.04,P242)
p(43.18,14.16,P243)
p(44.17,14.31,P244)
p(43.54,15.09,P245)
p(44.07,15.94,P246)
p(45.06,16.09,P247)
p(44.70,15.16,P248)
p(45.16,14.27,P249)
p(46.15,14.43,P250)
p(45.52,15.21,P251)
p(46.06,16.05,P252)
p(46.68,15.28,P253)
p(47.15,14.39,P254)
p(11.91,19.55,P255)
p(12.78,20.04,P256)
p(12.77,19.04,P257)
p(11.02,19.10,P258)
p(11.07,20.10,P259)
p(11.88,18.59,P260)
p(12.72,18.05,P262)
p(13.62,19.50,P263)
p(14.49,19.99,P264)
p(14.48,18.99,P265)
p(12.73,19.05,P266)
p(13.59,18.54,P267)
p(14.43,18.00,P268)
p(15.33,19.45,P269)
p(16.20,19.94,P270)
p(16.19,18.94,P271)
p(14.44,19.00,P272)
p(15.31,18.49,P273)
p(16.15,17.94,P274)
p(17.05,19.40,P275)
p(17.92,19.89,P276)
p(17.91,18.89,P277)
p(16.16,18.94,P278)
p(17.02,18.44,P279)
p(17.86,17.89,P280)
p(18.75,18.35,P282)
p(18.78,19.38,P283)
p(19.65,18.79,P311)
p(20.65,18.81,P313)
p(12.04,20.35,P396)
p(11.34,21.06,P397)
p(12.12,21.68,P398)
p(11.19,22.05,P399)
p(13.09,21.94,P400)
p(12.82,20.97,P401)
p(12.97,19.98,P402)
p(13.94,20.23,P403)
p(13.24,20.95,P404)
p(14.02,21.57,P405)
p(14.99,21.82,P406)
p(14.72,20.86,P407)
p(14.87,19.87,P408)
p(15.84,20.12,P409)
p(15.14,20.83,P410)
p(15.92,21.46,P411)
p(16.88,21.71,P412)
p(16.62,20.75,P413)
p(16.77,19.76,P414)
p(17.74,20.01,P415)
p(17.04,20.72,P416)
p(17.82,21.35,P417)
p(18.78,21.60,P418)
p(18.52,20.63,P419)
p(18.67,19.64,P420)
p(19.64,19.90,P421)
p(18.93,20.61,P422)
p(19.72,21.23,P423)
p(19.65,18.90,P424)
p(20.22,19.72,P425)
p(21.21,19.56,P426)
p(20.85,20.49,P427)
p(20.32,21.34,P428)
p(21.32,21.38,P429)
p(22.31,21.22,P430)
p(21.68,20.45,P431)
p(22.21,19.60,P432)
p(23.20,19.44,P433)
p(22.84,20.38,P434)
p(23.30,21.26,P435)
p(24.29,21.11,P436)
p(23.66,20.33,P437)
p(24.20,19.48,P438)
p(25.18,19.33,P439)
p(24.82,20.26,P440)
p(25.29,21.14,P441)
p(26.28,20.99,P442)
p(25.65,20.21,P443)
p(26.18,19.36,P444)
p(27.17,19.21,P445)
p(26.81,20.14,P446)
p(27.28,21.02,P447)
p(28.27,20.87,P448)
p(27.64,20.09,P449)
p(28.17,19.24,P450)
p(29.16,19.09,P451)
p(28.80,20.02,P452)
p(29.27,20.91,P453)
p(30.25,20.75,P454)
p(29.63,19.97,P455)
p(30.16,19.13,P456)
p(31.15,18.97,P457)
p(30.79,19.90,P458)
p(31.25,20.79,P459)
p(32.24,20.63,P460)
p(31.61,19.86,P461)
p(32.15,19.01,P462)
p(33.13,18.85,P463)
p(32.77,19.79,P464)
p(33.24,20.67,P465)
p(34.23,20.52,P466)
p(33.60,19.74,P467)
p(34.13,18.89,P468)
p(35.12,18.74,P469)
p(34.76,19.67,P470)
p(35.23,20.55,P471)
p(36.22,20.40,P472)
p(35.59,19.62,P473)
p(36.12,18.77,P474)
p(37.11,18.62,P475)
p(36.75,19.55,P476)
p(37.22,20.43,P477)
p(38.20,20.28,P478)
p(37.58,19.50,P479)
p(38.11,18.65,P480)
p(39.10,18.50,P481)
p(38.74,19.43,P482)
p(39.20,20.32,P483)
p(40.19,20.16,P484)
p(39.56,19.38,P485)
p(40.09,18.54,P486)
p(41.08,18.38,P487)
p(40.72,19.32,P488)
p(41.19,20.20,P489)
p(42.18,20.04,P490)
p(41.55,19.27,P491)
p(42.08,18.42,P492)
p(43.07,18.26,P493)
p(42.71,19.20,P494)
p(43.18,20.08,P495)
p(44.17,19.93,P496)
p(43.54,19.15,P497)
p(44.07,18.30,P498)
p(45.06,18.15,P499)
p(44.70,19.08,P500)
p(45.16,19.96,P501)
p(46.15,19.81,P502)
p(45.52,19.03,P503)
p(46.06,18.18,P504)
p(46.68,18.96,P505)
p(47.15,19.85,P506)
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(P145,P5) s(P144,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(P29,P22)
s(P25,P23) s(P26,P23) s(P28,P23) s(P29,P23)
s(P25,P24)
s(P26,P25)
s(P28,P26)
s(P55,P28) s(P58,P28)
s(P169,P29) s(P172,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(P258,P33) s(P260,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(P282,P57) s(P311,P57)
s(P59,P58) s(P60,P58)
s(P60,P59) s(P61,P59) s(P62,P59)
s(P172,P60) s(P173,P60)
s(P67,P61) s(P62,P61) s(P66,P61)
s(P63,P62) s(P64,P62)
s(P64,P63) s(P311,P63) s(P313,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(P252,P140) s(P141,P140) s(P253,P140)
s(P142,P141)
s(P504,P142) s(P505,P142)
s(P149,P144) s(P145,P144) s(P150,P144)
s(P146,P145) s(P147,P145)
s(P148,P146) s(P147,P146) s(P149,P146)
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(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(P170,P169) s(P172,P169)
s(P171,P170)
s(P173,P172)
s(P174,P173) s(P175,P173)
s(P180,P174) s(P175,P174) s(P179,P174)
s(P176,P175) s(P177,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(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(P253,P250) s(P254,P250)
s(P252,P251)
s(P253,P252)
s(P254,P253)
s(P256,P255) s(P257,P255) s(P258,P255) s(P259,P255)
s(P263,P256) s(P266,P256) s(P257,P256)
s(P260,P257) s(P262,P257)
s(P260,P258) s(P259,P258)
s(P396,P259) s(P397,P259)
s(P262,P260)
s(P267,P262) s(P266,P262)
s(P264,P263) s(P265,P263) s(P266,P263)
s(P269,P264) s(P272,P264) s(P265,P264)
s(P267,P265) s(P268,P265)
s(P267,P266)
s(P268,P267)
s(P273,P268) s(P272,P268)
s(P270,P269) s(P271,P269) s(P272,P269)
s(P275,P270) s(P278,P270) s(P271,P270)
s(P273,P271) s(P274,P271)
s(P273,P272)
s(P274,P273)
s(P279,P274) s(P278,P274)
s(P276,P275) s(P277,P275) s(P278,P275)
s(P277,P276) s(P283,P276)
s(P279,P277) s(P280,P277) s(P282,P277) s(P283,P277)
s(P279,P278)
s(P280,P279)
s(P282,P280)
s(P311,P282)
s(P421,P283) s(P424,P283)
s(P313,P311)
s(P424,P313) s(P425,P313)
s(P401,P396) s(P397,P396) s(P402,P396)
s(P398,P397) s(P399,P397)
s(P400,P398) s(P399,P398) s(P401,P398)
s(P404,P400) s(P405,P400) s(P401,P400)
s(P402,P401)
s(P403,P402) s(P404,P402)
s(P407,P403) s(P404,P403) s(P408,P403)
s(P405,P404)
s(P406,P405) s(P407,P405)
s(P410,P406) s(P411,P406) s(P407,P406)
s(P408,P407)
s(P409,P408) s(P410,P408)
s(P413,P409) s(P410,P409) s(P414,P409)
s(P411,P410)
s(P412,P411) s(P413,P411)
s(P416,P412) s(P417,P412) s(P413,P412)
s(P414,P413)
s(P415,P414) s(P416,P414)
s(P419,P415) s(P416,P415) s(P420,P415)
s(P417,P416)
s(P418,P417) s(P419,P417)
s(P422,P418) s(P423,P418) s(P419,P418)
s(P420,P419)
s(P421,P420) s(P422,P420)
s(P422,P421) s(P424,P421)
s(P423,P422)
s(P425,P424)
s(P426,P425) s(P427,P425)
s(P432,P426) s(P427,P426) s(P431,P426)
s(P428,P427) s(P429,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(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(P505,P502) s(P506,P502)
s(P504,P503)
s(P505,P504)
s(P506,P505)
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(P5,P145)
color(#008000) s(P29,P169)
color(#008000) s(P33,P258)
color(#EE82EE) s(P23,P60)
color(blue)
color(orange)
color(red)
\geooff
\geoprint()
|
Profil
|
haribo
Senior
Dabei seit: 25.10.2012
Mitteilungen: 4376
| Beitrag No.1436, eingetragen 2018-09-21
|
habe im 1,5 grad winkel eine lösung mit 50 dreiecken gefunden, mit ein mal speichenseitenwechseln
bei der mit minimaler aufstellung des weissen dreieckes eine überschneidung stattfindet, und bei maximaler aufstellung eine unterschneidung des gleichen dreiecks, dazwischen gibt es also eine exakte lösung nachgewiesen ohne verwendung des graphenprograms
macht also 240*50=12000 dreiecke
dargestellt oben die maximale aufstellung(dabei ist der blaue winkel 120°)
die unterschneidung beträgt 0,00142 (in der zeichnung steht der zehnfache wert da ich gösser gezeichnet hatte)
ich hab alle deine winkel eingetragen, evtl nutzt das was als startwerte?
kann mans bei dir lesen? na ich mach die winkel nochmal als detail...
https://www.matheplanet.com/matheplanet/nuke/html/uploads/b/35059_harbort-felge15-50.png
https://www.matheplanet.com/matheplanet/nuke/html/uploads/b/35059_harbort-felge15-50-detail.png
hier die minimale aufstellung des weissen dreiecks und deine winkel, bei welcher das weisse dreieck also gar nicht afgestellt ist(die linken oberen und unteren dreiecke berühren sich also noch...)
die überschneidung des rechtesten 19en roten dreiecks (im detail nicht dargestellt) beträgt 0,0142(spannenderweise exakt der zehnfache betrag wie die unterschneidung)
https://www.matheplanet.com/matheplanet/nuke/html/uploads/b/35059_harbort-felge15-50minimal.png
|
Profil
|
Slash
Aktiv
Dabei seit: 23.03.2005
Mitteilungen: 9108
| Beitrag No.1437, vom Themenstarter, eingetragen 2018-09-21
|
Oh Mann, ich habe die Dreiecke immer doppelt gezählt. :-o Es sind also im ersten großen Ring nur 63071 und im kleineren sogar nur 10976 Dreiecke. Die Rotationssymmetrie halbiert sich auch auf 292 und 112, also die Anzahl der Girlanden-Speichen.
Speichenseitenwechsel müsste man mal testen, erfordert aber eine neue Eingabe mit zwei weiteren Winkeln in der Speiche. Ist mit einem Speichenwechsel schon das Optimum erreicht? Keine Ahnung wie man da Argumentieren müsste.
|
Profil
|
Slash
Aktiv
Dabei seit: 23.03.2005
Mitteilungen: 9108
| Beitrag No.1438, vom Themenstarter, eingetragen 2018-09-22
|
Erster Versuch mit Doppelspeichen. 50 Dreiecke im Teilgraph und 276 Teilgraphen macht 13800 Dreiecke. Das passt aber noch nicht im Ring. Nur dieser Teilgraph stimmt. Vielleicht kann Stefan helfen.
239 Knoten, 10×Grad 2, 229×Grad 4
468 Kanten, minimal 0.99999999997755095738, maximal 1.00000000002824562806
einstellbare Kanten R(j,k):
|P55-P28|=0.99999999999967115194
|P33-P158|=0.99999999999934718886
|P56-P57|=0.99999999999999900080
|P93-P94|=1.00000000000000244249
|P94-P247|=0.99999999997755095738
|P27-P60|=2.74208692844726309445
\geo
ebene(740.24,126.23)
x(11.09,50.52)
y(10.85,17.58)
form(.)
#//Eingabe war:
#
#// 360/276 = 1,30434782608695652173
#// Tortenwinkel = 1,30434782608225163791
#
#Ring-Graph
#
#
#
#
#
#
#
#
#
#P[1]=[37.53639500418903,25.45972415011599];
#P[2]=[54.168131100659394,16.74897731802681]; 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,[61,70]));
#M(95,92,91,sechsterWinkel); N(96,92,95);
#M(97,95,96,siebenterWinkel); N(98,95,97);
#A(96,98,ab(96,98,92,95,97,"gespiegelt"));
#A(101,99,ab(99,101,92,[95,100]));
#A(105,102,ab(102,105,92,[95,108]));
#A(111,108,ab(108,111,92,[95,120]));
#A(123,120,ab(120,123,[120,127])); N(150,147,149); N(151,147,150);
#N(152,150,149);
#A(31,151,ab(31,151,[1,152],"gespiegelt"));
#R(33,158); R(56,57); R(93,94); R(94,247);
#//A(60,150,ab(60,150,[1,302],"gespiegelt"));
#//R(5,333); R(97,545); R(29,508);
#RW(27,60,56,62,1.30434782608695652173);
#
#//ergänzt von Button "Knoten zusammenfassen":
#C(7,184); C(30,183); C(32,182); C(33,159); C(34,187); C(35,186); C(36,185);
#C(37,190); C(38,189); C(39,188); C(40,193); C(41,192); C(42,191); C(43,196);
#C(44,195); C(45,194); C(46,199); C(47,198); C(48,197); C(49,202); C(50,201);
#C(51,200); C(52,205); C(53,204); C(54,203); C(55,208); C(56,207); C(57,206);
#C(59,214); C(61,215); C(62,213); C(63,210); C(64,212); C(65,218); C(66,217);
#C(67,216); C(68,221); C(69,220); C(70,219); C(71,224); C(72,223); C(73,222);
#C(74,227); C(75,226); C(76,225); C(77,230); C(78,229); C(79,228); C(80,233);
#C(81,232); C(82,231); C(83,236); C(84,235); C(85,234); C(86,239); C(87,238);
#C(88,237); C(89,242); C(90,241); C(91,240); C(92,245); C(93,244); C(94,243);
#
#
#
#//Ende der Eingabe, weiter mit fedgeo:
p(12.00,11.36,P1)
p(12.89,10.89,P2)
p(12.84,11.89,P3)
p(11.13,11.85,P4)
p(11.14,10.85,P5)
p(11.98,12.39,P6)
p(11.09,12.85,P7)
p(12.84,12.89,P8)
p(13.75,11.40,P9)
p(14.64,10.93,P10)
p(14.59,11.93,P11)
p(12.88,11.89,P12)
p(13.73,12.43,P13)
p(14.59,12.93,P14)
p(15.50,11.43,P15)
p(16.39,10.97,P16)
p(16.34,11.97,P17)
p(14.63,11.93,P18)
p(15.48,12.47,P19)
p(16.34,12.97,P20)
p(17.25,11.47,P21)
p(18.14,11.01,P22)
p(18.09,12.01,P23)
p(16.38,11.97,P24)
p(17.23,12.51,P25)
p(18.09,13.01,P26)
p(18.13,12.01,P27)
p(18.98,12.54,P28)
p(19.00,11.51,P29)
p(12.06,13.10,P30)
p(11.36,13.82,P31)
p(12.06,14.53,P32)
p(11.09,14.78,P33)
p(13.03,14.78,P34)
p(12.76,13.82,P35)
p(13.03,12.85,P36)
p(14.00,13.10,P37)
p(13.30,13.82,P38)
p(14.00,14.53,P39)
p(14.96,14.78,P40)
p(14.70,13.82,P41)
p(14.96,12.85,P42)
p(15.93,13.10,P43)
p(15.23,13.82,P44)
p(15.93,14.53,P45)
p(16.90,14.78,P46)
p(16.63,13.82,P47)
p(16.90,12.85,P48)
p(17.87,13.10,P49)
p(17.17,13.82,P50)
p(17.87,14.53,P51)
p(18.84,14.78,P52)
p(18.57,13.82,P53)
p(18.84,12.85,P54)
p(19.81,13.10,P55)
p(19.11,13.82,P56)
p(19.81,14.53,P57)
p(19.87,12.10,P58)
p(20.40,12.95,P59)
p(20.87,12.07,P60)
p(21.40,12.95,P61)
p(20.91,13.82,P62)
p(20.40,14.68,P63)
p(21.40,14.69,P64)
p(22.40,14.68,P65)
p(21.89,13.82,P66)
p(22.40,12.95,P67)
p(23.40,12.95,P68)
p(22.91,13.82,P69)
p(23.40,14.69,P70)
p(24.40,14.68,P71)
p(23.89,13.82,P72)
p(24.40,12.95,P73)
p(25.40,12.95,P74)
p(24.91,13.82,P75)
p(25.40,14.69,P76)
p(26.40,14.68,P77)
p(25.89,13.82,P78)
p(26.40,12.95,P79)
p(27.40,12.95,P80)
p(26.91,13.82,P81)
p(27.40,14.69,P82)
p(28.40,14.68,P83)
p(27.89,13.82,P84)
p(28.40,12.95,P85)
p(29.40,12.95,P86)
p(28.91,13.82,P87)
p(29.40,14.69,P88)
p(30.40,14.68,P89)
p(29.89,13.82,P90)
p(30.40,12.95,P91)
p(31.40,12.95,P92)
p(30.91,13.82,P93)
p(31.40,14.69,P94)
p(32.19,12.34,P95)
p(32.32,13.33,P96)
p(31.44,11.69,P97)
p(32.38,11.36,P98)
p(33.27,13.00,P99)
p(32.51,12.35,P100)
p(33.30,11.74,P101)
p(35.17,11.79,P102)
p(34.38,12.40,P103)
p(34.25,11.41,P104)
p(35.13,13.05,P105)
p(34.19,13.38,P106)
p(34.06,12.39,P107)
p(38.91,11.90,P108)
p(38.11,12.51,P109)
p(37.98,11.52,P110)
p(38.87,13.16,P111)
p(37.93,13.49,P112)
p(37.04,11.85,P113)
p(37.80,12.50,P114)
p(37.00,13.11,P115)
p(35.93,12.45,P116)
p(36.06,13.44,P117)
p(36.11,11.46,P118)
p(36.24,12.45,P119)
p(46.37,12.12,P120)
p(45.58,12.72,P121)
p(45.45,11.73,P122)
p(46.34,13.38,P123)
p(45.39,13.71,P124)
p(44.51,12.06,P125)
p(45.27,12.72,P126)
p(44.47,13.32,P127)
p(42.60,13.27,P128)
p(43.40,12.66,P129)
p(43.53,13.65,P130)
p(42.64,12.01,P131)
p(43.58,11.68,P132)
p(43.71,12.67,P133)
p(39.66,12.55,P134)
p(39.79,13.55,P135)
p(39.85,11.57,P136)
p(40.74,13.22,P137)
p(39.98,12.56,P138)
p(40.77,11.96,P139)
p(41.85,12.62,P140)
p(41.72,11.63,P141)
p(41.66,13.60,P142)
p(41.53,12.61,P143)
p(47.13,12.77,P144)
p(47.26,13.76,P145)
p(47.32,11.79,P146)
p(48.21,13.43,P147)
p(47.45,12.78,P148)
p(48.24,12.17,P149)
p(49.00,12.82,P150)
p(49.13,13.82,P151)
p(49.19,11.84,P152)
p(12.00,16.27,P153)
p(12.89,16.74,P154)
p(12.84,15.74,P155)
p(11.13,15.78,P156)
p(11.14,16.78,P157)
p(11.98,15.24,P158)
p(12.84,14.74,P160)
p(13.75,16.24,P161)
p(14.64,16.70,P162)
p(14.59,15.70,P163)
p(12.88,15.74,P164)
p(13.73,15.20,P165)
p(14.59,14.70,P166)
p(15.50,16.20,P167)
p(16.39,16.66,P168)
p(16.34,15.66,P169)
p(14.63,15.70,P170)
p(15.48,15.16,P171)
p(16.34,14.66,P172)
p(17.25,16.16,P173)
p(18.14,16.62,P174)
p(18.09,15.62,P175)
p(16.38,15.66,P176)
p(17.23,15.12,P177)
p(18.09,14.62,P178)
p(18.13,15.62,P179)
p(18.98,15.09,P180)
p(19.00,16.12,P181)
p(19.87,15.53,P209)
p(20.87,15.56,P211)
p(32.19,15.29,P246)
p(32.32,14.30,P247)
p(31.44,15.95,P248)
p(32.38,16.28,P249)
p(33.27,14.63,P250)
p(32.51,15.28,P251)
p(33.30,15.89,P252)
p(35.17,15.84,P253)
p(34.38,15.23,P254)
p(34.25,16.22,P255)
p(35.13,14.58,P256)
p(34.19,14.25,P257)
p(34.06,15.24,P258)
p(38.91,15.73,P259)
p(38.11,15.12,P260)
p(37.98,16.11,P261)
p(38.87,14.47,P262)
p(37.93,14.14,P263)
p(37.04,15.78,P264)
p(37.80,15.13,P265)
p(37.00,14.52,P266)
p(35.93,15.18,P267)
p(36.06,14.19,P268)
p(36.11,16.17,P269)
p(36.24,15.18,P270)
p(46.37,15.51,P271)
p(45.58,14.91,P272)
p(45.45,15.90,P273)
p(46.34,14.25,P274)
p(45.39,13.92,P275)
p(44.51,15.57,P276)
p(45.27,14.91,P277)
p(44.47,14.31,P278)
p(42.60,14.36,P279)
p(43.40,14.97,P280)
p(43.53,13.98,P281)
p(42.64,15.62,P282)
p(43.58,15.95,P283)
p(43.71,14.96,P284)
p(39.66,15.08,P285)
p(39.79,14.09,P286)
p(39.85,16.06,P287)
p(40.74,14.42,P288)
p(39.98,15.07,P289)
p(40.77,15.68,P290)
p(41.85,15.01,P291)
p(41.72,16.01,P292)
p(41.66,14.03,P293)
p(41.53,15.02,P294)
p(47.13,14.86,P295)
p(47.26,13.87,P296)
p(47.32,15.84,P297)
p(48.21,14.20,P298)
p(47.45,14.85,P299)
p(48.24,15.46,P300)
p(49.00,14.81,P301)
p(49.19,15.79,P302)
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(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(P35,P30) s(P31,P30) s(P36,P30)
s(P33,P31) s(P32,P31)
s(P34,P32) s(P33,P32) s(P35,P32)
s(P156,P33) s(P158,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(P180,P57) s(P209,P57)
s(P59,P58) s(P60,P58)
s(P60,P59) s(P61,P59) s(P62,P59)
s(P67,P61) s(P62,P61) s(P66,P61)
s(P63,P62) s(P64,P62)
s(P64,P63) s(P209,P63) s(P211,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(P93,P92) s(P95,P92) s(P96,P92)
s(P94,P93)
s(P246,P94) s(P247,P94)
s(P96,P95) s(P97,P95) s(P98,P95)
s(P99,P96) s(P100,P96)
s(P98,P97)
s(P100,P98) s(P101,P98)
s(P107,P99) s(P100,P99) s(P106,P99)
s(P101,P100)
s(P104,P101) s(P107,P101)
s(P116,P102) s(P103,P102) s(P104,P102) s(P118,P102)
s(P104,P103) s(P105,P103) s(P106,P103)
s(P107,P104)
s(P106,P105) s(P116,P105) s(P117,P105)
s(P107,P106)
s(P134,P108) s(P109,P108) s(P110,P108) s(P136,P108)
s(P110,P109) s(P111,P109) s(P112,P109)
s(P113,P110) s(P114,P110)
s(P112,P111) s(P134,P111) s(P135,P111)
s(P114,P112) s(P115,P112)
s(P119,P113) s(P114,P113) s(P118,P113)
s(P115,P114)
s(P117,P115) s(P119,P115)
s(P117,P116) s(P118,P116)
s(P119,P117)
s(P119,P118)
s(P144,P120) s(P121,P120) s(P122,P120) s(P146,P120)
s(P122,P121) s(P123,P121) s(P124,P121)
s(P125,P122) s(P126,P122)
s(P124,P123) s(P144,P123) s(P145,P123)
s(P126,P124) s(P127,P124)
s(P133,P125) s(P126,P125) s(P132,P125)
s(P127,P126)
s(P130,P127) s(P133,P127)
s(P140,P128) s(P129,P128) s(P130,P128) s(P142,P128)
s(P130,P129) s(P131,P129) s(P132,P129)
s(P133,P130)
s(P132,P131) s(P140,P131) s(P141,P131)
s(P133,P132)
s(P135,P134) s(P136,P134)
s(P137,P135) s(P138,P135)
s(P138,P136) s(P139,P136)
s(P143,P137) s(P138,P137) s(P142,P137)
s(P139,P138)
s(P141,P139) s(P143,P139)
s(P141,P140) s(P142,P140)
s(P143,P141)
s(P143,P142)
s(P145,P144) s(P146,P144)
s(P147,P145) s(P148,P145)
s(P148,P146) s(P149,P146)
s(P148,P147) s(P150,P147) s(P151,P147)
s(P149,P148)
s(P150,P149) s(P152,P149)
s(P151,P150) s(P152,P150)
s(P298,P151) s(P301,P151)
s(P154,P153) s(P155,P153) s(P156,P153) s(P157,P153)
s(P161,P154) s(P164,P154) s(P155,P154)
s(P158,P155) s(P160,P155)
s(P158,P156) s(P157,P156)
s(P160,P158)
s(P165,P160) s(P164,P160)
s(P162,P161) s(P163,P161) s(P164,P161)
s(P167,P162) s(P170,P162) s(P163,P162)
s(P165,P163) s(P166,P163)
s(P165,P164)
s(P166,P165)
s(P171,P166) s(P170,P166)
s(P168,P167) s(P169,P167) s(P170,P167)
s(P173,P168) s(P176,P168) s(P169,P168)
s(P171,P169) s(P172,P169)
s(P171,P170)
s(P172,P171)
s(P177,P172) s(P176,P172)
s(P174,P173) s(P175,P173) s(P176,P173)
s(P175,P174) s(P179,P174) s(P181,P174)
s(P177,P175) s(P178,P175)
s(P177,P176)
s(P178,P177)
s(P179,P178) s(P180,P178)
s(P180,P179) s(P181,P179)
s(P209,P180)
s(P211,P209)
s(P247,P246) s(P248,P246) s(P249,P246)
s(P250,P247) s(P251,P247)
s(P249,P248)
s(P251,P249) s(P252,P249)
s(P258,P250) s(P251,P250) s(P257,P250)
s(P252,P251)
s(P255,P252) s(P258,P252)
s(P267,P253) s(P254,P253) s(P255,P253) s(P269,P253)
s(P255,P254) s(P256,P254) s(P257,P254)
s(P258,P255)
s(P257,P256) s(P267,P256) s(P268,P256)
s(P258,P257)
s(P285,P259) s(P260,P259) s(P261,P259) s(P287,P259)
s(P261,P260) s(P262,P260) s(P263,P260)
s(P264,P261) s(P265,P261)
s(P263,P262) s(P285,P262) s(P286,P262)
s(P265,P263) s(P266,P263)
s(P270,P264) s(P265,P264) s(P269,P264)
s(P266,P265)
s(P268,P266) s(P270,P266)
s(P268,P267) s(P269,P267)
s(P270,P268)
s(P270,P269)
s(P295,P271) s(P272,P271) s(P273,P271) s(P297,P271)
s(P273,P272) s(P274,P272) s(P275,P272)
s(P276,P273) s(P277,P273)
s(P275,P274) s(P295,P274) s(P296,P274)
s(P277,P275) s(P278,P275)
s(P284,P276) s(P277,P276) s(P283,P276)
s(P278,P277)
s(P281,P278) s(P284,P278)
s(P291,P279) s(P280,P279) s(P281,P279) s(P293,P279)
s(P281,P280) s(P282,P280) s(P283,P280)
s(P284,P281)
s(P283,P282) s(P291,P282) s(P292,P282)
s(P284,P283)
s(P286,P285) s(P287,P285)
s(P288,P286) s(P289,P286)
s(P289,P287) s(P290,P287)
s(P294,P288) s(P289,P288) s(P293,P288)
s(P290,P289)
s(P292,P290) s(P294,P290)
s(P292,P291) s(P293,P291)
s(P294,P292)
s(P294,P293)
s(P296,P295) s(P297,P295)
s(P298,P296) s(P299,P296)
s(P299,P297) s(P300,P297)
s(P299,P298) s(P301,P298)
s(P300,P299)
s(P301,P300) s(P302,P300)
s(P302,P301)
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)
color(#32CD32) m(P91,P92,MA15) m(P92,P95,MB15) b(P92,MA15,MB15)
color(#ADD8E6) m(P96,P95,MA16) m(P95,P97,MB16) b(P95,MA16,MB16)
pen(2)
color(#008000) s(P55,P28)
color(#008000) s(P33,P158)
color(#008000) s(P56,P57)
color(#008000) s(P93,P94)
color(#008000) s(P94,P247)
color(#EE82EE) s(P27,P60)
color(blue)
color(orange)
color(red)
\geooff
\geoprint()
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StefanVogel
Senior
Dabei seit: 26.11.2005
Mitteilungen: 4248
Wohnort: Raun
| Beitrag No.1439, eingetragen 2018-09-22
|
Hallo haribo, auch von mir Glückwunsch zur gefundenen Lösung. Ich freue mich unendlich für dich, bei einer möglicherweise unlösbaren Aufgabe darf man das.
Zum selber Ausprobieren habe ich mir #1431 ausgesucht und erhalte auf einem etwas anderen Rechenweg die gleichen Winkel und Koordinaten.
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