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Kombinatorik & Graphentheorie » Graphentheorie » Streichholzgraphen 4-regulär und 4/n-regulär (n>4) und 2/5
Thema eröffnet 2016-02-17 22:35 von Slash
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Kein bestimmter Bereich Streichholzgraphen 4-regulär und 4/n-regulär (n>4) und 2/5
Slash
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  Beitrag No.480, vom Themenstarter, eingetragen 2016-08-12

Punktsymmetrie ist ja genau definiert. Jede punktsymmetrische Figur ist auch 2-fach rotationsysmmetrisch. Symmetrieoperationen hintereinander auszuführen ist ja wieder etwas ganz anders. 4/9 mit 277 habe ich jetzt auch konstruieren können. Hier nochmal die Eigenschaften: 1) The graph is rigid. 2) The graph has no point, rotational or mirror symmetry. 3) The graph has an asymmetric outer cycle or outer shape. 4) There is no way to rearrange the subgraphs to a symmetric graph or outer shape. Der Punkt mit den Teilgraphen konnte raus, wegen Punkt 5), jetzt 4). Punkt 2) muss so bleiben.


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haribo
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  Beitrag No.481, eingetragen 2016-08-12

ist die definition punktsymetrie nicht: "nach spiegelung an einem punkt ist die figur gleich wie vor der spiegelung" ???


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Slash
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  Beitrag No.482, vom Themenstarter, eingetragen 2016-08-12

Eine (ebene) geometrische Figur (zum Beispiel ein Viereck) heißt punktsymmetrisch, wenn es eine Punktspiegelung gibt, die diese Figur auf sich abbildet. Der Punkt, an dem diese Spiegelung erfolgt, wird als Symmetriezentrum bezeichnet. In der Ebene (zweidimensionaler Raum) entspricht die Punktspiegelung einer Drehung der geometrischen Figur um 180°. Hier ist die Punktsymmetrie ein Spezialfall der Drehsymmetrie. Eine Figur mit Spiegelsymmetrie ist nicht punktsymmetrisch. Ein Dreieck ist niemals punktsymmetrisch. Es können aber zwei Dreiecke zueinander punktsymmetrisch sein. Der Kreis ist eine besondere Figur.


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haribo
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  Beitrag No.483, eingetragen 2016-08-12

ahha, dann sind also zwei gleiche graphen die 180° verdreht angeordnet sind nur "zueinander" punktsymetrisch und ansonsten halt nur "zwei graphen", es sei denn sie berühren sich mit einem knoten im symetriezentrum...


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Slash
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  Beitrag No.484, vom Themenstarter, eingetragen 2016-08-12

http://www.matheplanet.de/matheplanet/nuke/html/uploads/a/8038_4_8_komplett_asym_mit_180_slash.png


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haribo
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  Beitrag No.485, eingetragen 2016-08-12

zwo weniger geht öfter http://www.matheplanet.com/matheplanet/nuke/html/uploads/a/35059_st4-8-178-unsym.png 178 http://www.matheplanet.com/matheplanet/nuke/html/uploads/a/35059_st4-8-176-unsym.png 176


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Slash
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  Beitrag No.486, vom Themenstarter, eingetragen 2016-08-12

Sehr schön. :-)


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Slash
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  Beitrag No.487, vom Themenstarter, eingetragen 2016-08-13

http://www.matheplanet.de/matheplanet/nuke/html/uploads/a/8038_4_7_kite_versuch_slash.png


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StefanVogel
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  Beitrag No.488, eingetragen 2016-08-13

Bei #473 und #474 erhalte ich die gleichen Ergebnisse. Punkt P2 und der orange Winkel sind nur zum Ausrichten des Graphen da. \geo ebene(409.87,407.94) x(1.26,9.45) y(6,14.16) form(.) #//Eingabe war: #//blauerWinkel=0; gruenerWinkel=0; orangerWinkel=15; #//No.473 4/9 starr #//orangerWinkel=15 #D=50; P[1]=[0,0]; P[2]=[D,0]; M(3,1,2,orangerWinkel); L(4,1,3); L(5,4,3); L(6,5,3); L(7,4,5); M(8,1,4,28.955024371859853); L(9,1,8); L(10,9,8); L(11,9,10); L(12,10,8); A(12,7); L(13,12,7); M(14,11,10,10.320021257740494); L(15,11,14); L(16,15,14); L(17,16,14); L(18,15,16); A(17,13); L(19,17,13); H(20,18,19,2); A(18,20); A(20,19); L(21,18,20); L(22,20,19); A(21,22); L(23,21,22); M(24,23,22,10.320021257740494); L(25,23,24); L(26,25,24); L(27,26,24); L(28,25,26); A(27,13); L(29,27,13); H(30,28,29,2); A(28,30); A(30,29); L(31,28,30); L(32,31,30); A(32,29); N(33,32,13); M(34,13,7,15.52248781407008); L(35,13,34); L(36,35,34); L(37,36,34); L(38,35,36); A(6,37); L(39,37,6); H(40,38,39,2); A(38,40); A(40,39); L(41,38,40); L(42,40,39); A(41,42); L(43,41,42); Q(44,33,43,3*D,D); A(33,44); H(45,33,44,3); H(46,44,45,2); A(33,45); A(45,46); A(46,44); L(47,33,45); L(48,47,45); A(48,46); L(49,48,46); A(49,44); L(50,44,43); N(51,31,47); Q(52,51,49,ab(23,13),D);A(51,52); Q(53,51,52,2*D,D); A(51,53); H(54,51,53,2); A(51,54); A(54,53); L(55,51,54); L(56,54,53); A(55,56); L(57,55,56); L(58,53,52); H(59,57,58,2); A(57,59); A(59,58); L(60,57,59); L(61,59,58); A(60,61); L(62,60,61); Q(63,62,50,ab(62,52),ab(52,50)); A(62,63); A(63,50); R(63,52); # #//Ende der Eingabe, weiter mit fedgeo: p(4,6,P1) p(5,6,P2) p(4.965925826289068,6.258819045102521,P3) p(4.258819045102521,6.965925826289068,P4) p(5.224744871391589,7.224744871391589,P5) p(5.931851652578136,6.5176380902050415,P6) p(4.5176380902050415,7.931851652578136,P7) p(3.7588398346035556,6.970485329423356,P8) p(3.0389549680210424,6.276391835097501,P9) p(2.797794802624598,7.246877164520856,P10) p(2.0779099360420843,6.552783670195001,P11) p(3.5176796692071113,7.9409706588467115,P12) p(4.025556170791932,8.802400551024807,P13) p(2.6618047835916707,7.364612966910169,P14) p(1.6667925653250872,7.464366089669369,P15) p(2.250687412874673,8.276195386384536,P16) p(3.2456996311412567,8.176442263625338,P17) p(1.2556751946080897,8.375948509143736,P18) p(3.0935321223692545,9.164796981969983,P19) p(2.174603658488672,8.770372745556859,P20) p(1.3735580179463374,9.368976021331493,P21) p(2.292486481826919,9.763400257744618,P22) p(1.4914408412845845,10.36200353351925,P23) p(2.3867649525658994,9.916588293817773,P24) p(2.3248438097394555,10.914669338658856,P25) p(3.2201679210207703,10.469254098957379,P26) p(3.2820890638472138,9.471173054116296,P27) p(3.158246778194327,11.467335143798461,P28) p(4.232996594349311,9.7806482040628,P29) p(3.695621686271819,10.62399167393063,P30) p(4.15729110125433,11.511043730615981,P31) p(4.694666009331822,10.667700260748152,P32) p(4.4872255857744205,9.689452607710166,P33) p(4.7326629519784795,8.095293769838259,P34) p(4.991481997081,9.061219596127327,P35) p(5.698588778267548,8.35411281494078,P36) p(5.439769733165027,7.388186988651711,P37) p(5.957407823370068,9.320038641229846,P38) p(6.439728154162957,7.379067982383136,P39) p(6.198567988766513,8.349553311806492,P40) p(6.9184528553490265,9.043646806132347,P41) p(7.1596130207454705,8.073161476708991,P42) p(7.879497887327984,8.767254971034847,P43) p(7.48722466622829,9.687103719475628,P44) p(5.487225279259044,9.68866964496532,P45) p(6.487224972743666,9.687886682220473,P46) p(4.987903498143986,10.555086264672077,P47) p(5.987903191628609,10.55430330192723,P48) p(6.987902885113232,10.553520339182386,P49) p(8.479973660567175,9.566897919951922,P50) p(5.156850921165753,11.540711329417443,P51) p(7.985811049876592,10.618167803932572,P52) p(7.1063616497408635,11.094160191057524,P53) p(6.131606285453309,11.317435760237483,P54) p(5.837590918263805,12.273236452775642,P55) p(6.81234628255136,12.04996088359568,P56) p(6.518330915361858,13.005761576133839,P57) p(7.958307849066934,11.617789519355574,P58) p(7.238319382214396,12.311775547744706,P59) p(7.479334679244584,13.282296864665382,P60) p(8.199323146097122,12.588310836276248,P61) p(8.440338443127311,13.558832153196924,P62) p(8.953165158017814,10.627772493834078,P63) nolabel() s(P1,P3) s(P1,P4) s(P3,P4) s(P4,P5) s(P3,P5) s(P5,P6) s(P3,P6) s(P37,P6) s(P4,P7) s(P5,P7) s(P1,P8) s(P1,P9) s(P8,P9) s(P9,P10) s(P8,P10) s(P9,P11) s(P10,P11) s(P10,P12) s(P8,P12) s(P7,P12) s(P12,P13) s(P7,P13) s(P11,P14) s(P11,P15) s(P14,P15) s(P15,P16) s(P14,P16) s(P16,P17) s(P14,P17) s(P13,P17) s(P15,P18) s(P16,P18) s(P20,P18) s(P17,P19) s(P13,P19) s(P19,P20) s(P18,P21) s(P20,P21) s(P22,P21) s(P20,P22) s(P19,P22) s(P21,P23) s(P22,P23) s(P23,P24) s(P23,P25) s(P24,P25) s(P25,P26) s(P24,P26) s(P26,P27) s(P24,P27) s(P13,P27) s(P25,P28) s(P26,P28) s(P30,P28) s(P27,P29) s(P13,P29) s(P29,P30) s(P28,P31) s(P30,P31) s(P31,P32) s(P30,P32) s(P29,P32) s(P32,P33) s(P13,P33) s(P45,P33) s(P13,P34) s(P13,P35) s(P34,P35) s(P35,P36) s(P34,P36) s(P36,P37) s(P34,P37) s(P35,P38) s(P36,P38) s(P40,P38) s(P37,P39) s(P6,P39) s(P39,P40) s(P38,P41) s(P40,P41) s(P42,P41) s(P40,P42) s(P39,P42) s(P41,P43) s(P42,P43) s(P43,P44) s(P46,P45) s(P44,P46) s(P33,P47) s(P45,P47) s(P47,P48) s(P45,P48) s(P46,P48) s(P48,P49) s(P46,P49) s(P44,P49) s(P44,P50) s(P43,P50) s(P31,P51) s(P47,P51) s(P54,P51) s(P49,P52) s(P52,P53) s(P53,P54) s(P51,P55) s(P54,P55) s(P56,P55) s(P54,P56) s(P53,P56) s(P55,P57) s(P56,P57) s(P59,P57) s(P53,P58) s(P52,P58) s(P58,P59) s(P57,P60) s(P59,P60) s(P61,P60) s(P59,P61) s(P58,P61) s(P60,P62) s(P61,P62) color(blue) pen(2) color(maroon) pen(2) color(gold) pen(2) m(P2,P1,MA30) m(P1,P3,MB30) f(P1,MA30,MB30) pen(2) color(red) s(P63,P52) abstand(P63,P52,A0) print(abs(P63,P52):,1.26,14.159) print(A0,2.56,14.159) \geooff \geoprint() \geo ebene(332.54,321.52) x(1.71,8.36) y(6,12.43) form(.) #//Eingabe war: #//blauerWinkel=0; gruenerWinkel=0; orangerWinkel=5; #//No.474 4/5/9 #//orangerWinkel=55 #D=50; P[1]=[0,0]; P[2]=[D,0]; M(3,1,2,orangerWinkel); L(4,1,3); L(5,4,3); L(6,5,3); L(7,4,5); M(8,1,4,28.955024371859853); L(9,1,8); L(10,9,8); L(11,9,10); L(12,10,8); A(12,7); L(13,12,7); M(14,11,10,10.320021257740494); L(15,11,14); L(16,15,14); L(17,16,14); L(18,15,16); A(17,13); L(19,17,13); H(20,18,19,2); A(18,20); A(20,19); L(21,18,20); L(22,20,19); A(21,22); L(23,21,22); M(24,23,22,10.320021257740494); L(25,23,24); L(26,25,24); L(27,26,24); L(28,25,26); A(27,13); L(29,27,13); H(30,28,29,2); A(28,30); A(30,29); L(31,28,30); L(32,30,29); A(31,32); L(33,31,32); Q(34,33,13,D,2*D); A(34,13); H(35,34,13,2); A(13,35); A(35,34); L(36,33,34); L(37,34,35); L(38,35,13); A(37,38); L(39,34,37); L(40,38,13); N(41,40,6); L(42,40,41); L(43,42,41); L(44,42,43); N(45,43,6); Q(46,36,45,ab(34,36),ab(34,45)); A(45,46); A(36,46); Q(47,36,45,ab(37,36),ab(37,45)); A(47,36); A(47,45); A(47,46); L(48,47,46); R(39,48); Q(49,36,45,ab(42,36),ab(42,45)); A(36,49); A(49,45); Q(50,36,45,ab(43,36),ab(43,45)); A(36,50); A(50,49); L(51,50,49); R(44,51); # #//Ende der Eingabe, weiter mit fedgeo: p(4,6,P1) p(5,6,P2) p(4.996194698091745,6.087155742747658,P3) p(4.422618261740699,6.90630778703665,P4) p(5.4188129598324455,6.993463529784308,P5) p(5.9923893961834915,6.174311485495316,P6) p(4.8452365234813985,7.8126155740733,P7) p(3.931026608306732,6.997618499847675,P8) p(3.1015503399999567,6.439076540532293,P9) p(3.0325769483066884,7.436695040379968,P10) p(2.2031006799999133,6.8781530810645855,P11) p(3.862053216613463,7.995236999695351,P12) p(4.511799663911457,8.755388007208749,P13) p(2.9190975307618423,7.576256590366037,P14) p(1.9565237318547553,7.847276297504797,P15) p(2.6725205826166833,8.545379806806247,P16) p(3.6350943815237704,8.274360099667486,P17) p(1.7099467837095967,8.816399513945008,P18) p(3.656864634857609,9.274123099617865,P19) p(2.683405709283603,9.045261306781436,P20) p(1.998476119944601,9.773870569451017,P21) p(2.971935045518607,10.002732362287446,P22) p(2.287005456179605,10.731341624957025,P23) p(3.0913820377489682,10.137221843243955,P24) p(3.2037165708186697,11.130892287948845,P25) p(4.008093152388033,10.536772506235774,P26) p(3.8957586193183316,9.543102061530886,P27) p(4.120427685457735,11.530442950940664,P28) p(4.885959523575901,9.682752228761366,P29) p(4.5031936045168175,10.606597589851017,P30) p(5.11188419685932,11.400005280003905,P31) p(5.494650115918403,10.476159918914256,P32) p(6.103340708260905,11.269567609067144,P33) p(5.729180848596419,10.342203387514548,P34) p(5.120490256253938,9.548795697361648,P35) p(6.719381752853991,10.481853554744982,P36) p(6.111946767655523,9.418358026424912,P37) p(5.503256175313042,8.624950336272013,P38) p(6.720637359998005,10.211765716577812,P39,nolabel) print(\P39,6.3,10.4) p(4.894565582970561,7.8315426461191135,P40) p(5.535150776155827,7.06365553835405,P41) p(5.879867922126298,8.002362142823184,P42) p(6.520453115311565,7.2344750350581215,P43) p(6.865170261282035,8.173181639527257,P44,nolabel) print(\P44,6.4,8.3) p(6.977691735339229,6.345130982199389,P45) p(7.7192634252769095,10.466470409658646,P46) p(7.4543983409881855,9.502184929562254,P47) p(6.7517351608685985,10.21370756117999,P48) p(7.860826038635382,8.12605940494453,P49) p(7.320743021757499,7.284447656642448,P50) p(6.861927376043403,8.172979143562275,P51) nolabel() s(P1,P3) s(P1,P4) s(P3,P4) s(P4,P5) s(P3,P5) s(P5,P6) s(P3,P6) s(P4,P7) s(P5,P7) s(P1,P8) s(P1,P9) s(P8,P9) s(P9,P10) s(P8,P10) s(P9,P11) s(P10,P11) s(P10,P12) s(P8,P12) s(P7,P12) s(P12,P13) s(P7,P13) s(P35,P13) s(P11,P14) s(P11,P15) s(P14,P15) s(P15,P16) s(P14,P16) s(P16,P17) s(P14,P17) s(P13,P17) s(P15,P18) s(P16,P18) s(P20,P18) s(P17,P19) s(P13,P19) s(P19,P20) s(P18,P21) s(P20,P21) s(P22,P21) s(P20,P22) s(P19,P22) s(P21,P23) s(P22,P23) s(P23,P24) s(P23,P25) s(P24,P25) s(P25,P26) s(P24,P26) s(P26,P27) s(P24,P27) s(P13,P27) s(P25,P28) s(P26,P28) s(P30,P28) s(P27,P29) s(P13,P29) s(P29,P30) s(P28,P31) s(P30,P31) s(P32,P31) s(P30,P32) s(P29,P32) s(P31,P33) s(P32,P33) s(P33,P34) s(P34,P35) s(P33,P36) s(P34,P36) s(P34,P37) s(P35,P37) s(P38,P37) s(P35,P38) s(P13,P38) s(P34,P39) s(P37,P39) s(P38,P40) s(P13,P40) s(P40,P41) s(P6,P41) s(P40,P42) s(P41,P42) s(P42,P43) s(P41,P43) s(P42,P44) s(P43,P44) s(P43,P45) s(P6,P45) s(P46,P47) s(P47,P48) s(P46,P48) s(P45,P50) s(P49,P50) s(P50,P51) s(P49,P51) color(blue) pen(2) color(maroon) pen(2) color(gold) pen(2) m(P2,P1,MA30) m(P1,P3,MB30) f(P1,MA30,MB30) pen(2) color(red) s(P39,P48) abstand(P39,P48,A0) print(abs(P39,P48):,1.71,12.43) print(A0,3.01,12.43) color(red) s(P44,P51) abstand(P44,P51,A1) print(abs(P44,P51):,1.71,12.13) print(A1,3.01,12.13) \geooff \geoprint() Bei den symmetrischen Graphen hat es ja gereicht, den halben oder viertel Graph zu zeichnen und symmetrisch dazu einige zusätzliche Punkte auf der anderen Seite. Bei asymmetrischen Graphen ab #475-1 geht das nicht mehr \geo ebene(659.09,369.69) x(-0.73,12.46) y(4.34,11.73) form(.) #//Eingabe war: #//blauerWinkel=0; gruenerWinkel=0; orangerWinkel=55; #//No.475-1 #//orangerWinkel=55 #D=50; P[1]=[0,0]; P[2]=[D,0]; M(3,1,2,orangerWinkel); L(4,1,3); L(5,4,3); L(6,5,3); L(7,4,5); M(8,1,4,28.955024371859853); L(9,1,8); L(10,9,8); L(11,9,10); L(12,10,8); A(12,7); L(13,12,7); M(14,11,10,10.320021257740494); L(15,11,14); L(16,15,14); L(17,16,14); L(18,15,16); A(17,13); L(19,17,13); H(20,18,19,2); A(18,20); A(20,19); L(21,18,20); L(22,20,19); A(21,22); L(23,21,22); M(24,23,22,10.320021257740494); L(25,23,24); L(26,25,24); L(27,26,24); L(28,25,26); A(27,13); L(29,27,13); H(30,28,29,2); A(28,30); A(30,29); L(31,28,30); L(32,30,29); A(31,32); L(33,31,32); Q(34,33,13,D,2*D); A(34,13); H(35,34,13,2); A(13,35); A(35,34); L(36,33,34); L(37,34,35); L(38,35,13); A(37,38); L(39,37,38); H(40,36,39,2); A(36,40); A(40,39); L(41,36,40); L(42,40,39); A(41,42); L(43,41,42); Q(44,43,6,ab(33,13),D); A(44,43); Q(45,43,44,2*D,D); A(43,45); H(46,43,45,2); A(46,43); A(46,45); L(47,43,46); L(48,46,45); A(47,48); L(49,47,48); L(50,45,44); H(51,49,50,2); A(49,51); A(51,50); L(52,49,51); L(53,51,50); A(52,53); L(54,52,53); L(55,44,6); Q(56,54,55,ab(23,6),ab(23,6)); A(54,56); A(55,56); Q(57,54,56,D,ab(6,21)); A(56,57); L(58,57,54); L(59,57,58); L(60,57,59); L(61,59,58); M(62,60,59,28.955024371859853); L(63,60,62); L(64,63,62); L(65,63,64); L(66,64,62); A(66,61); L(67,66,61); M(68,65,64,10.320021257740494); L(69,65,68); L(70,69,68); L(71,69,70); L(72,70,68); A(72,67); L(73,72,67); H(74,71,73,2); A(71,74); A(74,73); L(75,71,74); L(76,74,73); A(75,76); A(56,75); A(56,76); Q(77,56,55,D,ab(6,21)); A(77,55); L(78,77,56); L(79,77,78); L(80,79,78); L(81,77,79); M(82,81,79,28.955024371859853); L(83,81,82); L(84,83,82); L(85,83,84); L(86,84,82); A(86,80); L(87,86,80); M(88,85,84,10.320021257740494); L(89,85,88); L(90,89,88); L(91,89,90); L(92,90,88); A(92,87); L(93,92,87); H(94,91,93,2); A(91,94); A(94,93); L(95,91,94); L(96,94,93); A(95,96); A(95,55); A(55,96); # #//Ende der Eingabe, weiter mit fedgeo: p(4,6,P1) p(5,6,P2) p(4.573576436351046,6.819152044288992,P3) p(3.5773817382593007,6.90630778703665,P4) p(4.150958174610347,7.725459831325642,P5) p(5.147152872702092,7.638304088577984,P6) p(3.154763476518601,7.8126155740733,P7) p(3.191444650260508,6.5884201274664616,P8) p(3.0861355466462204,5.593980590493019,P9) p(2.277580196906728,6.182400717959481,P10) p(2.1722710932924407,5.187961180986038,P11) p(2.3828893005210157,7.176840254932923,P12) p(2.218228811045084,8.163190559442201,P13) p(2.097726683514557,6.185178875860567,P14) p(1.2713830315387993,5.622012675845538,P15) p(1.1968386217609153,6.619230370720065,P16) p(2.0231822737366727,7.182396570735094,P17) p(0.3704949697851574,6.056064170705037,P18) p(1.2713130322914559,7.841708821317921,P19) p(0.8209040010383069,6.948886496011479,P20) p(-0.17750732936954083,6.8925409965174245,P21) p(0.27290170188360907,7.7853633218238665,P22) p(-0.7255096285242386,7.729017822329812,P23) p(0.2466558289589198,7.963313198461229,P24) p(-0.4423326475016962,8.688085493257656,P25) p(0.5298328099814622,8.922380869389073,P26) p(1.2188212864420778,8.197608574592646,P27) p(-0.1591556664791538,9.6471531641855,P28) p(1.7483319242117035,9.045911872056948,P29) p(0.7945881288662746,9.346532518121224,P30) p(0.5780613475873144,10.322809196624288,P31) p(1.5318051429327424,10.022188550560013,P32) p(1.3152783616537818,10.998465229063079,P33) p(1.7851752484871395,10.115743916448322,P34) p(2.0017020297661117,9.139467237945262,P35) p(2.3146858862567847,10.96404721391261,P36) p(2.738919043832569,9.815123270384058,P37) p(2.9554458251115414,8.838846591880998,P38) p(3.692662839177999,9.514502624319794,P39) p(3.003674362717392,10.239274919116202,P40) p(3.2868513437399205,11.198342590044028,P41) p(3.9758398202005285,10.47357029524762,P42) p(4.259016801223058,11.432637966175449,P43) p(5.263054238622484,8.631564816371945,P44) p(5.100458233816827,9.618257544236723,P45) p(4.679737517519943,10.525447755206086,P46) p(5.255026928135532,11.343397688902254,P47) p(5.675747644432417,10.436207477932893,P48) p(6.251037055048006,11.254157411629063,P49) p(6.03625720427992,9.26572345101989,P50) p(6.143647129663964,10.259940431324477,P51) p(7.0583592541736095,10.664046517983673,P52) p(6.950969328789567,9.669829537679085,P53) p(7.865681453299213,10.073935624338283,P54) p(6.065292578513278,8.034560925254588,P55) p(11.248849661631153,5.2728350516640194,P56) p(8.865511618495297,10.092364969523913,P57) p(8.381556817003124,9.217271974401298,P58) p(9.381386982199208,9.23570131958693,P59) p(9.865341783691381,10.110794314709548,P60) p(8.897432180707035,8.360608324464314,P61) p(9.865533906947313,9.11079433316522,P62) p(10.731463233120703,9.610960707557679,P63) p(10.731655356376635,8.610960726013353,P64) p(11.597584682550025,9.111127100405811,P65) p(9.865726030203247,8.110794351620893,P66) p(9.165233858752423,7.39713426605066,P67) p(10.835266740231596,8.463924385007154,P68) p(11.77691970432432,8.127339038898043,P69) p(11.014601762005892,7.480136323499384,P70) p(11.956254726098614,7.143550977390274,P71) p(10.072948797913167,7.816721669608494,P72) p(9.982464678921833,6.820823771121725,P73) p(10.969359702510223,6.982187374255999,P74) p(11.602552193864891,6.208193014527149,P75) p(10.6156571702765,6.046829411392873,P76) p(10.36456927908245,4.805878731394639,P77) p(10.402313434545817,5.805166166884727,P78) p(9.518033051997115,5.338209846615347,P79) p(9.55577720746048,6.337497282105435,P80) p(9.48028889653375,4.3389224111252584,P81) p(9.029537083098266,5.231571727869871,P82) p(8.481856004844351,4.394884548260531,P83) p(8.031104191408868,5.287533865005143,P84) p(7.483423113154954,4.450846685395804,P85) p(8.57878526966278,6.124221044614482,P86) p(8.882578598870902,7.076959000785352,P87) p(7.8723549097886565,5.372113236165601,P88) p(6.880048774848294,5.248304777005012,P89) p(7.268980571481998,6.169571327774809,P90) p(6.276674436541636,6.045762868614221,P91) p(8.26128670642236,6.2933797869353985,P92) p(7.893333147575133,7.223223955886121,P93) p(7.085003792058384,6.634493412250171,P94) p(6.170983507527454,7.0401618969344035,P95) p(6.979312863044202,7.628892440570353,P96) nolabel() s(P1,P3) s(P1,P4) s(P3,P4) s(P4,P5) s(P3,P5) s(P5,P6) s(P3,P6) s(P4,P7) s(P5,P7) s(P1,P8) s(P1,P9) s(P8,P9) s(P9,P10) s(P8,P10) s(P9,P11) s(P10,P11) s(P10,P12) s(P8,P12) s(P7,P12) s(P12,P13) s(P7,P13) s(P35,P13) s(P11,P14) s(P11,P15) s(P14,P15) s(P15,P16) s(P14,P16) s(P16,P17) s(P14,P17) s(P13,P17) s(P15,P18) s(P16,P18) s(P20,P18) s(P17,P19) s(P13,P19) s(P19,P20) s(P18,P21) s(P20,P21) s(P22,P21) s(P20,P22) s(P19,P22) s(P21,P23) s(P22,P23) s(P23,P24) s(P23,P25) s(P24,P25) s(P25,P26) s(P24,P26) s(P26,P27) s(P24,P27) s(P13,P27) s(P25,P28) s(P26,P28) s(P30,P28) s(P27,P29) s(P13,P29) s(P29,P30) s(P28,P31) s(P30,P31) s(P32,P31) s(P30,P32) s(P29,P32) s(P31,P33) s(P32,P33) s(P33,P34) s(P34,P35) s(P33,P36) s(P34,P36) s(P40,P36) s(P34,P37) s(P35,P37) s(P38,P37) s(P35,P38) s(P13,P38) s(P37,P39) s(P38,P39) s(P39,P40) s(P36,P41) s(P40,P41) s(P42,P41) s(P40,P42) s(P39,P42) s(P41,P43) s(P42,P43) s(P6,P44) s(P44,P45) s(P43,P46) s(P45,P46) s(P43,P47) s(P46,P47) s(P48,P47) s(P46,P48) s(P45,P48) s(P47,P49) s(P48,P49) s(P51,P49) s(P45,P50) s(P44,P50) s(P50,P51) s(P49,P52) s(P51,P52) s(P53,P52) s(P51,P53) s(P50,P53) s(P52,P54) s(P53,P54) s(P44,P55) s(P6,P55) s(P96,P55) s(P75,P56) s(P76,P56) s(P54,P57) s(P57,P58) s(P54,P58) s(P57,P59) s(P58,P59) s(P57,P60) s(P59,P60) s(P59,P61) s(P58,P61) s(P60,P62) s(P60,P63) s(P62,P63) s(P63,P64) s(P62,P64) s(P63,P65) s(P64,P65) s(P64,P66) s(P62,P66) s(P61,P66) s(P66,P67) s(P61,P67) s(P65,P68) s(P65,P69) s(P68,P69) s(P69,P70) s(P68,P70) s(P69,P71) s(P70,P71) s(P74,P71) s(P70,P72) s(P68,P72) s(P67,P72) s(P72,P73) s(P67,P73) s(P73,P74) s(P71,P75) s(P74,P75) s(P76,P75) s(P74,P76) s(P73,P76) s(P56,P77) s(P77,P78) s(P56,P78) s(P77,P79) s(P78,P79) s(P79,P80) s(P78,P80) s(P77,P81) s(P79,P81) s(P81,P82) s(P81,P83) s(P82,P83) s(P83,P84) s(P82,P84) s(P83,P85) s(P84,P85) s(P84,P86) s(P82,P86) s(P80,P86) s(P86,P87) s(P80,P87) s(P85,P88) s(P85,P89) s(P88,P89) s(P89,P90) s(P88,P90) s(P89,P91) s(P90,P91) s(P94,P91) s(P90,P92) s(P88,P92) s(P87,P92) s(P92,P93) s(P87,P93) s(P93,P94) s(P91,P95) s(P94,P95) s(P96,P95) s(P55,P95) s(P94,P96) s(P93,P96) color(blue) pen(2) color(maroon) pen(2) color(gold) pen(2) m(P2,P1,MA30) m(P1,P3,MB30) f(P1,MA30,MB30) pen(2) \geooff \geoprint() Beim #475-2 lässt sich der blaue Winkel variieren und auch das extra GAP-Programm sagt "3-fach beweglich", zweifache Beweglichkeit wird von Punkt P2 verursacht und für den Graph bleibt einfache Beweglichkeit übrig. \geo ebene(725.27,584.74) x(-5.41,9.1) y(5.19,16.88) form(.) #//Eingabe war: #//blauerWinkel=64; gruenerWinkel=0; orangerWinkel=55; #//No.475-2 #//blauerWinkel=64; #//orangerWinkel=55 #D=50; P[1]=[0,0]; P[2]=[D,0]; M(3,1,2,orangerWinkel); L(4,1,3); L(5,4,3); L(6,5,3); L(7,4,5); M(8,1,4,28.955024371859853); L(9,1,8); L(10,9,8); L(11,9,10); L(12,10,8); A(12,7); L(13,12,7); M(14,11,10,10.320021257740494); L(15,11,14); L(16,15,14); L(17,16,14); L(18,15,16); A(17,13); L(19,17,13); H(20,18,19,2); A(18,20); A(20,19); L(21,18,20); L(22,20,19); A(21,22); L(23,21,22); Q(24,23,13,D,2*D); A(24,13); H(25,13,24,2); A(25,24); A(25,13); L(26,23,24); L(27,24,25); L(28,25,13); A(27,28); L(29,27,28); H(30,26,29,2); A(26,30); A(30,29); L(31,26,30); L(32,30,29); A(31,32); L(33,31,32); Q(34,13,6,2*D,D); A(13,34); H(35,13,34,2); A(13,35); A(35,34); L(36,13,35); L(37,35,34); A(36,37); L(38,36,37); L(39,34,6); H(40,38,39,2); A(38,40); A(40,39); L(41,38,40); L(42,40,39); A(41,42); L(43,41,42); M(44,13,35,blauerWinkel);L(45,13,44); L(46,45,44); L(47,46,44); L(48,45,46); Q(49,48,47,D,2*D); A(49,47); H(50,49,47,2); A(49,50); A(50,47); L(51,49,50); L(52,50,47); A(51,52); L(53,51,52); L(54,48,49); Q(55,33,54,D,2*D); A(55,54); H(56,55,54,2); A(55,56); A(56,54); L(57,55,56); L(58,56,54); A(57,58); L(59,57,58); L(60,33,55); Q(61,60,59,ab(6,23),ab(6,23)); A(59,61); A(61,60); Q(62,60,61,D,ab(6,21)); A(61,62); L(63,62,60); L(64,62,63); L(65,62,64); L(66,64,63); M(67,65,64,28.955024371859853); L(68,65,67); L(69,68,67); L(70,68,69); L(71,69,67); A(71,66); L(72,71,66); M(73,70,69,10.320021257740494); L(74,70,73); L(75,74,73); L(76,74,75); L(77,75,73); A(77,72); L(78,77,72); H(79,76,78,2); A(76,79); A(79,78); L(80,76,79); L(81,79,78); A(80,81); A(61,81); A(80,61); Q(82,61,59,D,ab(6,21)); A(59,82); L(83,82,61); L(84,82,83); L(85,82,84); L(86,84,83); M(87,85,84,28.955024371859853); L(88,85,87); L(89,88,87); L(90,88,89); L(91,89,87); A(91,86); L(92,91,86); M(93,90,89,10.320021257740494); L(94,90,93); L(95,94,93); L(96,94,95); L(97,95,93); A(97,92); L(98,97,92); H(99,98,96,2); A(96,99); A(99,98); L(100,96,99); L(101,99,98); A(100,101); A(100,59); A(101,59); Q(102,53,43,ab(6,23),ab(6,23)); A(43,102); A(102,53); Q(103,53,102,D,ab(6,21)); A(102,103); L(104,103,53); L(105,103,104); L(106,105,104); L(107,103,105); M(108,107,105,28.955024371859853); L(109,107,108); L(110,109,108); L(111,109,110); L(112,110,108); A(112,106); L(113,112,106); M(114,111,110,10.320021257740494); L(115,111,114); L(116,115,114); L(117,115,116); L(118,116,114); A(118,113); L(119,118,113); H(120,117,119,2); A(117,120); A(120,119); L(121,117,120); L(122,120,119); A(121,122); A(121,102); A(102,122); Q(123,102,43,D,ab(6,21)); A(123,43); L(124,123,102); L(125,123,124); L(126,123,125); L(127,125,124); M(128,126,125,28.955024371859853); L(129,126,128); L(130,129,128); L(131,129,130); L(132,130,128); A(132,127); L(133,132,127); M(134,131,130,10.320021257740494); L(135,131,134); L(136,135,134); L(137,135,136); L(138,136,134); A(138,133); L(139,138,133); H(140,139,137,2); A(137,140); A(140,139); L(141,137,140); L(142,140,139); A(141,142); A(141,43); A(43,142); # #//Ende der Eingabe, weiter mit fedgeo: p(4,6,P1) p(5,6,P2) p(4.573576436351046,6.819152044288992,P3) p(3.5773817382593007,6.90630778703665,P4) p(4.150958174610347,7.725459831325642,P5) p(5.147152872702092,7.638304088577984,P6) p(3.154763476518601,7.8126155740733,P7) p(3.191444650260508,6.5884201274664616,P8) p(3.0861355466462204,5.593980590493019,P9) p(2.277580196906728,6.182400717959481,P10) p(2.1722710932924407,5.187961180986038,P11) p(2.3828893005210157,7.176840254932923,P12) p(2.218228811045084,8.163190559442201,P13) p(2.097726683514557,6.185178875860567,P14) p(1.2713830315387993,5.622012675845538,P15) p(1.1968386217609153,6.619230370720065,P16) p(2.0231822737366727,7.182396570735094,P17) p(0.3704949697851574,6.056064170705037,P18) p(1.2713130322914559,7.841708821317921,P19) p(0.8209040010383069,6.948886496011479,P20) p(-0.17750732936954083,6.8925409965174245,P21) p(0.27290170188360907,7.7853633218238665,P22) p(-0.7255096285242386,7.729017822329812,P23) nolabel() p(0.22140615022939114,8.05049956045409,P24) p(1.219817480637238,8.106845059948146,P25) p(-0.5304630912158244,8.70981181103692,P26) p(0.6718151814825397,8.943321885760533,P27) p(1.6702265118903856,8.999667385254586,P28) p(1.1222242127356883,9.836144211066973,P29) p(0.2958805607599322,9.272978011051945,P30) p(-0.6050075009937075,9.707029505911445,P31) p(0.22133615098204817,10.270195705926472,P32) p(-0.6795519107715906,10.704247200785968,P33) p(4.210618207228575,7.9888790739468885,P34) p(3.2144235091368296,8.076034816694545,P35) p(2.7918052473961286,8.982342603731194,P36) p(3.7879999454878743,8.895186860983538,P37) p(3.365381683747173,9.801494648020185,P38) p(4.9824923832261625,8.624654393087262,P39) p(4.173937033486668,9.213074520553725,P40) p(4.279246137100953,10.207514057527169,P41) p(5.087801486840449,9.619093930060707,P42) p(5.193110590454734,10.613533467034152,P43,label) p(2.7332668859551363,9.020357860144314,P44) p(1.7334191907987453,9.037810266581596,P45) p(2.2484572657087982,9.89497756728371,P46) p(3.2483049608651893,9.877525160846428,P47) p(1.2486095705524063,9.912429973720991,P48) p(1.5154697142122138,10.876165240132813,P49) p(2.3818873375387017,10.37684520048962,P50) p(2.381102364825116,11.376844892398493,P51) p(3.2475199881516037,10.8775248527553,P52) p(3.246735015438019,11.877524544664173,P53,label) p(0.5474204191467082,10.62540527059386,P54) p(-1.2325145456487654,11.537453252390069,P55) p(-0.342547063251029,11.081429261491966,P56) p(-0.3926024435969744,12.080175705239537,P57) p(0.4973650388007611,11.624151714341433,P58) p(0.44730965845481485,12.622898158089004,P59) p(-1.6776108354862576,10.641970537440807,P60) p(-4.495726498687452,15.795087840939843,P61) p(-2.6731037978600094,10.736805983684977,P62) p(-2.0932274110464473,11.551510455267188,P63) p(-3.088720373420199,11.646345901511358,P64) p(-3.6685967602337612,10.83164142992915,P65) p(-2.508843986606638,12.46105037309357,P66) p(-3.55562202808672,11.825239291187065,P67) p(-4.472590383155483,11.426279348583186,P68) p(-4.359615651008442,12.419877209841104,P69) p(-5.2765840060772025,12.020917267237223,P70) p(-3.44264729593968,12.818837152444981,P71) p(-2.665893201216618,13.448641150789669,P72) p(-4.445921990435645,12.57769425649801,P73) p(-5.343436015198879,13.018680169371992,P74) p(-4.5127739995573215,13.575457158632776,P75) p(-5.410288024320556,14.01644307150676,P76) p(-3.615259974794088,13.134471245758792,P77) p(-3.4126557068666363,14.11373194170119,P78) p(-4.411471865593596,14.065087506603975,P79) p(-4.953007261504007,14.905765456223303,P80) p(-3.954191102777048,14.95440989132052,P81) p(-3.5765545676597483,16.18894436457606,P82) p(-3.6950507782584125,15.195989860042362,P83) p(-2.7758788472307083,15.589846383678575,P84) p(-2.657382636632044,16.58280088821227,P85) p(-2.8943750578293725,14.596891879144879,P86) p(-2.280354788455795,15.656598965465623,P87) p(-1.6667543184113311,16.44621562129376,P88) p(-1.289726470235082,15.520013698547114,P89) p(-0.6761260001906182,16.30963035437525,P90) p(-1.9033269402795465,14.730397042718975,P91) p(-2.283232135862895,13.805371614761032,P92) p(-1.1383432740270711,15.422863647869422,P93) p(-0.1392721420445362,15.46595509991198,P94) p(-0.6014894158809891,14.57918839340615,P95) p(0.39758171610154536,14.622279845448709,P96) p(-1.6005605478635232,14.536096941363592,P97) p(-1.3090696458367121,13.579523340412992,P98) p(-0.4557439648675832,14.10090159293085,P99) label() p(0.4224456872781843,13.622589001768858,P100) p(-0.43087999369094554,13.101210749251,P101) p(7.35573288058573,16.074253077582718,P102) p(3.047535734975246,12.857483547206172,P103) p(3.9958047660752647,12.540015683231516,P104) p(3.796605485612491,13.519974685773516,P105) p(4.7448745167125095,13.20250682179886,P106) p(2.8483364545124727,13.837442549748172,P107) p(3.8317653254912254,14.018736939417176,P108) p(3.1830453429848977,14.779764129665322,P109) p(4.16647421396365,14.961058519334326,P110) p(3.517754231457322,15.722085709582473,P111) p(4.815194196469978,14.200031329086178,P112) p(5.643915920799618,13.640370446386562,P113) p(4.2923145295638445,15.089585634802134,P114) p(4.452795513165914,16.0766245671154,P115) p(5.227355811272436,15.44412449233506,P116) p(5.387836794874505,16.431163424648325,P117) p(5.066874827670367,14.457085560021795,P118) p(6.0626914102977985,14.548460248881652,P119) p(5.725264102586151,15.48981183676499,P120) p(6.371784837730118,16.252708251115532,P121) p(6.709212145441764,15.311356663232194,P122) p(7.91896751767154,15.247956070697894,P123) p(6.921756000095334,15.173329070132684,P124) p(7.484990637181143,14.347032063247863,P125) p(8.48220215475735,14.421659063813074,P126) p(6.487779119604937,14.272405062682653,P127) p(7.645770718173978,13.873587488291154,P128) p(8.538630343959806,13.423252403447002,P129) p(7.7021989073764345,12.875180827925082,P130) p(8.595058533162263,12.42484574308093,P131) p(6.809339281590605,13.325515912769237,P132) p(5.828529142204901,13.520481218601317,P133) p(7.635967412387738,12.707943291730622,P134) p(7.870343303895266,11.735797242270946,P135) p(6.911252183120739,12.018894790920639,P136) p(7.145628074628268,11.046748741460965,P137) p(6.676876291613212,12.991040840380315,P138) p(5.794193899580427,12.521070846875107,P139) p(6.469910987104347,11.783909794168036,P140) p(6.169369332541505,10.830141104247552,P141) p(5.493652245017584,11.567302156954623,P142) nolabel() s(P1,P3) s(P1,P4) s(P3,P4) s(P4,P5) s(P3,P5) s(P5,P6) s(P3,P6) s(P4,P7) s(P5,P7) s(P1,P8) s(P1,P9) s(P8,P9) s(P9,P10) s(P8,P10) s(P9,P11) s(P10,P11) s(P10,P12) s(P8,P12) s(P7,P12) s(P12,P13) s(P7,P13) s(P35,P13) s(P11,P14) s(P11,P15) s(P14,P15) s(P15,P16) s(P14,P16) s(P16,P17) s(P14,P17) s(P13,P17) s(P15,P18) s(P16,P18) s(P20,P18) s(P17,P19) s(P13,P19) s(P19,P20) s(P18,P21) s(P20,P21) s(P22,P21) s(P20,P22) s(P19,P22) s(P21,P23) s(P22,P23) s(P23,P24) s(P24,P25) s(P13,P25) s(P23,P26) s(P24,P26) s(P30,P26) s(P24,P27) s(P25,P27) s(P28,P27) s(P25,P28) s(P13,P28) s(P27,P29) s(P28,P29) s(P29,P30) s(P26,P31) s(P30,P31) s(P32,P31) s(P30,P32) s(P29,P32) s(P31,P33) s(P32,P33) s(P6,P34) s(P34,P35) s(P13,P36) s(P35,P36) s(P37,P36) s(P35,P37) s(P34,P37) s(P36,P38) s(P37,P38) s(P40,P38) s(P34,P39) s(P6,P39) s(P39,P40) s(P38,P41) s(P40,P41) s(P42,P41) s(P40,P42) s(P39,P42) s(P41,P43) s(P42,P43) s(P142,P43) s(P13,P44) s(P13,P45) s(P44,P45) s(P45,P46) s(P44,P46) s(P46,P47) s(P44,P47) s(P45,P48) s(P46,P48) s(P48,P49) s(P50,P49) s(P47,P50) s(P49,P51) s(P50,P51) s(P52,P51) s(P50,P52) s(P47,P52) s(P51,P53) s(P52,P53) s(P48,P54) s(P49,P54) s(P33,P55) s(P56,P55) s(P54,P56) s(P55,P57) s(P56,P57) s(P58,P57) s(P56,P58) s(P54,P58) s(P57,P59) s(P58,P59) s(P33,P60) s(P55,P60) s(P81,P61) s(P60,P62) s(P62,P63) s(P60,P63) s(P62,P64) s(P63,P64) s(P62,P65) s(P64,P65) s(P64,P66) s(P63,P66) s(P65,P67) s(P65,P68) s(P67,P68) s(P68,P69) s(P67,P69) s(P68,P70) s(P69,P70) s(P69,P71) s(P67,P71) s(P66,P71) s(P71,P72) s(P66,P72) s(P70,P73) s(P70,P74) s(P73,P74) s(P74,P75) s(P73,P75) s(P74,P76) s(P75,P76) s(P79,P76) s(P75,P77) s(P73,P77) s(P72,P77) s(P77,P78) s(P72,P78) s(P78,P79) s(P76,P80) s(P79,P80) s(P81,P80) s(P61,P80) s(P79,P81) s(P78,P81) s(P61,P82) s(P82,P83) s(P61,P83) s(P82,P84) s(P83,P84) s(P82,P85) s(P84,P85) s(P84,P86) s(P83,P86) s(P85,P87) s(P85,P88) s(P87,P88) s(P88,P89) s(P87,P89) s(P88,P90) s(P89,P90) s(P89,P91) s(P87,P91) s(P86,P91) s(P91,P92) s(P86,P92) s(P90,P93) s(P90,P94) s(P93,P94) s(P94,P95) s(P93,P95) s(P94,P96) s(P95,P96) s(P99,P96) s(P95,P97) s(P93,P97) s(P92,P97) s(P97,P98) s(P92,P98) s(P98,P99) s(P96,P100) s(P99,P100) s(P101,P100) s(P59,P100) s(P99,P101) s(P98,P101) s(P59,P101) s(P122,P102) s(P53,P103) s(P103,P104) s(P53,P104) s(P103,P105) s(P104,P105) s(P105,P106) s(P104,P106) s(P103,P107) s(P105,P107) s(P107,P108) s(P107,P109) s(P108,P109) s(P109,P110) s(P108,P110) s(P109,P111) s(P110,P111) s(P110,P112) s(P108,P112) s(P106,P112) s(P112,P113) s(P106,P113) s(P111,P114) s(P111,P115) s(P114,P115) s(P115,P116) s(P114,P116) s(P115,P117) s(P116,P117) s(P120,P117) s(P116,P118) s(P114,P118) s(P113,P118) s(P118,P119) s(P113,P119) s(P119,P120) s(P117,P121) s(P120,P121) s(P122,P121) s(P102,P121) s(P120,P122) s(P119,P122) s(P102,P123) s(P123,P124) s(P102,P124) s(P123,P125) s(P124,P125) s(P123,P126) s(P125,P126) s(P125,P127) s(P124,P127) s(P126,P128) s(P126,P129) s(P128,P129) s(P129,P130) s(P128,P130) s(P129,P131) s(P130,P131) s(P130,P132) s(P128,P132) s(P127,P132) s(P132,P133) s(P127,P133) s(P131,P134) s(P131,P135) s(P134,P135) s(P135,P136) s(P134,P136) s(P135,P137) s(P136,P137) s(P140,P137) s(P136,P138) s(P134,P138) s(P133,P138) s(P138,P139) s(P133,P139) s(P139,P140) s(P137,P141) s(P140,P141) s(P142,P141) s(P43,P141) s(P140,P142) s(P139,P142) color(blue) pen(2) m(P35,P13,MA10) m(P13,P44,MB10) f(P13,MA10,MB10) color(maroon) pen(2) color(gold) pen(2) m(P2,P1,MA30) m(P1,P3,MB30) f(P1,MA30,MB30) pen(2) \geooff \geoprint() Bei Graph #476 habe ich mir eine Möglichkeit überlegt, wie ich das Eingeben der Kites vereinfachen könnte. Beim vorhergehenden Graph habe ich den rechten oberen Teil eingegeben beginnend mit Q(102,53,43,ab(6,23),ab(6,23)). Das bedeutet, ich zeichne Punkt P102 so, dass der Abstand P102-P53 gleich Abstand P6-P23 ist und Abstand P102-P43 ebenfalls gleich Abstand P6-P23. Darin will ich die Funktion ab(...) so erweitern, dass noch mehr Argumente möglich sind. Statt ab(6,23) soll dann ab(6,23,1,[3,5],[7,23]) stehen mit der Bedeutung, dass 1 bezeichnet Punkt P1 [3,5] bezeichnet alle Punkte von P3 bis P5 [7,23] bezeichnet alle Punkte P7 bis P23 Die zusätzlich aufgeführten Punkte mitsamt ihren Verbindungskanten sollen so bezüglich Punkt P102,P53 gezeichnet werden wie in der Ursprungslage bezüglich P6,P23. Schließlich habe ich noch #485-2 probiert, starr mit blauerWinkel=104.87849569518802°. \geo ebene(583.24,464.47) x(1.71,13.37) y(2.84,12.13) form(.) #//Eingabe war: #//blauerWinkel=104.87849569518802; gruenerWinkel=0; orangerWinkel=5; #//No.485-2 #//orangerWinkel=55 #//orangerWinkel=55 #D=50; P[1]=[0,0]; P[2]=[D,0]; M(3,1,2,orangerWinkel); L(4,1,3); L(5,4,3); L(6,5,3); L(7,4,5); M(8,1,4,28.955024371859853); L(9,1,8); L(10,9,8); L(11,9,10); L(12,10,8); A(12,7); L(13,12,7); M(14,11,10,10.320021257740494); L(15,11,14); L(16,15,14); L(17,16,14); L(18,15,16); A(17,13); L(19,17,13); H(20,18,19,2); A(18,20); A(20,19); L(21,18,20); L(22,20,19); A(21,22); L(23,21,22); M(24,23,22,10.320021257740494); L(25,23,24); L(26,25,24); L(27,26,24); L(28,25,26); A(27,13); L(29,27,13); H(30,28,29,2); A(28,30); A(30,29); L(31,28,30); L(32,31,30); A(29,32); L(33,31,32); M(34,33,32,10.320021257740494); L(35,33,34); L(36,35,34); L(37,35,36); L(38,36,34); A(38,13); L(39,38,13); H(40,39,37,2); A(37,40); A(40,39); L(41,37,40); L(42,40,39); A(41,42); Q(43,42,6,D,2*D); A(43,6); H(44,43,6,2); A(43,44); A(44,6); L(45,43,44); L(46,44,6); A(45,46); N(47,41,43); M(48,47,43,blauerWinkel); L(49,47,48); L(50,49,48); L(51,49,50); L(52,50,48); M(53,51,50,28.955024371859853); L(54,51,53); L(55,54,53); L(56,54,55); L(57,55,53); A(57,52); L(58,57,52); M(59,56,55,10.320021257740494); L(60,56,59); L(61,60,59); L(62,60,61); L(63,61,59); A(63,58); L(64,63,58); H(65,62,64,2); A(62,65); A(65,64); L(66,62,65); L(67,65,64); A(66,67); L(68,66,67); Q(69,68,45,ab(6,22),D); A(68,69); Q(70,68,69,ab(6,21),D); A(68,70); R(46,70); L(71,69,70); L(72,69,71); L(73,71,70); Q(74,72,73,D,2*D); A(74,73); H(75,73,74,2); A(74,75); A(75,73); L(76,72,74); L(77,74,75); L(78,75,73); A(78,77); L(79,77,78); Q(80,76,79,D,2*D); A(80,79); H(81,80,79,2); A(80,81); A(81,79); L(82,80,81); L(83,81,79); A(82,83); L(84,82,83); L(85,76,80); H(86,85,84,2); A(85,86); A(86,84); L(87,85,86); L(88,86,84); A(87,88); A(88,68); A(87,68); A(70,46); # # #//Ende der Eingabe, weiter mit fedgeo: p(4,6,P1) p(5,6,P2) p(4.996194698091745,6.087155742747658,P3) p(4.422618261740699,6.90630778703665,P4) p(5.4188129598324455,6.993463529784308,P5) p(5.9923893961834915,6.174311485495316,P6) p(4.8452365234813985,7.8126155740733,P7) p(3.931026608306732,6.997618499847675,P8) p(3.1015503399999567,6.439076540532293,P9) p(3.0325769483066884,7.436695040379968,P10) p(2.2031006799999133,6.8781530810645855,P11) p(3.862053216613463,7.995236999695351,P12) p(4.511799663911457,8.755388007208749,P13) p(2.9190975307618423,7.576256590366037,P14) p(1.9565237318547553,7.847276297504797,P15) p(2.6725205826166833,8.545379806806247,P16) p(3.6350943815237704,8.274360099667486,P17) p(1.7099467837095967,8.816399513945008,P18) p(3.656864634857609,9.274123099617865,P19) p(2.683405709283603,9.045261306781436,P20) p(1.998476119944601,9.773870569451017,P21) p(2.971935045518607,10.002732362287446,P22) p(2.287005456179605,10.731341624957025,P23) p(3.0913820377489682,10.137221843243955,P24) p(3.2037165708186697,11.130892287948845,P25) p(4.008093152388033,10.536772506235774,P26) p(3.8957586193183316,9.543102061530886,P27) p(4.120427685457735,11.530442950940664,P28) p(4.885959523575901,9.682752228761366,P29) p(4.5031936045168175,10.606597589851017,P30) p(5.11188419685932,11.400005280003905,P31) p(5.494650115918403,10.476159918914256,P32) p(6.103340708260905,11.269567609067144,P33) p(5.64663303124166,10.37995078270217,P34) p(6.645417641017438,10.429238745482614,P35) p(6.188709963998194,9.539621919117641,P36) p(7.187494573773972,9.588909881898083,P37) p(5.1899253542224155,9.4903339563372,P38) p(5.48734437142064,8.535586907004824,P39) p(6.337419472597306,9.062248394451455,P40) p(7.21855925050932,8.58939250543115,P41) p(6.368484149332653,8.06273101798452,P42) p(7.296638402049366,7.690535258787992,P43) p(6.644513899116429,6.932423372141654,P44) p(7.6271203033295745,6.746722929494599,P45) p(6.974995800396638,5.9886110428482615,P46) p(8.146713503226028,8.217196746234611,P47) p(8.873991203975372,7.5308534312728135,P48) nolabel() p(9.104743100075243,8.50386605320858,P49) p(9.832020800824584,7.817522738246781,P50) p(10.062772696924455,8.790535360182549,P51) p(9.601268904724716,6.844510116311015,P52) p(10.331922497887923,7.8274370346511795,P53) p(11.03141521365861,8.542076762474753,P54) p(11.300565014622077,7.578978436943384,P55) p(12.000057730392763,8.293618164766956,P56) p(10.601072298851392,6.864338709119811,P57) p(10.118342666881768,5.988569274611806,P58) p(11.439905915339537,7.4652281937432985,P59) p(12.437388582012893,7.394317477443071,P60) p(11.877236766959669,6.565927506419413,P61) p(12.874719433633022,6.495016790119187,P62) p(10.879754100286311,6.636838222719641,P63) p(11.06046576113004,5.653302104605465,P64) p(11.96759259738153,6.074159447362326,P65) p(12.785629165703932,5.498993234092358,P66) p(11.878502329452441,5.0781358913354975,P67) p(12.696538897774845,4.50296967806553,P68) p(8.001086110486153,5.819280437974112,P69) p(7.348961607553223,5.06116855132777,P70,label) p(8.331568011766368,4.875468108680723,P71) p(8.9836925146993,5.633579995327065,P72) p(7.6794435088334385,4.117356222034381,P73) p(9.554700066851861,4.8126351887872225,P74) p(8.61707178784265,4.464995705410802,P75) p(9.980155348343985,5.71761463797403,P76) p(9.386950551309734,3.826805538170351,P77) p(8.449322272300524,3.4791660547939305,P78) p(9.219201035767608,2.8409758875534807,P79) p(9.902487427227857,4.720635353319881,P80) p(9.56084423149773,3.7808056204366807,P81) p(10.54558225327159,3.954848800345893,P82) p(10.203939057541463,3.0150190674626938,P83) p(11.188677079315319,3.1890622473719055,P84) p(10.804730775343252,5.151862602901263,P85) p(10.996703927329285,4.170462425136584,P86) p(11.750634836559044,4.8274161404833995,P87) p(11.94260798854508,3.846015962718721,P88) nolabel() s(P1,P3) s(P1,P4) s(P3,P4) s(P4,P5) s(P3,P5) s(P5,P6) s(P3,P6) s(P4,P7) s(P5,P7) s(P1,P8) s(P1,P9) s(P8,P9) s(P9,P10) s(P8,P10) s(P9,P11) s(P10,P11) s(P10,P12) s(P8,P12) s(P7,P12) s(P12,P13) s(P7,P13) s(P11,P14) s(P11,P15) s(P14,P15) s(P15,P16) s(P14,P16) s(P16,P17) s(P14,P17) s(P13,P17) s(P15,P18) s(P16,P18) s(P20,P18) s(P17,P19) s(P13,P19) s(P19,P20) s(P18,P21) s(P20,P21) s(P22,P21) s(P20,P22) s(P19,P22) s(P21,P23) s(P22,P23) s(P23,P24) s(P23,P25) s(P24,P25) s(P25,P26) s(P24,P26) s(P26,P27) s(P24,P27) s(P13,P27) s(P25,P28) s(P26,P28) s(P30,P28) s(P27,P29) s(P13,P29) s(P32,P29) s(P29,P30) s(P28,P31) s(P30,P31) s(P31,P32) s(P30,P32) s(P31,P33) s(P32,P33) s(P33,P34) s(P33,P35) s(P34,P35) s(P35,P36) s(P34,P36) s(P35,P37) s(P36,P37) s(P40,P37) s(P36,P38) s(P34,P38) s(P13,P38) s(P38,P39) s(P13,P39) s(P39,P40) s(P37,P41) s(P40,P41) s(P42,P41) s(P40,P42) s(P39,P42) s(P42,P43) s(P44,P43) s(P6,P44) s(P43,P45) s(P44,P45) s(P46,P45) s(P44,P46) s(P6,P46) s(P41,P47) s(P43,P47) s(P47,P48) s(P47,P49) s(P48,P49) s(P49,P50) s(P48,P50) s(P49,P51) s(P50,P51) s(P50,P52) s(P48,P52) s(P51,P53) s(P51,P54) s(P53,P54) s(P54,P55) s(P53,P55) s(P54,P56) s(P55,P56) s(P55,P57) s(P53,P57) s(P52,P57) s(P57,P58) s(P52,P58) s(P56,P59) s(P56,P60) s(P59,P60) s(P60,P61) s(P59,P61) s(P60,P62) s(P61,P62) s(P65,P62) s(P61,P63) s(P59,P63) s(P58,P63) s(P63,P64) s(P58,P64) s(P64,P65) s(P62,P66) s(P65,P66) s(P67,P66) s(P65,P67) s(P64,P67) s(P66,P68) s(P67,P68) s(P45,P69) s(P69,P70) s(P46,P70) s(P69,P71) s(P70,P71) s(P69,P72) s(P71,P72) s(P71,P73) s(P70,P73) s(P72,P74) s(P75,P74) s(P73,P75) s(P72,P76) s(P74,P76) s(P74,P77) s(P75,P77) s(P75,P78) s(P73,P78) s(P77,P78) s(P77,P79) s(P78,P79) s(P76,P80) s(P81,P80) s(P79,P81) s(P80,P82) s(P81,P82) s(P83,P82) s(P81,P83) s(P79,P83) s(P82,P84) s(P83,P84) s(P76,P85) s(P80,P85) s(P86,P85) s(P84,P86) s(P85,P87) s(P86,P87) s(P88,P87) s(P68,P87) s(P86,P88) s(P84,P88) s(P68,P88) color(blue) pen(2) m(P43,P47,MA10) m(P47,P48,MB10) f(P47,MA10,MB10) color(maroon) pen(2) color(gold) pen(2) m(P2,P1,MA30) m(P1,P3,MB30) f(P1,MA30,MB30) pen(2) color(red) s(P46,P70) abstand(P46,P70,A0) print(abs(P46,P70):,1.71,12.13) print(A0,3.01,12.13) \geooff \geoprint() und #487 geht auch noch \geo ebene(460.61,346.22) x(2.61,11.82) y(5.48,12.41) form(.) #//Eingabe war: #//blauerWinkel=104.87849569518802; gruenerWinkel=0; orangerWinkel=-15; #//No.487 #//blauerWinkel=104.87849569518802 #//orangerWinkel=55 #D=50; P[1]=[0,0]; P[2]=[D,0]; M(3,1,2,orangerWinkel); L(4,1,3); L(5,4,3); L(6,5,3); L(7,4,5); M(8,1,4,28.955024371859853); L(9,1,8); L(10,9,8); L(11,9,10); L(12,10,8); A(12,7); L(13,12,7); M(14,11,10,10.320021257740494); L(15,11,14); L(16,15,14); L(17,16,14); L(18,15,16); A(17,13); L(19,17,13); H(20,18,19,2); A(18,20); A(20,19); L(21,18,20); L(22,20,19); A(21,22); L(23,21,22); M(24,23,22,10.320021257740494); L(25,23,24); L(26,25,24); L(27,26,24); L(28,25,26); A(27,13); L(29,27,13); Q(30,28,29,2*D,D); A(28,30); H(31,28,30,2); A(28,31); A(31,30); L(32,28,31); L(33,31,30); A(32,33); L(34,32,33); Q(35,34,6,D,ab(34,5)); A(6,35); L(36,34,35); L(37,36,35); L(38,36,37); L(39,37,35); M(40,38,37,28.955024371859853); L(41,38,40); L(42,41,40); L(43,41,42); L(44,42,40); A(44,39); L(45,44,39); M(46,43,42,10.320021257740494); L(47,43,46); L(48,47,46); L(49,48,46); L(50,47,48); A(49,45); L(51,49,45); H(52,50,51,2); A(50,52); A(52,51); L(53,50,52); L(54,52,51); A(54,53); L(55,53,54); M(56,55,54,10.320021257740494); L(57,55,56); L(58,57,56); L(59,57,58); L(60,58,56); A(60,45); L(61,60,45); H(62,59,6,2); A(6,62); A(62,59); L(63,6,62); L(64,62,59); A(64,63); L(65,63,64); A(65,61); L(66,61,45); L(67,29,13); A(30,66); A(66,67); A(67,65); R(30,66); R(66,67); R(67,65); #//Ende der Eingabe, weiter mit fedgeo: p(4,6,P1) p(5,6,P2) p(4.965925826289068,5.741180954897479,P3) p(4.707106781186548,6.707106781186548,P4) p(5.673032607475616,6.448287736084026,P5) p(5.931851652578136,5.4823619097949585,P6) p(5.414213562373095,7.414213562373095,P7) p(4.2763918350975,6.961045031978958,P8) p(3.305906505674144,6.719884866582514,P9) p(3.5822983407716444,7.680929898561471,P10) p(2.611813011348289,7.439769733165027,P11) p(4.552783670195001,7.922090063957915,P12) p(5.42333256864167,8.414171983371025,P13) p(3.523395430822657,7.850887103882025,P14) p(2.711566134107488,8.434781951431612,P15) p(3.623148553581856,8.84589932214861,P16) p(4.434977850297025,8.262004474599022,P17) p(2.8113192568666867,9.429794169698194,P18) p(4.797374281242202,9.1940285230217,P19) p(3.8043467690544444,9.311911346359947,P20) p(3.4099225326413207,10.230839810240532,P21) p(4.402950044829079,10.112956986902283,P22) p(4.008525808415955,11.031885450782866,P23) p(4.561191613555561,10.198482482327995,P24) p(5.006606853257038,11.09380659360931,P25) p(5.559272658396644,10.260403625154439,P26) p(5.113857418695167,9.365079513873123,P27) p(6.004687898098121,11.155727736435754,P28) p(6.092105071733161,9.157639090315746,P29) p(7.0484984313623915,9.44972082828838,P30) p(6.526593164730256,10.302724282362067,P31) p(7.004363192157873,11.181209228671229,P32) p(7.526268458790009,10.328205774597542,P33) p(8.004038486217626,11.206690720906707,P34) p(8.262857531320147,10.240764894617637,P35) p(8.969964312506693,10.947871675804185,P36) p(9.228783357609213,9.981945849515117,P37) p(9.935890138795763,10.689052630701664,P38) p(8.521676576422667,9.27483906832857,P39) p(9.659498303698262,9.728007598722707,P40) p(10.629983633121618,9.969167764119153,P41) p(10.353591798024118,9.008122732140194,P42) p(11.324077127447474,9.249282897536638,P43) p(9.383106468600761,8.76696256674375,P44) p(8.512557570154092,8.27488064733064,P45) p(10.412494707973107,8.83816552681964,P46) p(11.224324004688276,8.254270679270054,P47) p(10.31274158521391,7.843153308553055,P48) p(9.50091228849874,8.42704815610264,P49) p(11.12457088192908,7.259258461003471,P50) p(9.13851585755356,7.495024107679961,P51) p(10.131543369741319,7.377141284341716,P52) p(10.525967606154445,6.4582128204611315,P53) p(9.532940093966687,6.576095643799378,P54) p(9.927364330379811,5.657167179918794,P55) p(9.374698525240206,6.490570148373664,P56) p(8.929283285538729,5.595246037092349,P57) p(8.376617480399123,6.42864900554722,P58) p(7.931202240697646,5.533324894265905,P59) p(8.822032720100598,7.323973116828535,P60) p(7.843785067062596,7.531413540385915,P61) p(6.9315269466378915,5.507843402030431,P62) p(6.409621680005758,6.360846856104121,P63) p(7.409296974065514,6.386328348339595,P64) p(6.88739170743338,7.239331802413285,P65) p(7.534309917116092,8.48232107088802,P66) p(6.401580221679666,8.206731559813647,P67) nolabel() s(P1,P3) s(P1,P4) s(P3,P4) s(P4,P5) s(P3,P5) s(P5,P6) s(P3,P6) s(P62,P6) s(P4,P7) s(P5,P7) s(P1,P8) s(P1,P9) s(P8,P9) s(P9,P10) s(P8,P10) s(P9,P11) s(P10,P11) s(P10,P12) s(P8,P12) s(P7,P12) s(P12,P13) s(P7,P13) s(P11,P14) s(P11,P15) s(P14,P15) s(P15,P16) s(P14,P16) s(P16,P17) s(P14,P17) s(P13,P17) s(P15,P18) s(P16,P18) s(P20,P18) s(P17,P19) s(P13,P19) s(P19,P20) s(P18,P21) s(P20,P21) s(P22,P21) s(P20,P22) s(P19,P22) s(P21,P23) s(P22,P23) s(P23,P24) s(P23,P25) s(P24,P25) s(P25,P26) s(P24,P26) s(P26,P27) s(P24,P27) s(P13,P27) s(P25,P28) s(P26,P28) s(P31,P28) s(P27,P29) s(P13,P29) s(P29,P30) s(P66,P30) s(P30,P31) s(P28,P32) s(P31,P32) s(P33,P32) s(P31,P33) s(P30,P33) s(P32,P34) s(P33,P34) s(P34,P35) s(P34,P36) s(P35,P36) s(P36,P37) s(P35,P37) s(P36,P38) s(P37,P38) s(P37,P39) s(P35,P39) s(P38,P40) s(P38,P41) s(P40,P41) s(P41,P42) s(P40,P42) s(P41,P43) s(P42,P43) s(P42,P44) s(P40,P44) s(P39,P44) s(P44,P45) s(P39,P45) s(P43,P46) s(P43,P47) s(P46,P47) s(P47,P48) s(P46,P48) s(P48,P49) s(P46,P49) s(P45,P49) s(P47,P50) s(P48,P50) s(P52,P50) s(P49,P51) s(P45,P51) s(P51,P52) s(P50,P53) s(P52,P53) s(P52,P54) s(P51,P54) s(P53,P54) s(P53,P55) s(P54,P55) s(P55,P56) s(P55,P57) s(P56,P57) s(P57,P58) s(P56,P58) s(P57,P59) s(P58,P59) s(P58,P60) s(P56,P60) s(P45,P60) s(P60,P61) s(P45,P61) s(P59,P62) s(P6,P63) s(P62,P63) s(P62,P64) s(P59,P64) s(P63,P64) s(P63,P65) s(P64,P65) s(P61,P65) s(P61,P66) s(P45,P66) s(P67,P66) s(P29,P67) s(P13,P67) s(P65,P67) color(blue) pen(2) color(maroon) pen(2) color(gold) pen(2) m(P2,P1,MA30) m(P1,P3,MB30) f(P1,MA30,MB30) pen(2) color(red) s(P30,P66) abstand(P30,P66,A0) print(abs(P30,P66):,2.61,12.407) print(A0,3.91,12.407) color(red) s(P66,P67) abstand(P66,P67,A1) print(abs(P66,P67):,2.61,12.107) print(A1,3.91,12.107) color(red) s(P67,P65) abstand(P67,P65,A2) print(abs(P67,P65):,2.61,11.807) print(A2,3.91,11.807) \geooff \geoprint()


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haribo
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  Beitrag No.489, eingetragen 2016-08-13

hi stefan #475-2 hatte ich schon in #128 auf eine stabile version reduziert, das ist immer noch der aktuelle rekord 4/10 der ist auch asymetrisch, besteht halt aus lauter kites, drum hatte slash ihm, vorübergehend, die asymetrie-medaille aberkannt


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Slash
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  Beitrag No.490, vom Themenstarter, eingetragen 2016-08-13

Wie immer vielen Dank für deine Prüfungen Stefan! :-) Der 4/10 wurde ja nach Überarbeitung der Definition offiziell rehabilitiert als einziger bekannter kleinster und komplett asymmetrischer Graph. :-) Apropos komplett asymmetrisch: Das ganze läuft natürlich auf ein neues Paper hinaus, welches schon fast fertig ist - in seiner ersten Version. Alles weitere dazu werden wir drei dann persönlich per Mail besprechen und austauschen - ohne MP Publikum. :-) Gruß, Slash PS: Es darf noch gerne am 4/8-asym geforscht werden. Vielleicht gibt es ja eine Version ganz ohne Doppel-Kite-Klammer.


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Slash
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  Beitrag No.491, vom Themenstarter, eingetragen 2016-08-14

Der 4/11 mit 817 Kanten komplett asymmetrisch zum ersten Mal mit genauen Winkeln bei den 11er-Knoten. http://www.matheplanet.de/matheplanet/nuke/html/uploads/a/8038_4_11_mit_817_kom_asym_slash_stefan.png


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haribo
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  Beitrag No.492, eingetragen 2016-08-15

\quoteon(2016-08-11 07:12 - Slash in Beitrag No. 475) Ein komplett asymmetrischer (4,n)-regulärer Streichholzgraph Die Fälle n=4, n=5, n=6, n=7 und n=11 sind (fürs erste) erledigt. \quoteoff ist diese liste der unsymetrischen correkt? 4/4 126 4/5 126 4/6 121 4/7 ??? (159+104=263) 4/8 176 4/9 277 4/10 231 4/11 817


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Slash
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  Beitrag No.493, vom Themenstarter, eingetragen 2016-08-15

Meine Liste komplett unsymmetrischer Graphen ist 4/4 132 4/5 125 4/6 128 - zwei Versionen 4/7 185 4/8 176 4/9 277 4/10 231 4/11 817 Welche Graphen hattest du bei n=4, 5 und 6 im Sinn? Gruß, Slash


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Slash
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  Beitrag No.494, vom Themenstarter, eingetragen 2016-08-15

Meine Liste komplett unsymmetrischer Graphen ist 4/4 132 4/5 125 4/6 128 - zwei Versionen 4/7 185 4/8 176 4/9 277 4/10 231 4/11 817 Welche Graphen hattest du bei n=4, 5 und 6 im Sinn? "Nur" unsymmetrische Graphen wären 4/4 126 4/5 121 - mehrere Versionen 4/6 121 - mehrere Versionen 4/7 159 - unendlich viele Versionen, da flexibel 4/8 168 - oder weniger, vielleicht auch nur 126? 4/9 273 4/10 231 4/11 811 Bei n=4, 9 und 11 braucht man nur eine Doppel-Kite-Klammer unsymmetrisch gestalten. Gruß, Slash


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haribo
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  Beitrag No.495, eingetragen 2016-08-16

ok, dann fehlt mir im moment nur der 132iger mit 4/4 sowie die definition für "komplett" unsymetrisch grus haribo


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Slash
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  Beitrag No.496, vom Themenstarter, eingetragen 2016-08-16

4/4 mit 132 komp. asym. Definition eines komplett unsymmetrischen Graphen: 1) starr 2) keine Punkt-, Rotations-, oder Spiegelsymmetrie 3) keine symmetrische äußere Form (siehe 2) 4) kann nicht in starre Teilgraphen zerlegt und neuartig zusammengesetzt werden, so dass mind. einer der drei ersten Punkte nicht erfüllt ist


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StefanVogel
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  Beitrag No.497, eingetragen 2016-09-03

\quoteon(2016-08-29 01:18 - Slash) Die roten Strecken sind gleich lang und messen ca. 6,854. Die grüne Strecken sind gleich lang und messen ca. 5,854, sind also genau eine Kantenlänge kürzer. Alle Strecken sind parallel bei ca. 15,52 Grad. http://www.matheplanet.de/matheplanet/nuke/html/uploads/a/8038_Figur_8_-_4_7_b.png \quoteoff \quoteon(2016-08-29 01:06 - Slash) Beim 4/7 sind alle Kanten parallel, die parallel erscheinen. Die blauen Kanten und die roten Strecken liegen parallel bei ca. 15,52 Grad. Vielleicht hilt das beim Geometriebeweis. http://www.matheplanet.de/matheplanet/nuke/html/uploads/a/8038_Figur_8_-_4_7_a.png \quoteoff Alles sehr aussichtsreiche Anzeichen dafür, dass der Graph irgendwie systematisch aufgebaut ist und deshalb jede Kante exakt Länge 1 hat. Es lässt sich weiter verfeinern, beispielsweise sieht es in der nächsten Darstellung so aus, als ob der rechte blauen Kantenzug durch eine Parallelverschiebung aus dem linken entstanden ist. Das hätte zur Folge, dass auch der rote Kantenzug durch eine Parallelverschiebung aus dem grünen Kantenzug erzeugt werden kann. Das wiederum ist wichtig, wenn bewiesen werden muss, dass auch die inneren Verbindungen zwischen linken und rechten Teilgraph exakt Kantenlänge 1 haben. \geo ebene(540.88,416.89) x(1.57,12.39) y(5.3,13.64) form(.) #//Eingabe war: #//blauerWinkel=15.522486812413007; gruenerWinkel=104.47751274368893; orangerWinkel=15.5224878898908; #//Figure 8: 91 185 #//blauerWinkel=15.522486812413007 #//gruenerWinkel=104.47751274368893 #//orangerWinkel=15.5224878898908 #D=50; P[1]=[0,0]; P[2]=[D,0]; A(2,1); L(3,1,2); L(4,3,2); L(5,4,2); M(6,1,3,blauerWinkel,2);N(10,6,3); R(62,50); R(87,13); N(11,10,4); N(12,11,5); L(13,12,5); L(14,10,11); M(15,9,8,60-blauerWinkel); N(16,15,8); N(17,16,14); L(18,17,14); L(19,17,18); L(20,9,15); L(21,20,15); L(22,20,21); N(23,21,16); N(24,22,23); L(25,22,24); L(26,25,24); L(27,25,26); N(28,26,23); A(28,19); R(28,19); N(29,27,28); L(30,27,29); L(31,30,29); L(32,30,31); N(33,31,19); N(34,32,33); L(35,32,34); L(36,35,34); L(37,35,36); N(38,36,33); N(39,37,38); L(40,37,39); L(41,40,39); L(42,40,41); N(43,41,38); N(44,42,43); L(45,42,44); L(46,45,44); L(47,45,46); N(48,46,43); N(49,48,18); L(50,48,49); M(51,47,46,gruenerWinkel,2); M(55,54,53,orangerWinkel,2); N(59,55,53); N(60,59,51); L(61,59,60); L(62,61,60); A(62,50); L(63,62,50); N(64,63,49); R(61,57); H(65,61,57,2); A(61,65); A(65,57); N(66,58,65); L(67,58,66); L(68,67,66); L(69,67,68); N(70,68,65); A(70,61); R(70,61); N(71,69,70); L(72,69,71); Q(73,71,61,ab(12,14,11),D); N(75,72,74); L(76,72,75); L(77,76,75); L(78,76,77); N(79,77,74); A(79,73); R(79,73); N(80,78,79); L(81,78,80); L(82,81,80); L(83,81,82); R(82,73); H(84,82,73,2); A(82,84); A(84,73); N(85,83,84); L(86,83,85); L(87,86,85); N(88,87,84); A(88,73); R(88,73); L(89,73,61); A(89,63); R(89,63); L(90,73,89); R(12,64); A(86,13); A(13,87); R(86,13); H(91,12,64,2); A(12,91); A(91,64); L(92,64,91); L(93,92,91); A(92,90); A(93,90); R(92,90); R(90,93); A(93,88); R(93,88); # #//Ende der Eingabe, weiter mit fedgeo: p(4,6,P1) p(5,6,P2) p(4.5,6.866025403784438,P3) p(5.5,6.866025403784438,P4) p(6,6,P5) nolabel() p(4.250000016927081,6.9682458321813,P6) p(3.28647452068613,6.700629281696042,P7,label) p(3.5364745376132105,7.668875113877343,P8) p(2.5729490413722598,7.4012585633920835,P9,label) p(4.750000016927081,7.83427123596574,P10) p(5.750000016927081,7.834271235965739,P11) p(6.25000001692708,6.9682458321813,P12,label) p(6.963525496240951,6.267616550485259,P13,label) p(5.250000016927081,8.700296639750178,P14) p(3.0729490413722593,8.267283967176523,P15) p(4.03647453761321,8.534900517661782,P16) p(4.536474537613211,9.40092592144622,P17) p(5.500000033854162,9.66854247193148,P18) p(4.786474554540291,10.369171753627521,P19) p(2.0729490413722598,8.267283967176523,P20,label) p(2.5729490413722598,9.133309370960962,P21) p(1.5729490413722598,9.133309370960962,P22,label) p(3.5364745376132105,9.40092592144622,P23) p(2.5364745376132105,9.40092592144622,P24,label) p(1.82294905829934,10.101555203142262,P25,label) p(2.7864745545402902,10.369171753627521,P26) p(2.0729490752264197,11.069801035323561,P27,label) p(3.7864745545402902,10.369171753627521,P28) p(3.0729490752264197,11.069801035323563,P29) p(2.5729490752264192,11.935826439108,P30,label) p(3.5729490752264184,11.935826439108002,P31) p(3.072949075226418,12.801851842892438,P32,label) p(4.286474554540285,11.235197157411957,P33) p(3.786474554540288,12.101222561196396,P34,label) p(4.036474571467369,13.069468393377697,P35,label) p(4.75000005078124,12.368839111681655,P36) p(5.000000067708321,13.337084943862955,P37,label) p(5.250000050781236,11.502813707897214,P38) p(5.500000067708317,12.471059540078516,P39) p(6.00000006770832,13.337084943862951,P40,label) p(6.500000067708317,12.471059540078514,P41) p(7.000000067708319,13.337084943862948,P42,label) p(6.250000050781236,11.502813707897213,P43) p(6.750000050781243,12.368839111681647,P44,label) p(7.7135255470221935,12.636455662166911,P45,label) p(7.463525530095118,11.66820982998561,P46,label) p(8.427051026336068,11.935826380470875,P47,label) p(6.9635255300951115,10.802184426201174,P48) p(6.463525530095113,9.936159022416733,P49) p(7.463525530095113,9.936159022416737,P50) p(8.927051019626557,11.069800972812697,P51) p(9.427051026336068,11.935826372723398,P52,label) p(9.927051019626557,11.06980096506522,P53) p(10.427051026336066,11.93582636497592,P54,label) p(10.177051020115906,10.967580530030105,P55) p(11.140576513397537,11.235197091170088,P56,label) p(10.890576507177377,10.266951256224273,P57) p(11.854102000459008,10.534567817364255,P58,label) p(9.677051013406395,10.101555130119404,P59) p(8.677051013406395,10.101555137866882,P60) p(9.177051006696882,9.235529730208704,P61) p(8.177051006696882,9.235529737956181,P62) p(7.213525509417843,8.967913191201928,P63) p(6.213525509417843,8.967913191203728,P64,label) p(10.033813756937128,9.75124049321649,P65) p(10.997339249578108,10.018857056663071,P66) p(11.87233924479078,9.534734129734565,P67,label) p(11.01557649390988,9.019023369033382,P68) p(11.890576489122552,8.534900442104876,P69,label) p(10.0520510012689,8.751406805586798,P70) p(10.927050996481572,8.267283878658292,P71) p(11.640576485220294,7.566654606560579,P72,label) p(8.927050996481572,8.267283896294431,P73,label) p(9.927050996481572,8.267283887476362,P74) p(10.640576485220294,7.566654615378649,P75) p(11.14057647758362,6.700629207185176,P76,label) p(10.14057647758362,6.700629216003246,P77) p(10.640576469946947,5.834603807809772,P78,label) p(9.4270509888449,7.401258488100958,P79) p(9.927050981208225,6.535233079907483,P80) p(9.677050977305969,5.566987244363187,P81,label) p(8.963525488567246,6.2676165164608975,P82,label) p(8.71352548466499,5.299370680916601,P83,label) p(8.94528824252441,7.2674502063776645,P84) p(8.695288247008406,6.299204368668048,P85) p(7.838525492684466,5.7834936136868675,P86,label) p(7.820288255027881,6.783327301438314,P87,label) p(8.070288250543886,7.751573139147931,P88) p(8.21352551231102,8.967913173044396,P89) p(7.963525502095709,7.999667339130124,P90,label) p(6.231762763172462,7.968079511692514,P91) p(7.088525502311132,8.483790276494883,P92) p(7.10676275606575,7.4839565969836706,P93) nolabel() s(P1,P2) s(P1,P3) s(P2,P3) s(P3,P4) s(P2,P4) s(P4,P5) s(P2,P5) s(P1,P6) s(P1,P7) s(P6,P7) s(P7,P8) s(P6,P8) s(P7,P9) s(P8,P9) s(P6,P10) s(P3,P10) s(P10,P11) s(P4,P11) s(P11,P12) s(P5,P12) s(P91,P12) s(P12,P13) s(P5,P13) s(P87,P13) s(P10,P14) s(P11,P14) s(P9,P15) s(P15,P16) s(P8,P16) s(P16,P17) s(P14,P17) s(P17,P18) s(P14,P18) s(P17,P19) s(P18,P19) s(P9,P20) s(P15,P20) s(P20,P21) s(P15,P21) s(P20,P22) s(P21,P22) s(P21,P23) s(P16,P23) s(P22,P24) s(P23,P24) s(P22,P25) s(P24,P25) s(P25,P26) s(P24,P26) s(P25,P27) s(P26,P27) s(P26,P28) s(P23,P28) s(P19,P28) s(P27,P29) s(P28,P29) s(P27,P30) s(P29,P30) s(P30,P31) s(P29,P31) s(P30,P32) s(P31,P32) s(P31,P33) s(P19,P33) s(P32,P34) s(P33,P34) s(P32,P35) s(P34,P35) s(P35,P36) s(P34,P36) s(P35,P37) s(P36,P37) s(P36,P38) s(P33,P38) s(P37,P39) s(P38,P39) s(P37,P40) s(P39,P40) s(P40,P41) s(P39,P41) s(P40,P42) s(P41,P42) s(P41,P43) s(P38,P43) s(P42,P44) s(P43,P44) s(P42,P45) s(P44,P45) s(P45,P46) s(P44,P46) s(P45,P47) s(P46,P47) s(P46,P48) s(P43,P48) s(P48,P49) s(P18,P49) s(P48,P50) s(P49,P50) s(P47,P51) s(P47,P52) s(P51,P52) s(P52,P53) s(P51,P53) s(P52,P54) s(P53,P54) s(P54,P55) s(P54,P56) s(P55,P56) s(P56,P57) s(P55,P57) s(P56,P58) s(P57,P58) s(P55,P59) s(P53,P59) s(P59,P60) s(P51,P60) s(P59,P61) s(P60,P61) s(P65,P61) s(P61,P62) s(P60,P62) s(P50,P62) s(P62,P63) s(P50,P63) s(P63,P64) s(P49,P64) s(P57,P65) s(P58,P66) s(P65,P66) s(P58,P67) s(P66,P67) s(P67,P68) s(P66,P68) s(P67,P69) s(P68,P69) s(P68,P70) s(P65,P70) s(P61,P70) s(P69,P71) s(P70,P71) s(P74,P71) s(P69,P72) s(P71,P72) s(P74,P73) s(P61,P73) s(P72,P75) s(P74,P75) s(P72,P76) s(P75,P76) s(P76,P77) s(P75,P77) s(P76,P78) s(P77,P78) s(P77,P79) s(P74,P79) s(P73,P79) s(P78,P80) s(P79,P80) s(P78,P81) s(P80,P81) s(P81,P82) s(P80,P82) s(P84,P82) s(P81,P83) s(P82,P83) s(P73,P84) s(P83,P85) s(P84,P85) s(P83,P86) s(P85,P86) s(P13,P86) s(P86,P87) s(P85,P87) s(P87,P88) s(P84,P88) s(P73,P88) s(P73,P89) s(P61,P89) s(P63,P89) s(P73,P90) s(P89,P90) s(P64,P91) s(P64,P92) s(P91,P92) s(P90,P92) s(P92,P93) s(P91,P93) s(P90,P93) s(P88,P93) pen(2) color(blue) s(P64,P12) s(P13,P12) s(P81,P82) s(P82,P73) color(maroon) s(P13,P83) s(P83,P81) color(red) s(P64,P90) s(P90,P73) \geooff \geoprint() Es hilft auch, Teile des Graphen zur Überdeckung zu bringen, beispielsweise kann man den rechten Teilgraph spiegeln und so auf den linken Teilgraph legen, dass Punkt P13 auf P5 zu liegen kommt, P86 auf P2 und so weiter, \geo ebene(540.88,416.89) x(1.57,12.39) y(5.3,13.64) form(.) #//Eingabe war: #//blauerWinkel=15.522486812413007; gruenerWinkel=104.47751274368893; orangerWinkel=15.5224878898908; #//Figure 8: 91 185 #//blauerWinkel=15.522486812413007 #//gruenerWinkel=104.47751274368893 #//orangerWinkel=15.5224878898908 #D=50; P[1]=[0,0]; P[2]=[D,0]; A(2,1); L(3,1,2); L(4,3,2); L(5,4,2); M(6,1,3,blauerWinkel,2);N(10,6,3); R(62,50); R(87,13); N(11,10,4); N(12,11,5); L(13,12,5); L(14,10,11); M(15,9,8,60-blauerWinkel); N(16,15,8); N(17,16,14); L(18,17,14); L(19,17,18); L(20,9,15); L(21,20,15); L(22,20,21); N(23,21,16); N(24,22,23); L(25,22,24); L(26,25,24); L(27,25,26); N(28,26,23); A(28,19); R(28,19); N(29,27,28); L(30,27,29); L(31,30,29); L(32,30,31); N(33,31,19); N(34,32,33); L(35,32,34); L(36,35,34); L(37,35,36); N(38,36,33); N(39,37,38); L(40,37,39); L(41,40,39); L(42,40,41); N(43,41,38); N(44,42,43); L(45,42,44); L(46,45,44); L(47,45,46); N(48,46,43); N(49,48,18); L(50,48,49); M(51,47,46,gruenerWinkel,2); M(55,54,53,orangerWinkel,2); N(59,55,53); N(60,59,51); L(61,59,60); L(62,61,60); A(62,50); L(63,62,50); N(64,63,49); R(61,57); H(65,61,57,2); A(61,65); A(65,57); N(66,58,65); L(67,58,66); L(68,67,66); L(69,67,68); N(70,68,65); A(70,61); R(70,61); N(71,69,70); L(72,69,71); Q(73,71,61,ab(12,14,11),D); N(75,72,74); L(76,72,75); L(77,76,75); L(78,76,77); N(79,77,74); A(79,73); R(79,73); N(80,78,79); L(81,78,80); L(82,81,80); L(83,81,82); R(82,73); H(84,82,73,2); A(82,84); A(84,73); N(85,83,84); L(86,83,85); L(87,86,85); N(88,87,84); A(88,73); R(88,73); L(89,73,61); A(89,63); R(89,63); L(90,73,89); R(12,64); A(86,13); A(13,87); R(86,13); H(91,12,64,2); A(12,91); A(91,64); L(92,64,91); L(93,92,91); A(92,90); A(93,90); R(92,90); R(90,93); A(93,88); R(93,88); # #//Ende der Eingabe, weiter mit fedgeo: p(4,6,P1) p(5,6,P2) p(4.5,6.866025403784438,P3) p(5.5,6.866025403784438,P4) p(6,6,P5) nolabel() p(4.250000016927081,6.9682458321813,P6) p(3.28647452068613,6.700629281696042,P7,label) p(3.5364745376132105,7.668875113877343,P8) p(2.5729490413722598,7.4012585633920835,P9,label) p(4.750000016927081,7.83427123596574,P10) p(5.750000016927081,7.834271235965739,P11) p(6.25000001692708,6.9682458321813,P12,label) p(6.963525496240951,6.267616550485259,P13,label) p(5.250000016927081,8.700296639750178,P14) p(3.0729490413722593,8.267283967176523,P15) p(4.03647453761321,8.534900517661782,P16) p(4.536474537613211,9.40092592144622,P17) p(5.500000033854162,9.66854247193148,P18) p(4.786474554540291,10.369171753627521,P19) p(2.0729490413722598,8.267283967176523,P20,label) p(2.5729490413722598,9.133309370960962,P21) p(1.5729490413722598,9.133309370960962,P22,label) p(3.5364745376132105,9.40092592144622,P23) p(2.5364745376132105,9.40092592144622,P24,label) p(1.82294905829934,10.101555203142262,P25,label) p(2.7864745545402902,10.369171753627521,P26) p(2.0729490752264197,11.069801035323561,P27,label) p(3.7864745545402902,10.369171753627521,P28) p(3.0729490752264197,11.069801035323563,P29) p(2.5729490752264192,11.935826439108,P30,label) p(3.5729490752264184,11.935826439108002,P31) p(3.072949075226418,12.801851842892438,P32,label) p(4.286474554540285,11.235197157411957,P33) p(3.786474554540288,12.101222561196396,P34,label) p(4.036474571467369,13.069468393377697,P35,label) p(4.75000005078124,12.368839111681655,P36) p(5.000000067708321,13.337084943862955,P37,label) p(5.250000050781236,11.502813707897214,P38) p(5.500000067708317,12.471059540078516,P39) p(6.00000006770832,13.337084943862951,P40,label) p(6.500000067708317,12.471059540078514,P41) p(7.000000067708319,13.337084943862948,P42,label) p(6.250000050781236,11.502813707897213,P43) p(6.750000050781243,12.368839111681647,P44,label) p(7.7135255470221935,12.636455662166911,P45,label) p(7.463525530095118,11.66820982998561,P46,label) p(8.427051026336068,11.935826380470875,P47,label) p(6.9635255300951115,10.802184426201174,P48) p(6.463525530095113,9.936159022416733,P49) p(7.463525530095113,9.936159022416737,P50) p(8.927051019626557,11.069800972812697,P51) p(9.427051026336068,11.935826372723398,P52,label) p(9.927051019626557,11.06980096506522,P53) p(10.427051026336066,11.93582636497592,P54,label) p(10.177051020115906,10.967580530030105,P55) p(11.140576513397537,11.235197091170088,P56,label) p(10.890576507177377,10.266951256224273,P57) p(11.854102000459008,10.534567817364255,P58,label) p(9.677051013406395,10.101555130119404,P59) p(8.677051013406395,10.101555137866882,P60) p(9.177051006696882,9.235529730208704,P61) p(8.177051006696882,9.235529737956181,P62) p(7.213525509417843,8.967913191201928,P63) p(6.213525509417843,8.967913191203728,P64,label) p(10.033813756937128,9.75124049321649,P65) p(10.997339249578108,10.018857056663071,P66) p(11.87233924479078,9.534734129734565,P67,label) p(11.01557649390988,9.019023369033382,P68) p(11.890576489122552,8.534900442104876,P69,label) p(10.0520510012689,8.751406805586798,P70) p(10.927050996481572,8.267283878658292,P71) p(11.640576485220294,7.566654606560579,P72,label) p(8.927050996481572,8.267283896294431,P73,label) p(9.927050996481572,8.267283887476362,P74) p(10.640576485220294,7.566654615378649,P75) p(11.14057647758362,6.700629207185176,P76,label) p(10.14057647758362,6.700629216003246,P77) p(10.640576469946947,5.834603807809772,P78,label) p(9.4270509888449,7.401258488100958,P79) p(9.927050981208225,6.535233079907483,P80) p(9.677050977305969,5.566987244363187,P81,label) p(8.963525488567246,6.2676165164608975,P82,label) p(8.71352548466499,5.299370680916601,P83,label) p(8.94528824252441,7.2674502063776645,P84) p(8.695288247008406,6.299204368668048,P85) p(7.838525492684466,5.7834936136868675,P86,label) p(7.820288255027881,6.783327301438314,P87,label) p(8.070288250543886,7.751573139147931,P88) p(8.21352551231102,8.967913173044396,P89) p(7.963525502095709,7.999667339130124,P90,label) p(6.231762763172462,7.968079511692514,P91) p(7.088525502311132,8.483790276494883,P92) p(7.10676275606575,7.4839565969836706,P93) p(8.195288262734259,9.967746874861847,P94) p(8.213525502023934,8.967913187140187,P95) p(7.33852550925266,9.452036118481264,P96) p(6.606762780608984,11.152499066967277,P97) p(6.588525533573113,12.152332754547647,P98) p(5.731762784086984,11.63662199152931,P99) p(5.713525537051115,12.636455679109677,P100) p(5.46352552881382,11.668209844684682,P101) p(4.7500000432119664,12.368839119976997,P102) p(4.500000034974669,11.400593285552002,P103) p(3.7864745493728096,12.101222560844317,P104) p(5.481762775849687,10.668376157104316,P105) p(6.356762772371692,10.184253232542284,P106) p(5.500000022885552,9.668542469523949,P107) p(6.375000019407549,9.18441954496192,P108) p(7.088525515471608,8.48379028032188,P109) p(7.963525508243752,7.999667348982382,P110) p(5.00000002893011,10.534567877537976,P111) p(4.286474545005503,11.235197154538408,P112) p(3.286474545005503,11.235197159581343,P113) p(3.7864745406381917,10.369171753275436,P114) p(2.7864745406381948,10.369171758318371,P115) p(4.500000024562803,9.668542476275004,P116) p(3.5000000245628025,9.668542481317935,P117) p(2.536474530082997,9.400925924491856,P118) p(5.2500000186434095,8.700296634067413,P119) p(4.375000021603105,9.184419557692674,P120) p(3.4114745271232976,8.916803000866594,P121) p(2.5547117781892776,8.401092236931015,P122) p(3.4297117752295803,7.916969313305755,P123) p(2.5729490262955586,7.401258549370175,P124) p(4.393237269709384,8.184585870131833,P125) p(3.536474520775365,7.668875106196252,P126) p(3.2864745102201662,6.700629272369738,P127) p(4.250000004699973,6.968245829195814,P128) p(3.999999994144775,5.9999999953693,P129) p(4.750000011671691,7.834271231631613,P130) p(4.49999999273024,6.866025399970421,P131) p(4.999999994144774,5.999999997002664,P132) p(5.49999999273024,6.8660254016037845,P133) p(5.750000011671689,7.834271233264977,P134) p(6.213525511378326,8.967913197175767,P135) p(5.963525507136185,7.999667361719229,P136) p(7.463525499561793,7.133641959384893,P137) p(6.963525516189028,7.9996673635946545,P138) p(6.4635255075070726,7.133641973997165,P139) nolabel() s(P1,P2) s(P1,P3) s(P2,P3) s(P3,P4) s(P2,P4) s(P4,P5) s(P2,P5) s(P1,P6) s(P1,P7) s(P6,P7) s(P7,P8) s(P6,P8) s(P7,P9) s(P8,P9) s(P6,P10) s(P3,P10) s(P10,P11) s(P4,P11) s(P11,P12) s(P5,P12) s(P91,P12) s(P12,P13) s(P5,P13) s(P87,P13) s(P10,P14) s(P11,P14) s(P9,P15) s(P15,P16) s(P8,P16) s(P16,P17) s(P14,P17) s(P17,P18) s(P14,P18) s(P17,P19) s(P18,P19) s(P9,P20) s(P15,P20) s(P20,P21) s(P15,P21) s(P20,P22) s(P21,P22) s(P21,P23) s(P16,P23) s(P22,P24) s(P23,P24) s(P22,P25) s(P24,P25) s(P25,P26) s(P24,P26) s(P25,P27) s(P26,P27) s(P26,P28) s(P23,P28) s(P19,P28) s(P27,P29) s(P28,P29) s(P27,P30) s(P29,P30) s(P30,P31) s(P29,P31) s(P30,P32) s(P31,P32) s(P31,P33) s(P19,P33) s(P32,P34) s(P33,P34) s(P32,P35) s(P34,P35) s(P35,P36) s(P34,P36) s(P35,P37) s(P36,P37) s(P36,P38) s(P33,P38) s(P37,P39) s(P38,P39) s(P37,P40) s(P39,P40) s(P40,P41) s(P39,P41) s(P40,P42) s(P41,P42) s(P41,P43) s(P38,P43) s(P42,P44) s(P43,P44) s(P42,P45) s(P44,P45) s(P45,P46) s(P44,P46) s(P45,P47) s(P46,P47) s(P46,P48) s(P43,P48) s(P48,P49) s(P18,P49) s(P48,P50) s(P49,P50) s(P47,P51) s(P47,P52) s(P51,P52) s(P52,P53) s(P51,P53) s(P52,P54) s(P53,P54) s(P54,P55) s(P54,P56) s(P55,P56) s(P56,P57) s(P55,P57) s(P56,P58) s(P57,P58) s(P55,P59) s(P53,P59) s(P59,P60) s(P51,P60) s(P59,P61) s(P60,P61) s(P65,P61) s(P61,P62) s(P60,P62) s(P50,P62) s(P62,P63) s(P50,P63) s(P63,P64) s(P49,P64) s(P57,P65) s(P58,P66) s(P65,P66) s(P58,P67) s(P66,P67) s(P67,P68) s(P66,P68) s(P67,P69) s(P68,P69) s(P68,P70) s(P65,P70) s(P61,P70) s(P69,P71) s(P70,P71) s(P74,P71) s(P69,P72) s(P71,P72) s(P74,P73) s(P61,P73) s(P72,P75) s(P74,P75) s(P72,P76) s(P75,P76) s(P76,P77) s(P75,P77) s(P76,P78) s(P77,P78) s(P77,P79) s(P74,P79) s(P73,P79) s(P78,P80) s(P79,P80) s(P78,P81) s(P80,P81) s(P81,P82) s(P80,P82) s(P84,P82) s(P81,P83) s(P82,P83) s(P73,P84) s(P83,P85) s(P84,P85) s(P83,P86) s(P85,P86) s(P13,P86) s(P86,P87) s(P85,P87) s(P87,P88) s(P84,P88) s(P73,P88) s(P73,P89) s(P61,P89) s(P63,P89) s(P73,P90) s(P89,P90) s(P64,P91) s(P64,P92) s(P91,P92) s(P90,P92) s(P92,P93) s(P91,P93) s(P90,P93) s(P88,P93) pen(2) color(gold) s(P94,P95) s(P94,P96) s(P95,P96) s(P46,P97) s(P46,P98) s(P97,P98) s(P97,P99) s(P98,P99) s(P98,P100) s(P99,P100) s(P100,P101) s(P100,P102) s(P101,P102) s(P101,P103) s(P102,P103) s(P102,P104) s(P103,P104) s(P99,P105) s(P101,P105) s(P97,P106) s(P105,P106) s(P105,P107) s(P106,P107) s(P111,P107) s(P96,P108) s(P106,P108) s(P107,P108) s(P96,P109) s(P108,P109) s(P95,P110) s(P109,P110) s(P103,P111) s(P104,P112) s(P111,P112) s(P104,P113) s(P112,P113) s(P112,P114) s(P113,P114) s(P113,P115) s(P114,P115) s(P107,P116) s(P111,P116) s(P114,P116) s(P115,P117) s(P116,P117) s(P120,P117) s(P115,P118) s(P117,P118) s(P107,P119) s(P120,P119) s(P118,P121) s(P120,P121) s(P118,P122) s(P121,P122) s(P121,P123) s(P122,P123) s(P122,P124) s(P123,P124) s(P119,P125) s(P120,P125) s(P123,P125) s(P124,P126) s(P125,P126) s(P124,P127) s(P126,P127) s(P126,P128) s(P127,P128) s(P130,P128) s(P127,P129) s(P128,P129) s(P119,P130) s(P129,P131) s(P130,P131) s(P5,P132) s(P129,P132) s(P131,P132) s(P131,P133) s(P132,P133) s(P119,P134) s(P130,P134) s(P133,P134) s(P107,P135) s(P109,P135) s(P119,P135) s(P119,P136) s(P135,P136) s(P110,P137) s(P110,P138) s(P136,P138) s(P137,P138) s(P134,P139) s(P136,P139) s(P137,P139) s(P138,P139) \geooff \geoprint() und es sieht ganz danach aus, dass P72 genau auf P24 zu liegen kommt und P58 auf P34 und P47 auf P46. Das beweist dann Strecke P5-P13 ist parallel Strecke P46-P47. Die Punktbezeichnungen sind nicht so leicht erkenn- und auffindbar, im Streichholzprogramm kann man dafür die Browser-Suchfunktion verwenden. Dass P72 genau auf P24 landet, hat mich dann auf eine weitere Beweismöglichkeit gebracht. Dann wäre das grüne Dreieck P22-P9-P24 in der nachfolgenden Darstellung ein gleichschenkliges Dreieck mit den beiden gleichlangen Seiten P22-P9 und P24-P9. \geo ebene(540.88,416.89) x(1.57,12.39) y(5.3,13.64) form(.) #//Eingabe war: #//blauerWinkel=15.522486812413007; gruenerWinkel=104.47751274368893; orangerWinkel=15.5224878898908; #//Figure 8: 91 185 #//blauerWinkel=15.522486812413007 #//gruenerWinkel=104.47751274368893 #//orangerWinkel=15.5224878898908 #D=50; P[1]=[0,0]; P[2]=[D,0]; A(2,1); L(3,1,2); L(4,3,2); L(5,4,2); M(6,1,3,blauerWinkel,2);N(10,6,3); R(62,50); R(87,13); N(11,10,4); N(12,11,5); L(13,12,5); L(14,10,11); M(15,9,8,60-blauerWinkel); N(16,15,8); N(17,16,14); L(18,17,14); L(19,17,18); L(20,9,15); L(21,20,15); L(22,20,21); N(23,21,16); N(24,22,23); L(25,22,24); L(26,25,24); L(27,25,26); N(28,26,23); A(28,19); R(28,19); N(29,27,28); L(30,27,29); L(31,30,29); L(32,30,31); N(33,31,19); N(34,32,33); L(35,32,34); L(36,35,34); L(37,35,36); N(38,36,33); N(39,37,38); L(40,37,39); L(41,40,39); L(42,40,41); N(43,41,38); N(44,42,43); L(45,42,44); L(46,45,44); L(47,45,46); N(48,46,43); N(49,48,18); L(50,48,49); M(51,47,46,gruenerWinkel,2); M(55,54,53,orangerWinkel,2); N(59,55,53); N(60,59,51); L(61,59,60); L(62,61,60); A(62,50); L(63,62,50); N(64,63,49); R(61,57); H(65,61,57,2); A(61,65); A(65,57); N(66,58,65); L(67,58,66); L(68,67,66); L(69,67,68); N(70,68,65); A(70,61); R(70,61); N(71,69,70); L(72,69,71); Q(73,71,61,ab(12,14,11),D); N(75,72,74); L(76,72,75); L(77,76,75); L(78,76,77); N(79,77,74); A(79,73); R(79,73); N(80,78,79); L(81,78,80); L(82,81,80); L(83,81,82); R(82,73); H(84,82,73,2); A(82,84); A(84,73); N(85,83,84); L(86,83,85); L(87,86,85); N(88,87,84); A(88,73); R(88,73); L(89,73,61); A(89,63); R(89,63); L(90,73,89); R(12,64); A(86,13); A(13,87); R(86,13); H(91,12,64,2); A(12,91); A(91,64); L(92,64,91); L(93,92,91); A(92,90); A(93,90); R(92,90); R(90,93); A(93,88); R(93,88); # #//Ende der Eingabe, weiter mit fedgeo: p(4,6,P1) p(5,6,P2) p(4.5,6.866025403784438,P3) p(5.5,6.866025403784438,P4) p(6,6,P5) nolabel() p(4.250000016927081,6.9682458321813,P6) p(3.28647452068613,6.700629281696042,P7,label) p(3.5364745376132105,7.668875113877343,P8) p(2.5729490413722598,7.4012585633920835,P9,label) p(4.750000016927081,7.83427123596574,P10) p(5.750000016927081,7.834271235965739,P11) p(6.25000001692708,6.9682458321813,P12,label) p(6.963525496240951,6.267616550485259,P13,label) p(5.250000016927081,8.700296639750178,P14) p(3.0729490413722593,8.267283967176523,P15) p(4.03647453761321,8.534900517661782,P16) p(4.536474537613211,9.40092592144622,P17) p(5.500000033854162,9.66854247193148,P18) p(4.786474554540291,10.369171753627521,P19) p(2.0729490413722598,8.267283967176523,P20,label) p(2.5729490413722598,9.133309370960962,P21,label) p(1.5729490413722598,9.133309370960962,P22) print(\P22,1.5,8.8) p(3.5364745376132105,9.40092592144622,P23) p(2.5364745376132105,9.40092592144622,P24,label) p(1.82294905829934,10.101555203142262,P25,label) p(2.7864745545402902,10.369171753627521,P26) p(2.0729490752264197,11.069801035323561,P27,label) p(3.7864745545402902,10.369171753627521,P28) p(3.0729490752264197,11.069801035323563,P29) p(2.5729490752264192,11.935826439108,P30,label) p(3.5729490752264184,11.935826439108002,P31) p(3.072949075226418,12.801851842892438,P32,label) p(4.286474554540285,11.235197157411957,P33) p(3.786474554540288,12.101222561196396,P34,label) p(4.036474571467369,13.069468393377697,P35,label) p(4.75000005078124,12.368839111681655,P36) p(5.000000067708321,13.337084943862955,P37,label) p(5.250000050781236,11.502813707897214,P38) p(5.500000067708317,12.471059540078516,P39) p(6.00000006770832,13.337084943862951,P40,label) p(6.500000067708317,12.471059540078514,P41) p(7.000000067708319,13.337084943862948,P42,label) p(6.250000050781236,11.502813707897213,P43) p(6.750000050781243,12.368839111681647,P44,label) p(7.7135255470221935,12.636455662166911,P45,label) p(7.463525530095118,11.66820982998561,P46,label) p(8.427051026336068,11.935826380470875,P47,label) p(6.9635255300951115,10.802184426201174,P48) p(6.463525530095113,9.936159022416733,P49) p(7.463525530095113,9.936159022416737,P50) p(8.927051019626557,11.069800972812697,P51) p(9.427051026336068,11.935826372723398,P52,label) p(9.927051019626557,11.06980096506522,P53) p(10.427051026336066,11.93582636497592,P54,label) p(10.177051020115906,10.967580530030105,P55) p(11.140576513397537,11.235197091170088,P56,label) p(10.890576507177377,10.266951256224273,P57) p(11.854102000459008,10.534567817364255,P58,label) p(9.677051013406395,10.101555130119404,P59) p(8.677051013406395,10.101555137866882,P60) p(9.177051006696882,9.235529730208704,P61) p(8.177051006696882,9.235529737956181,P62) p(7.213525509417843,8.967913191201928,P63) p(6.213525509417843,8.967913191203728,P64,label) p(10.033813756937128,9.75124049321649,P65) p(10.997339249578108,10.018857056663071,P66) p(11.87233924479078,9.534734129734565,P67,label) p(11.01557649390988,9.019023369033382,P68) p(11.890576489122552,8.534900442104876,P69,label) p(10.0520510012689,8.751406805586798,P70) p(10.927050996481572,8.267283878658292,P71) p(11.640576485220294,7.566654606560579,P72,label) p(8.927050996481572,8.267283896294431,P73,label) p(9.927050996481572,8.267283887476362,P74) p(10.640576485220294,7.566654615378649,P75) p(11.14057647758362,6.700629207185176,P76,label) p(10.14057647758362,6.700629216003246,P77) p(10.640576469946947,5.834603807809772,P78,label) p(9.4270509888449,7.401258488100958,P79) p(9.927050981208225,6.535233079907483,P80) p(9.677050977305969,5.566987244363187,P81,label) p(8.963525488567246,6.2676165164608975,P82,label) p(8.71352548466499,5.299370680916601,P83,label) p(8.94528824252441,7.2674502063776645,P84) p(8.695288247008406,6.299204368668048,P85) p(7.838525492684466,5.7834936136868675,P86,label) p(7.820288255027881,6.783327301438314,P87,label) p(8.070288250543886,7.751573139147931,P88) p(8.21352551231102,8.967913173044396,P89) p(7.963525502095709,7.999667339130124,P90,label) p(6.231762763172462,7.968079511692514,P91) p(7.088525502311132,8.483790276494883,P92) p(7.10676275606575,7.4839565969836706,P93) nolabel() s(P1,P2) s(P1,P3) s(P2,P3) s(P3,P4) s(P2,P4) s(P4,P5) s(P2,P5) s(P1,P6) s(P1,P7) s(P6,P7) s(P7,P8) s(P6,P8) s(P7,P9) s(P8,P9) s(P6,P10) s(P3,P10) s(P10,P11) s(P4,P11) s(P11,P12) s(P5,P12) s(P91,P12) s(P12,P13) s(P5,P13) s(P87,P13) s(P10,P14) s(P11,P14) s(P9,P15) s(P15,P16) s(P8,P16) s(P16,P17) s(P14,P17) s(P17,P18) s(P14,P18) s(P17,P19) s(P18,P19) s(P9,P20) s(P15,P20) s(P20,P21) s(P15,P21) s(P20,P22) s(P21,P22) s(P21,P23) s(P16,P23) s(P22,P24) s(P23,P24) s(P22,P25) s(P24,P25) s(P25,P26) s(P24,P26) s(P25,P27) s(P26,P27) s(P26,P28) s(P23,P28) s(P19,P28) s(P27,P29) s(P28,P29) s(P27,P30) s(P29,P30) s(P30,P31) s(P29,P31) s(P30,P32) s(P31,P32) s(P31,P33) s(P19,P33) s(P32,P34) s(P33,P34) s(P32,P35) s(P34,P35) s(P35,P36) s(P34,P36) s(P35,P37) s(P36,P37) s(P36,P38) s(P33,P38) s(P37,P39) s(P38,P39) s(P37,P40) s(P39,P40) s(P40,P41) s(P39,P41) s(P40,P42) s(P41,P42) s(P41,P43) s(P38,P43) s(P42,P44) s(P43,P44) s(P42,P45) s(P44,P45) s(P45,P46) s(P44,P46) s(P45,P47) s(P46,P47) s(P46,P48) s(P43,P48) s(P48,P49) s(P18,P49) s(P48,P50) s(P49,P50) s(P47,P51) s(P47,P52) s(P51,P52) s(P52,P53) s(P51,P53) s(P52,P54) s(P53,P54) s(P54,P55) s(P54,P56) s(P55,P56) s(P56,P57) s(P55,P57) s(P56,P58) s(P57,P58) s(P55,P59) s(P53,P59) s(P59,P60) s(P51,P60) s(P59,P61) s(P60,P61) s(P65,P61) s(P61,P62) s(P60,P62) s(P50,P62) s(P62,P63) s(P50,P63) s(P63,P64) s(P49,P64) s(P57,P65) s(P58,P66) s(P65,P66) s(P58,P67) s(P66,P67) s(P67,P68) s(P66,P68) s(P67,P69) s(P68,P69) s(P68,P70) s(P65,P70) s(P61,P70) s(P69,P71) s(P70,P71) s(P74,P71) s(P69,P72) s(P71,P72) s(P74,P73) s(P61,P73) s(P72,P75) s(P74,P75) s(P72,P76) s(P75,P76) s(P76,P77) s(P75,P77) s(P76,P78) s(P77,P78) s(P77,P79) s(P74,P79) s(P73,P79) s(P78,P80) s(P79,P80) s(P78,P81) s(P80,P81) s(P81,P82) s(P80,P82) s(P84,P82) s(P81,P83) s(P82,P83) s(P73,P84) s(P83,P85) s(P84,P85) s(P83,P86) s(P85,P86) s(P13,P86) s(P86,P87) s(P85,P87) s(P87,P88) s(P84,P88) s(P73,P88) s(P73,P89) s(P61,P89) s(P63,P89) s(P73,P90) s(P89,P90) s(P64,P91) s(P64,P92) s(P91,P92) s(P90,P92) s(P92,P93) s(P91,P93) s(P90,P93) s(P88,P93) pen(2) color(maroon) s(P24,P22) s(P24,P9) s(P22,P9) color(blue) pen(2) m(P22,P21,MA10) m(P22,P24,MB10) f(P22,MA10,MB10) \geooff \geoprint() Die größere Höhe in dem grünen Dreieck ist eine Wurzel einer rationalen Zahl und Sinus und Kosinus vom Basiswinkel sind dann ebenfalls durch Wurzeln aus einer rationalen Zahl darstellbar. Für den 60°-Winkel gilt das ebenfalls. Sinus und Kosinus gehen in die Berechnung einer Rotation ein und vom GAP-Programm weiß ich, dass es mit Wurzeln rationaler Zahlen exakt rechnet. Also versuche ich das auf dieser Basis mit dem GAP-Programm zu rechnen. Nochmal kurz die Rotationsmatrix \ Wird der Vektor ( x_1 ; x_2 ) mit einem Winkel \phi um den Koordinatenursprung entgegen dem Uhrzeigersinn gedreht, entsteht daraus ein Vektor ( y_1 ; y_2 ) mit den Koordinaten ( y_1 ; y_2 ) = ( cos(\phi) , -sin(\phi) ; sin(\phi) , cos (\phi) ) ( x_1 ; x_2 ) Für \phi=60° gilt cos(\phi)=1/2 , sin(\phi) = 1/2 sqrt(3) und für den Basiswikel im gleichschenkligen Dreieck mit Seitenlängen 1, 2, 2 gilt cos(\phi)=1/4 , sin(\phi) = 1/4 sqrt(15) Für Drehung im Uhrzeigersinn muss man die Matrix invertieren und für aufeinanderfolgende Drehungen muss man die nachfolgende Rotationsmatrix von links an die vorhergehehende ranmultiplizieren. Soweit die Theorie, hinein damit ins GAP-Programm \sourceon GAP W60:=[[1/2,-1/2*Sqrt(3)],[1/2*Sqrt(3),1/2]]; Wbl:=[[1/4,-1/4*Sqrt(15)],[1/4*Sqrt(15),1/4]]*W60^-1; \sourceoff W60 bezeichnet die Rotationsmatrix für die 60°-Drehung entgegengesetzt Uhrzeigersinn und Wbl (kurz für blauerWinkel) ist die Rotationsmatrix, um Strecke P21-P22 um P22 nach P24-P22 zu drehen, sie setzt sich zusammen aus einer Drehung von P21-P22 nach P20-P22 und anschließend von P20-P22 nach P24-P22. \sourceon GAP P:=[]; P[1]:=[0,0]; P[2]:=[1,0]; P[3]:=P[1]+W60*(P[2]-P[1]); \sourceoff P[1] und P[2] sind gegeben. Der neue Punkt P[3] entsteht, indem an P[1] der um 60° gedrehte Richtungsvektor P[2]-P[1] angesetzt wird. Zur Probe müsste der Abstand P[3]-P[2] exakt 1 sein, \sourceon GAP-Logfile gap>(P[3]-P[2])^2; 1 \sourceoff Stimmt exakt, also weiter mit der Eingabe. Ich setze entlang des äußeren Randes fort und nehme dabei einfach mal so an, dass die kleineren spitzen Winkel wie in P1, P22, P32, P42 gleich dem blauen Winkel sind und die größeren Spitzen Winkel wie in P9, P27 alle gleich 60°-blauerWinkel sind. \sourceon GAP P[5]:=[2,0]; P[13]:=P[5]+Wbl*(P[2]-P[1]); P[7]:=P[1]+W60*Wbl*W60*(P[2]-P[1]); P[9]:=P[7]+(P[7]-P[1]); P[20]:=P[9]+W60*W60*Wbl^-1*W60*(P[7]-P[9]); P[22]:=P[20]+(P[20]-P[9]); P[25]:=P[22]+W60*Wbl*W60*(P[20]-P[22]); P[27]:=P[25]+(P[25]-P[22]); P[30]:=P[27]+W60*W60*Wbl^-1*W60*(P[25]-P[27]); P[32]:=P[30]+(P[30]-P[27]); P[35]:=P[32]+W60*Wbl*W60*(P[30]-P[32]); P[37]:=P[35]+(P[35]-P[32]); P[40]:=P[37]+W60*W60*Wbl^-1*W60*(P[35]-P[37]); P[42]:=P[40]+(P[40]-P[37]); (P[37]-P[1])^2=(P[40]-P[2])^2; P[45]:=P[42]+W60*Wbl*W60*(P[40]-P[42]); P[47]:=P[45]+(P[45]-P[42]); P[52]:=P[47]+W60*W60*W60*Wbl^-1*W60*(P[45]-P[47]); P[52]-P[47]; P[54]:=P[52]+(P[52]-P[47]); P[56]:=P[54]+W60*Wbl*W60*(P[52]-P[54]); P[58]:=P[56]+(P[56]-P[54]); P[67]:=P[58]+W60*Wbl*W60*(P[56]-P[58]); P[69]:=P[67]+(P[67]-P[58]); P[72]:=P[69]+W60*W60*Wbl^-1*W60*(P[67]-P[69]); P[76]:=P[72]+W60*W60*Wbl^-1*W60*(P[69]-P[72]); P[78]:=P[76]+(P[76]-P[72]); P[81]:=P[78]+W60*Wbl*W60*(P[76]-P[78]); P[83]:=P[81]+(P[81]-P[78]); P[86]:=P[83]+W60*Wbl*W60*(P[81]-P[83]); \sourceoff Die Randpunkte sind vollständig eingegeben. Wenn der Graph exakt ist, muss die verbleibende Kante P13-P89 auch Länge 1 haben. \sourceon GAP-Logfile gap>(P[86]-P[13])^2; 1 \sourceoff Stimmt. Also weiter mit den übrigen Punkten \sourceon GAP P[4]:=P[3]+(P[2]-P[1]); (P[4]-P[5])^2; P[6]:=P[1]+Wbl*(P[3]-P[1]); P[8]:=P[7]+W60*(P[6]-P[7]); P[10]:=P[6]+(P[3]-P[1]); P[11]:=P[4]+(P[10]-P[3]); P[12]:=P[5]+W60*(P[13]-P[5]); P[14]:=P[10]+(P[3]-P[1]); P[15]:=P[9]+W60^-1*(P[20]-P[9]); P[16]:=P[15]+(P[8]-P[9]); P[17]:=P[16]+(P[16]-P[8]); P[18]:=P[17]+W60*(P[14]-P[17]); P[19]:=P[17]+W60*(P[18]-P[17]); P[21]:=P[20]+W60^-1*(P[22]-P[20]); P[24]:=P[22]+W60^-1*(P[25]-P[22]); P[23]:=P[21]+(P[24]-P[22]); P[26]:=P[25]+W60^-1*(P[27]-P[25]); P[28]:=P[26]+(P[23]-P[24]); P[29]:=P[27]+W60^-1*(P[30]-P[27]); (P[28]-P[29])^2; P[31]:=P[30]+W60^-1*(P[32]-P[30]); P[34]:=P[32]+W60^-1*(P[35]-P[32]); P[33]:=P[31]+(P[34]-P[32]); (P[33]-P[19])^2; P[36]:=P[35]+W60^-1*(P[37]-P[35]); P[38]:=P[36]+(P[33]-P[34]); P[39]:=P[37]+W60^-1*(P[40]-P[37]); P[41]:=P[40]+W60^-1*(P[42]-P[40]); P[43]:=P[41]+(P[38]-P[39]); P[44]:=P[42]+W60^-1*(P[45]-P[42]); P[46]:=P[45]+W60^-1*(P[47]-P[45]); P[48]:=P[46]+(P[43]-P[44]); P[49]:=P[18]+(P[18]-P[17]); (P[49]-P[48])^2; P[50]:=P[49]+W60^-1*(P[48]-P[49]); P[51]:=P[47]+W60^-1*(P[52]-P[47]); P[53]:=P[52]+W60^-1*(P[54]-P[52]); P[55]:=P[54]+W60^-1*(P[56]-P[54]); P[57]:=P[56]+W60^-1*(P[58]-P[56]); P[59]:=P[53]+(P[55]-P[54]); P[60]:=P[51]+(P[59]-P[53]); P[61]:=P[59]+(P[59]-P[55]); P[62]:=P[61]+(P[60]-P[59]); (P[50]-P[62])^2; P[63]:=P[50]+W60^-1*(P[62]-P[50]); P[64]:=P[63]+(P[62]-P[61]); (P[64]-P[12])^2; P[66]:=P[58]+W60^-1*(P[67]-P[58]); P[65]:=P[57]+(P[66]-P[58]); P[68]:=P[67]+W60^-1*(P[69]-P[67]); P[70]:=P[68]+(P[65]-P[66]); P[71]:=P[69]+W60^-1*(P[72]-P[69]); P[75]:=P[72]+W60^-1*(P[76]-P[72]); P[74]:=P[71]+(P[75]-P[72]); P[73]:=P[74]+(P[74]-P[71]); P[77]:=P[76]+W60^-1*(P[78]-P[76]); P[79]:=P[74]+(P[77]-P[75]); P[80]:=P[78]+W60^-1*(P[81]-P[78]); P[82]:=P[81]+W60^-1*(P[83]-P[81]); P[85]:=P[83]+W60^-1*(P[86]-P[83]); P[84]:=P[82]+(P[85]-P[83]); P[87]:=P[86]+W60^-1*(P[13]-P[86]); P[88]:=P[87]+(P[84]-P[85]); P[89]:=P[61]+W60^-1*(P[73]-P[61]); (P[89]-P[63])^2; P[90]:=P[89]+W60^-1*(P[73]-P[89]); P[93]:=P[90]+(P[88]-P[73]); P[92]:=P[90]+W60^-1*(P[93]-P[90]); P[91]:=P[92]+W60^-1*(P[93]-P[92]); (P[91]-P[12])^2; \sourceoff Dazu eine Liste der Kanten, ein Eintrag [i,j] bedeutet, dass Punkt P[i] mit P[j] durch eine Kante verbunden ist. \sourceon GAP Liste_der_Kanten:=[ [ 1, 2 ], [ 1, 3 ], [ 2, 3 ], [ 3, 4 ], [ 2, 4 ], [ 4, 5 ], [ 2, 5 ], [ 1, 6 ], [ 1, 7 ], [ 6, 7 ], [ 7, 8 ], [ 6, 8 ], [ 7, 9 ], [ 8, 9 ], [ 6, 10 ], [ 3, 10 ], [ 10, 11 ], [ 4, 11 ], [ 11, 12 ], [ 5, 12 ], [ 12, 91 ], [ 12, 13 ], [ 5, 13 ], [ 13, 87 ], [ 10, 14 ], [ 11, 14 ], [ 9, 15 ], [ 15, 16 ], [ 8, 16 ], [ 16, 17 ], [ 14, 17 ], [ 17, 18 ], [ 14, 18 ], [ 17, 19 ], [ 18, 19 ], [ 9, 20 ], [ 15, 20 ], [ 20, 21 ], [ 15, 21 ], [ 20, 22 ], [ 21, 22 ], [ 21, 23 ], [ 16, 23 ], [ 22, 24 ], [ 23, 24 ], [ 22, 25 ], [ 24, 25 ], [ 25, 26 ], [ 24, 26 ], [ 25, 27 ], [ 26, 27 ], [ 26, 28 ], [ 23, 28 ], [ 19, 28 ], [ 27, 29 ], [ 28, 29 ], [ 27, 30 ], [ 29, 30 ], [ 30, 31 ], [ 29, 31 ], [ 30, 32 ], [ 31, 32 ], [ 31, 33 ], [ 19, 33 ], [ 32, 34 ], [ 33, 34 ], [ 32, 35 ], [ 34, 35 ], [ 35, 36 ], [ 34, 36 ], [ 35, 37 ], [ 36, 37 ], [ 36, 38 ], [ 33, 38 ], [ 37, 39 ], [ 38, 39 ], [ 37, 40 ], [ 39, 40 ], [ 40, 41 ], [ 39, 41 ], [ 40, 42 ], [ 41, 42 ], [ 41, 43 ], [ 38, 43 ], [ 42, 44 ], [ 43, 44 ], [ 42, 45 ], [ 44, 45 ], [ 45, 46 ], [ 44, 46 ], [ 45, 47 ], [ 46, 47 ], [ 46, 48 ], [ 43, 48 ], [ 48, 49 ], [ 18, 49 ], [ 48, 50 ], [ 49, 50 ], [ 47, 51 ], [ 47, 52 ], [ 51, 52 ], [ 52, 53 ], [ 51, 53 ], [ 52, 54 ], [ 53, 54 ], [ 54, 55 ], [ 54, 56 ], [ 55, 56 ], [ 56, 57 ], [ 55, 57 ], [ 56, 58 ], [ 57, 58 ], [ 55, 59 ], [ 53, 59 ], [ 59, 60 ], [ 51, 60 ], [ 59, 61 ], [ 60, 61 ], [ 61, 65 ], [ 61, 62 ], [ 60, 62 ], [ 50, 62 ], [ 62, 63 ], [ 50, 63 ], [ 63, 64 ], [ 49, 64 ], [ 57, 65 ], [ 58, 66 ], [ 65, 66 ], [ 58, 67 ], [ 66, 67 ], [ 67, 68 ], [ 66, 68 ], [ 67, 69 ], [ 68, 69 ], [ 68, 70 ], [ 65, 70 ], [ 61, 70 ], [ 69, 71 ], [ 70, 71 ], [ 71, 74 ], [ 69, 72 ], [ 71, 72 ], [ 73, 74 ], [ 61, 73 ], [ 72, 75 ], [ 74, 75 ], [ 72, 76 ], [ 75, 76 ], [ 76, 77 ], [ 75, 77 ], [ 76, 78 ], [ 77, 78 ], [ 77, 79 ], [ 74, 79 ], [ 73, 79 ], [ 78, 80 ], [ 79, 80 ], [ 78, 81 ], [ 80, 81 ], [ 81, 82 ], [ 80, 82 ], [ 82, 84 ], [ 81, 83 ], [ 82, 83 ], [ 73, 84 ], [ 83, 85 ], [ 84, 85 ], [ 83, 86 ], [ 85, 86 ], [ 13, 86 ], [ 86, 87 ], [ 85, 87 ], [ 87, 88 ], [ 84, 88 ], [ 73, 88 ], [ 73, 89 ], [ 61, 89 ], [ 63, 89 ], [ 73, 90 ], [ 89, 90 ], [ 64, 91 ], [ 64, 92 ], [ 91, 92 ], [ 90, 92 ], [ 92, 93 ], [ 91, 93 ], [ 90, 93 ], [ 88, 93 ] ]; \sourceoff Anschließende Ausgabe aller Kantenlängen \sourceon GAP-Logfile gap> for Kante in Liste_der_Kanten do Print(" ",(P[Kante[1]]-P[Kante[2]])^2); od; 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \sourceoff ergibt stets Länge 1 und jetzt überprüfe ich noch die am Anfang des Beitrages vermuteten Eigenschaften \geo ebene(540.88,416.89) x(1.57,12.39) y(5.3,13.64) form(.) #//Eingabe war: #//blauerWinkel=15.522486812413007; gruenerWinkel=104.47751274368893; orangerWinkel=15.5224878898908; #//Figure 8: 91 185 #//blauerWinkel=15.522486812413007 #//gruenerWinkel=104.47751274368893 #//orangerWinkel=15.5224878898908 #D=50; P[1]=[0,0]; P[2]=[D,0]; A(2,1); L(3,1,2); L(4,3,2); L(5,4,2); M(6,1,3,blauerWinkel,2);N(10,6,3); R(62,50); R(87,13); N(11,10,4); N(12,11,5); L(13,12,5); L(14,10,11); M(15,9,8,60-blauerWinkel); N(16,15,8); N(17,16,14); L(18,17,14); L(19,17,18); L(20,9,15); L(21,20,15); L(22,20,21); N(23,21,16); N(24,22,23); L(25,22,24); L(26,25,24); L(27,25,26); N(28,26,23); A(28,19); R(28,19); N(29,27,28); L(30,27,29); L(31,30,29); L(32,30,31); N(33,31,19); N(34,32,33); L(35,32,34); L(36,35,34); L(37,35,36); N(38,36,33); N(39,37,38); L(40,37,39); L(41,40,39); L(42,40,41); N(43,41,38); N(44,42,43); L(45,42,44); L(46,45,44); L(47,45,46); N(48,46,43); N(49,48,18); L(50,48,49); M(51,47,46,gruenerWinkel,2); M(55,54,53,orangerWinkel,2); N(59,55,53); N(60,59,51); L(61,59,60); L(62,61,60); A(62,50); L(63,62,50); N(64,63,49); R(61,57); H(65,61,57,2); A(61,65); A(65,57); N(66,58,65); L(67,58,66); L(68,67,66); L(69,67,68); N(70,68,65); A(70,61); R(70,61); N(71,69,70); L(72,69,71); Q(73,71,61,ab(12,14,11),D); N(75,72,74); L(76,72,75); L(77,76,75); L(78,76,77); N(79,77,74); A(79,73); R(79,73); N(80,78,79); L(81,78,80); L(82,81,80); L(83,81,82); R(82,73); H(84,82,73,2); A(82,84); A(84,73); N(85,83,84); L(86,83,85); L(87,86,85); N(88,87,84); A(88,73); R(88,73); L(89,73,61); A(89,63); R(89,63); L(90,73,89); R(12,64); A(86,13); A(13,87); R(86,13); H(91,12,64,2); A(12,91); A(91,64); L(92,64,91); L(93,92,91); A(92,90); A(93,90); R(92,90); R(90,93); A(93,88); R(93,88); # #//Ende der Eingabe, weiter mit fedgeo: p(4,6,P1) p(5,6,P2) p(4.5,6.866025403784438,P3) p(5.5,6.866025403784438,P4) p(6,6,P5) nolabel() p(4.250000016927081,6.9682458321813,P6) p(3.28647452068613,6.700629281696042,P7,label) p(3.5364745376132105,7.668875113877343,P8) p(2.5729490413722598,7.4012585633920835,P9,label) p(4.750000016927081,7.83427123596574,P10) p(5.750000016927081,7.834271235965739,P11) p(6.25000001692708,6.9682458321813,P12,label) p(6.963525496240951,6.267616550485259,P13,label) p(5.250000016927081,8.700296639750178,P14,label) p(3.0729490413722593,8.267283967176523,P15) p(4.03647453761321,8.534900517661782,P16) p(4.536474537613211,9.40092592144622,P17,label) p(5.500000033854162,9.66854247193148,P18) p(4.786474554540291,10.369171753627521,P19) p(2.0729490413722598,8.267283967176523,P20,label) p(2.5729490413722598,9.133309370960962,P21,label) p(1.5729490413722598,9.133309370960962,P22) print(\P22,1.5,8.8) p(3.5364745376132105,9.40092592144622,P23) p(2.5364745376132105,9.40092592144622,P24,label) p(1.82294905829934,10.101555203142262,P25,label) p(2.7864745545402902,10.369171753627521,P26) p(2.0729490752264197,11.069801035323561,P27,label) p(3.7864745545402902,10.369171753627521,P28) p(3.0729490752264197,11.069801035323563,P29) p(2.5729490752264192,11.935826439108,P30,label) p(3.5729490752264184,11.935826439108002,P31) p(3.072949075226418,12.801851842892438,P32,label) p(4.286474554540285,11.235197157411957,P33) p(3.786474554540288,12.101222561196396,P34,label) p(4.036474571467369,13.069468393377697,P35,label) p(4.75000005078124,12.368839111681655,P36) p(5.000000067708321,13.337084943862955,P37,label) p(5.250000050781236,11.502813707897214,P38) p(5.500000067708317,12.471059540078516,P39) p(6.00000006770832,13.337084943862951,P40,label) p(6.500000067708317,12.471059540078514,P41) p(7.000000067708319,13.337084943862948,P42,label) p(6.250000050781236,11.502813707897213,P43) p(6.750000050781243,12.368839111681647,P44,label) p(7.7135255470221935,12.636455662166911,P45,label) p(7.463525530095118,11.66820982998561,P46,label) p(8.427051026336068,11.935826380470875,P47,label) p(6.9635255300951115,10.802184426201174,P48) p(6.463525530095113,9.936159022416733,P49) p(7.463525530095113,9.936159022416737,P50) p(8.927051019626557,11.069800972812697,P51) p(9.427051026336068,11.935826372723398,P52,label) p(9.927051019626557,11.06980096506522,P53) p(10.427051026336066,11.93582636497592,P54,label) p(10.177051020115906,10.967580530030105,P55) p(11.140576513397537,11.235197091170088,P56,label) p(10.890576507177377,10.266951256224273,P57) p(11.854102000459008,10.534567817364255,P58,label) p(9.677051013406395,10.101555130119404,P59) p(8.677051013406395,10.101555137866882,P60) p(9.177051006696882,9.235529730208704,P61,label) p(8.177051006696882,9.235529737956181,P62) p(7.213525509417843,8.967913191201928,P63) p(6.213525509417843,8.967913191203728,P64,label) p(10.033813756937128,9.75124049321649,P65) p(10.997339249578108,10.018857056663071,P66) p(11.87233924479078,9.534734129734565,P67,label) p(11.01557649390988,9.019023369033382,P68) p(11.890576489122552,8.534900442104876,P69,label) p(10.0520510012689,8.751406805586798,P70) p(10.927050996481572,8.267283878658292,P71) p(11.640576485220294,7.566654606560579,P72,label) p(8.927050996481572,8.267283896294431,P73,label) p(9.927050996481572,8.267283887476362,P74) p(10.640576485220294,7.566654615378649,P75) p(11.14057647758362,6.700629207185176,P76,label) p(10.14057647758362,6.700629216003246,P77) p(10.640576469946947,5.834603807809772,P78,label) p(9.4270509888449,7.401258488100958,P79) p(9.927050981208225,6.535233079907483,P80) p(9.677050977305969,5.566987244363187,P81,label) p(8.963525488567246,6.2676165164608975,P82,label) p(8.71352548466499,5.299370680916601,P83,label) p(8.94528824252441,7.2674502063776645,P84) p(8.695288247008406,6.299204368668048,P85) p(7.838525492684466,5.7834936136868675,P86,label) p(7.820288255027881,6.783327301438314,P87,label) p(8.070288250543886,7.751573139147931,P88) p(8.21352551231102,8.967913173044396,P89) p(7.963525502095709,7.999667339130124,P90,label) p(6.231762763172462,7.968079511692514,P91) p(7.088525502311132,8.483790276494883,P92) p(7.10676275606575,7.4839565969836706,P93) nolabel() s(P1,P2) s(P1,P3) s(P2,P3) s(P3,P4) s(P2,P4) s(P4,P5) s(P2,P5) s(P1,P6) s(P1,P7) s(P6,P7) s(P7,P8) s(P6,P8) s(P7,P9) s(P8,P9) s(P6,P10) s(P3,P10) s(P10,P11) s(P4,P11) s(P11,P12) s(P5,P12) s(P91,P12) s(P12,P13) s(P5,P13) s(P87,P13) s(P10,P14) s(P11,P14) s(P9,P15) s(P15,P16) s(P8,P16) s(P16,P17) s(P14,P17) s(P17,P18) s(P14,P18) s(P17,P19) s(P18,P19) s(P9,P20) s(P15,P20) s(P20,P21) s(P15,P21) s(P20,P22) s(P21,P22) s(P21,P23) s(P16,P23) s(P22,P24) s(P23,P24) s(P22,P25) s(P24,P25) s(P25,P26) s(P24,P26) s(P25,P27) s(P26,P27) s(P26,P28) s(P23,P28) s(P19,P28) s(P27,P29) s(P28,P29) s(P27,P30) s(P29,P30) s(P30,P31) s(P29,P31) s(P30,P32) s(P31,P32) s(P31,P33) s(P19,P33) s(P32,P34) s(P33,P34) s(P32,P35) s(P34,P35) s(P35,P36) s(P34,P36) s(P35,P37) s(P36,P37) s(P36,P38) s(P33,P38) s(P37,P39) s(P38,P39) s(P37,P40) s(P39,P40) s(P40,P41) s(P39,P41) s(P40,P42) s(P41,P42) s(P41,P43) s(P38,P43) s(P42,P44) s(P43,P44) s(P42,P45) s(P44,P45) s(P45,P46) s(P44,P46) s(P45,P47) s(P46,P47) s(P46,P48) s(P43,P48) s(P48,P49) s(P18,P49) s(P48,P50) s(P49,P50) s(P47,P51) s(P47,P52) s(P51,P52) s(P52,P53) s(P51,P53) s(P52,P54) s(P53,P54) s(P54,P55) s(P54,P56) s(P55,P56) s(P56,P57) s(P55,P57) s(P56,P58) s(P57,P58) s(P55,P59) s(P53,P59) s(P59,P60) s(P51,P60) s(P59,P61) s(P60,P61) s(P65,P61) s(P61,P62) s(P60,P62) s(P50,P62) s(P62,P63) s(P50,P63) s(P63,P64) s(P49,P64) s(P57,P65) s(P58,P66) s(P65,P66) s(P58,P67) s(P66,P67) s(P67,P68) s(P66,P68) s(P67,P69) s(P68,P69) s(P68,P70) s(P65,P70) s(P61,P70) s(P69,P71) s(P70,P71) s(P74,P71) s(P69,P72) s(P71,P72) s(P74,P73) s(P61,P73) s(P72,P75) s(P74,P75) s(P72,P76) s(P75,P76) s(P76,P77) s(P75,P77) s(P76,P78) s(P77,P78) s(P77,P79) s(P74,P79) s(P73,P79) s(P78,P80) s(P79,P80) s(P78,P81) s(P80,P81) s(P81,P82) s(P80,P82) s(P84,P82) s(P81,P83) s(P82,P83) s(P73,P84) s(P83,P85) s(P84,P85) s(P83,P86) s(P85,P86) s(P13,P86) s(P86,P87) s(P85,P87) s(P87,P88) s(P84,P88) s(P73,P88) s(P73,P89) s(P61,P89) s(P63,P89) s(P73,P90) s(P89,P90) s(P64,P91) s(P64,P92) s(P91,P92) s(P90,P92) s(P92,P93) s(P91,P93) s(P90,P93) s(P88,P93) pen(2) color(maroon) s(P45,P27) s(P5,P72) color(red) s(P25,P47) s(P17,P56) s(P14,P58) s(P9,P61) \geooff \geoprint() \sourceon GAP-Logfile gap> (P[27]-P[45])^2=(P[5]-P[72])^2; #grüne Kanten vergleichen true gap> (P[25]-P[47])^2=(P[17]-P[56])^2; #rote Kanten vergleichen true gap> (P[25]-P[47])^2=(P[14]-P[58])^2; true gap> (P[25]-P[47])^2=(P[9]-P[61])^2; true gap> (P[27]-P[45])^2-(P[25]-P[47])^2=1; #Differenz rote, grüne Kante false \sourceoff Das letzte Ergebnis heißt, rote Kante wäre nicht um 1 länger als die grüne, da stimmt etwas nicht, eigentlich sollte 1 als Differenz herauskommen. :-? Muss ich später nochmal versuchen :-) (EDIT: War Doppelfehler. Kurze minus lange Kante ergibt -1, außerdem muss ich die Kantenlängen vergleichen und nicht deren Quadrate. \sourceon GAP-Logfile gap> (P[47]-P[25])-(P[45]-P[27])=(P[13]-P[5]); #Differenz rote, grüne Kante true \sourceoff END_EDIT) (EDIT2: Parallelität lässt sich durch Vergleich der Anstiege feststellen \sourceon GAP-Logfile gap> P[47][1]-P[25][1])/(P[47][2]-P[25][2])=(P[13][1]-P[5][1])/(P[13][2]-P[5][2]); true \sourceoff END_EDIT2) Für diese Berechnung musste überhaupt keine neue Programmfunktion programmiert werden. Das war also mal der richtige Dampfer und ich füge das hiermit an die nicht vorhandene Liste von Beweismethoden an, um die Exaktheit eines Streichholzgraphen festzustellen.


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Slash
Aktiv Letzter Besuch: in der letzten Woche
Dabei seit: 23.03.2005
Mitteilungen: 8559
Wohnort: Sahlenburg (Cuxhaven)
  Beitrag No.498, vom Themenstarter, eingetragen 2016-09-03

Super Beweis, Stefan! :-)


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haribo
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 25.10.2012
Mitteilungen: 3250
  Beitrag No.499, eingetragen 2016-09-04

http://www.matheplanet.com/matheplanet/nuke/html/uploads/a/35059_st-643fahrschein.PNG


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StefanVogel
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 26.11.2005
Mitteilungen: 3905
Wohnort: Raun
  Beitrag No.500, eingetragen 2016-09-04

Danke haribo! Damit dampfe ich gleich mal los durch die restlichen noch fehlenden asymmetrischen Graphen. #351-1 4/4 mit 132 Kanten hat ebenfalls nur solche 15.5224868°-Winkel \geo ebene(417.71,381.85) x(1.57,9.93) y(6,13.64) form(.) #//Eingabe war: #//blauerWinkel=15.5224878898908; gruenerWinkel=0; orangerWinkel=0; #//351-1: 132 Kanten #//blauerWinkel=15.5224878898908; #D=50; P[1]=[0,0]; P[2]=[D,0]; A(2,1); L(3,1,2); L(4,3,2); L(5,4,2); L(6,4,5); L(7,6,5); M(8,1,3,blauerWinkel,2); N(12,8,3); N(13,10,12); L(14,13,12); N(15,11,13); L(16,11,15); Q (17,15,14,ab(14,15,13),D); N(19,16,18); L(20,16,19); L(21,20,19); L(22,20,21); N(23,21,18); A(17,23); N(24,22,23); L(25,22,24); L(26,25,24); L(27,25,26); Q(28,26,17,ab(17,24,23),D); N(30,27,29); L(31,27,30); L(32,31,30); L(33,31,32); N(34,32,29); A(28,34); N(35,33,34); L(36,33,35); L(37,36,35); L(38,36,37); Q(39,37,28,ab(28,35,34),D); N(41,38,40); L(42,38,41); L(43,42,41); L(44,42,43); N(45,43,40); A(39,45); N(46,44,45); L(47,44,46); L(48,47,46); L(49,47,48); Q(50,48,39,ab(39,46,45),D); N(52,49,51); L(53,49,52); L(54,53,52); L(55,53,54); N(56,54,51); A(50,56); N(57,55,56); L(58,55,57); L(59,58,57); L(60,58,59); Q(61,59,50,ab(50,57,56),D); N(63,60,62); L(64,60,63); L(65,64,63); N(66,65,62); A(61,66); A(14,61); A(66,6); A(65,7); A(7,64); # #//Ende der Eingabe, weiter mit fedgeo: label() p(4,6,P1) p(5,6,P2) p(4.5,6.866025403784438,P3) p(5.5,6.866025403784438,P4) p(6,6,P5) p(6.5,6.866025403784438,P6) p(7,6,P7) p(4.2499999987187,6.9682458368826845,P8) p(3.2864745075104214,6.7006292682778135,P9) p(3.5364745062291214,7.668875105160498,P10) p(2.5729490150208427,7.401258536555627,P11) p(4.7499999987187,7.834271240667123,P12) p(4.036474506229122,8.534900508944936,P13) p(4.9999999974374,8.802517077549807,P14) p(3.072949015020843,8.267283940340064,P15) p(2.072949015020843,8.267283940340066,P16) p(4.499999996291371,9.668542480672587,P17) p(3.7864744952159177,8.967913221138684,P18) p(2.7864744952159173,8.967913221138684,P19) p(1.8229489993115564,9.2355297728358,P20) p(2.536474479506631,9.936159053634418,P21) p(1.5729489836022692,10.203775605331533,P22) p(3.5364744795066305,9.936159053634418,P23) p(2.572948983602269,10.203775605331533,P24) p(2.072948983602269,11.069801009115972,P25) p(3.072948983602269,11.069801009115972,P26) p(2.572948983602269,11.935826412900411,P27) p(4.999999996291371,10.534567884457026,P28) p(4.036474477512732,10.80218445024003,P29) p(3.5364744775127317,11.668209854024472,P30) p(3.2864744690174383,12.63645568838285,P31) p(4.249999962927901,12.36883912950691,P32) p(3.999999954432607,13.337084963865287,P33) p(4.749999962927901,11.50281372572247,P34) p(4.499999954432609,12.47105956008085,P35) p(4.9999999544326075,13.33708496386529,P36) p(5.499999954432609,12.471059560080851,P37) p(5.999999954432608,13.33708496386529,P38) p(5.999999996291372,10.534567884457028,P39) p(5.749999973748893,11.50281372851644,P40) p(6.24999997374889,12.36883913230088,P41) p(6.963525451333918,13.069468415757587,P42) p(7.2135254706502,12.101222584193177,P43) p(7.9270509482352285,12.801851867649884,P44) p(6.713525470650203,11.235197180408736,P45) p(7.42705094823523,11.935826463865444,P46) p(8.42705094823523,11.935826463865446,P47) p(7.927050948235231,11.069801060081005,P48) p(8.92705094823523,11.069801060081009,P49) p(6.499999996291374,9.668542480672588,P50) p(7.213525474565275,10.369171772637165,P51) p(8.213525474565273,10.369171772637166,P52) p(9.177050972962007,10.10155522991358,P53) p(8.463525499292054,9.400925942469739,P54) p(9.427050997688786,9.133309399746153,P55) p(7.463525499292053,9.400925942469737,P56) p(8.427050997688786,9.13330939974615,P57) p(8.927050997688788,8.267283995961712,P58) p(7.92705099768879,8.26728399596171,P59) p(8.427050997688792,7.401258592177273,P60) p(5.999999996291376,8.802517076888149,P61) p(6.963525498544344,8.534900535993238,P62) p(7.463525498544344,7.6688751322088,P63) p(7.713525525976371,6.7006293027398645,P64) p(6.750000026831924,6.968245842771391,P65) p(6.250000026831923,7.834271246555829,P66) nolabel() s(P1,P2) s(P1,P3) s(P2,P3) s(P3,P4) s(P2,P4) s(P4,P5) s(P2,P5) s(P4,P6) s(P5,P6) s(P6,P7) s(P5,P7) s(P64,P7) s(P1,P8) s(P1,P9) s(P8,P9) s(P9,P10) s(P8,P10) s(P9,P11) s(P10,P11) s(P8,P12) s(P3,P12) s(P10,P13) s(P12,P13) s(P13,P14) s(P12,P14) s(P61,P14) s(P11,P15) s(P13,P15) s(P18,P15) s(P11,P16) s(P15,P16) s(P18,P17) s(P14,P17) s(P23,P17) s(P16,P19) s(P18,P19) s(P16,P20) s(P19,P20) s(P20,P21) s(P19,P21) s(P20,P22) s(P21,P22) s(P21,P23) s(P18,P23) s(P22,P24) s(P23,P24) s(P22,P25) s(P24,P25) s(P25,P26) s(P24,P26) s(P29,P26) s(P25,P27) s(P26,P27) s(P29,P28) s(P17,P28) s(P34,P28) s(P27,P30) s(P29,P30) s(P27,P31) s(P30,P31) s(P31,P32) s(P30,P32) s(P31,P33) s(P32,P33) s(P32,P34) s(P29,P34) s(P33,P35) s(P34,P35) s(P33,P36) s(P35,P36) s(P36,P37) s(P35,P37) s(P40,P37) s(P36,P38) s(P37,P38) s(P40,P39) s(P28,P39) s(P45,P39) s(P38,P41) s(P40,P41) s(P38,P42) s(P41,P42) s(P42,P43) s(P41,P43) s(P42,P44) s(P43,P44) s(P43,P45) s(P40,P45) s(P44,P46) s(P45,P46) s(P44,P47) s(P46,P47) s(P47,P48) s(P46,P48) s(P51,P48) s(P47,P49) s(P48,P49) s(P51,P50) s(P39,P50) s(P56,P50) s(P49,P52) s(P51,P52) s(P49,P53) s(P52,P53) s(P53,P54) s(P52,P54) s(P53,P55) s(P54,P55) s(P54,P56) s(P51,P56) s(P55,P57) s(P56,P57) s(P55,P58) s(P57,P58) s(P58,P59) s(P57,P59) s(P62,P59) s(P58,P60) s(P59,P60) s(P62,P61) s(P50,P61) s(P66,P61) s(P60,P63) s(P62,P63) s(P60,P64) s(P63,P64) s(P64,P65) s(P63,P65) s(P7,P65) s(P65,P66) s(P62,P66) s(P6,P66) \geooff \geoprint() \sourceon GAP W60:=[[1/2,-1/2*Sqrt(3)],[1/2*Sqrt(3),1/2]]; Wbl:=[[1/4,-1/4*Sqrt(15)],[1/4*Sqrt(15),1/4]]*W60^-1; P:=[]; P[1]:=[0,0]; P[2]:=[1,0]; P[3]:=P[1]+W60*(P[2]-P[1]); P[4]:=P[2]+(P[3]-P[1]); P[5]:=[2,0]; P[6]:=P[5]+(P[3]-P[1]); P[7]:=[3,0]; P[8]:=P[1]+Wbl*(P[3]-P[1]); P[9]:=P[1]+W60*(P[8]-P[1]); P[10]:=P[9]+(P[8]-P[1]); P[11]:=P[9]+(P[9]-P[1]); P[12]:=P[8]+(P[3]-P[1]); P[13]:=P[10]+(P[3]-P[1]); P[14]:=P[12]+(P[12]-P[3]); P[15]:=P[11]+(P[3]-P[1]); P[16]:=P[11]+W60*(P[15]-P[11]); P[17]:=P[14]+(P[16]-P[11]); P[18]:=(P[17]+P[15])/2; P[19]:=P[16]+(P[18]-P[15]); P[20]:=P[16]+W60*(P[19]-P[16]); P[21]:=P[20]+(P[19]-P[16]); P[22]:=P[20]+(P[20]-P[16]); P[23]:=P[18]+(P[20]-P[16]); P[24]:=P[23]+(P[23]-P[17]); P[25]:=P[22]+W60*(P[24]-P[22]); P[26]:=P[24]+(P[25]-P[22]); P[27]:=P[25]+(P[25]-P[22]); P[28]:=P[17]+(P[26]-P[24]); P[29]:=(P[26]+P[28])/2; P[30]:=P[27]+(P[29]-P[26]); P[31]:=P[27]+W60*(P[30]-P[27]); P[32]:=P[31]+(P[30]-P[27]); P[33]:=P[31]+(P[31]-P[27]); P[34]:=P[29]+(P[31]-P[27]); P[35]:=P[34]+(P[34]-P[28]); P[36]:=P[33]+W60*(P[35]-P[33]); P[36]-P[33]; P[37]:=P[35]+(P[36]-P[33]); P[38]:=P[36]+(P[36]-P[33]); P[39]:=P[28]+(P[36]-P[33]); P[40]:=(P[39]+P[37])/2; P[41]:=P[40]+(P[38]-P[37]); P[42]:=P[38]+W60*(P[41]-P[38]); P[43]:=P[41]+(P[42]-P[38]); P[44]:=P[42]+(P[42]-P[38]); P[45]:=P[40]+(P[42]-P[38]); P[46]:=P[45]+(P[45]-P[39]); P[47]:=P[44]+W60*(P[46]-P[44]); P[48]:=P[46]+(P[47]-P[44]); P[49]:=P[47]+(P[47]-P[44]); P[50]:=P[39]+(P[47]-P[44]); P[51]:=(P[50]+P[48])/2; P[52]:=P[51]+(P[49]-P[48]); P[53]:=P[49]+W60*(P[52]-P[49]); P[54]:=P[52]+(P[53]-P[49]); P[55]:=P[53]+(P[53]-P[49]); P[56]:=P[51]+(P[53]-P[49]); P[57]:=P[56]+(P[55]-P[54]); P[58]:=P[55]+W60*(P[57]-P[55]); P[59]:=P[57]+(P[58]-P[55]); P[60]:=P[58]+(P[58]-P[55]); P[61]:=P[50]+(P[58]-P[55]); P[62]:=(P[61]+P[59])/2; P[63]:=P[62]+(P[60]-P[59]); P[64]:=P[60]+W60*(P[63]-P[60]); P[65]:=P[63]+(P[64]-P[60]); P[66]:=P[62]+(P[64]-P[60]); (P[7]-P[64])^2; (P[7]-P[65])^2; (P[6]-P[66])^2; (P[61]-P[66])^2; (P[17]-P[23])^2; (P[59]-P[62])^2; Liste_der_Kanten:=[ #[i,j] bedeutet eine Kante von P[i] nach P[j] [ 1, 2 ], [ 1, 3 ], [ 2, 3 ], [ 3, 4 ], [ 2, 4 ], [ 4, 5 ], [ 2, 5 ], [ 4, 6 ], [ 5, 6 ], [ 6, 7 ], [ 5, 7 ], [ 7, 64 ], [ 1, 8 ], [ 1, 9 ], [ 8, 9 ], [ 9, 10 ], [ 8, 10 ], [ 9, 11 ], [ 10, 11 ], [ 8, 12 ], [ 3, 12 ], [ 10, 13 ], [ 12, 13 ], [ 13, 14 ], [ 12, 14 ], [ 14, 61 ], [ 11, 15 ], [ 13, 15 ], [ 15, 18 ], [ 11, 16 ], [ 15, 16 ], [ 17, 18 ], [ 14, 17 ], [ 17, 23 ], [ 16, 19 ], [ 18, 19 ], [ 16, 20 ], [ 19, 20 ], [ 20, 21 ], [ 19, 21 ], [ 20, 22 ], [ 21, 22 ], [ 21, 23 ], [ 18, 23 ], [ 22, 24 ], [ 23, 24 ], [ 22, 25 ], [ 24, 25 ], [ 25, 26 ], [ 24, 26 ], [ 26, 29 ], [ 25, 27 ], [ 26, 27 ], [ 28, 29 ], [ 17, 28 ], [ 28, 34 ], [ 27, 30 ], [ 29, 30 ], [ 27, 31 ], [ 30, 31 ], [ 31, 32 ], [ 30, 32 ], [ 31, 33 ], [ 32, 33 ], [ 32, 34 ], [ 29, 34 ], [ 33, 35 ], [ 34, 35 ], [ 33, 36 ], [ 35, 36 ], [ 36, 37 ], [ 35, 37 ], [ 37, 40 ], [ 36, 38 ], [ 37, 38 ], [ 39, 40 ], [ 28, 39 ], [ 39, 45 ], [ 38, 41 ], [ 40, 41 ], [ 38, 42 ], [ 41, 42 ], [ 42, 43 ], [ 41, 43 ], [ 42, 44 ], [ 43, 44 ], [ 43, 45 ], [ 40, 45 ], [ 44, 46 ], [ 45, 46 ], [ 44, 47 ], [ 46, 47 ], [ 47, 48 ], [ 46, 48 ], [ 48, 51 ], [ 47, 49 ], [ 48, 49 ], [ 50, 51 ], [ 39, 50 ], [ 50, 56 ], [ 49, 52 ], [ 51, 52 ], [ 49, 53 ], [ 52, 53 ], [ 53, 54 ], [ 52, 54 ], [ 53, 55 ], [ 54, 55 ], [ 54, 56 ], [ 51, 56 ], [ 55, 57 ], [ 56, 57 ], [ 55, 58 ], [ 57, 58 ], [ 58, 59 ], [ 57, 59 ], [ 59, 62 ], [ 58, 60 ], [ 59, 60 ], [ 61, 62 ], [ 50, 61 ], [ 61, 66 ], [ 60, 63 ], [ 62, 63 ], [ 60, 64 ], [ 63, 64 ], [ 64, 65 ], [ 63, 65 ], [ 7, 65 ], [ 65, 66 ], [ 62, 66 ], [ 6, 66 ] ]; \sourceoff \sourceon GAP-Logfile gap> for Kante in Liste_der_Kanten do Print(" ",(P[Kante[1]]-P[Kante[2]])^2); od; 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \sourceoff Alle Kanten haben Länge 1. Nächster Graph #375-1 4/5 mit 125 Kanten \geo ebene(417.71,338.55) x(1.07,9.43) y(6,12.77) form(.) #//Eingabe war: #//blauerWinkel=44.47751218593006; gruenerWinkel=0; orangerWinkel=0; #//Figure 5: 62 125 #//blauerWinkel=44.47751218593006; #D=50; P[1]=[0,0]; P[2]=[D,0]; A(2,1); L(3,1,2); L(4,3,2); L(5,4,2); M(6,1,3,blauerWinkel,2); N(10,6,3); N(11,8,10); L(12,11,10); N(13,9,11); L(14,9,13); L(15,14,13); L(16,14,15); H(17,12,15,2); A(15,17); A(17,12); N(18,16,17); L(19,16,18); L(20,19,18); L(21,19,20); N(22,20,17); A(22,12); N(23,21,22); L(24,21,23); Q(25,23,12,ab(12,13,11),D); N(27,24,26); L(28,24,27); L(29,28,27); L(30,28,29); N(31,29,26); A(31,25); N(32,30,31); L(33,30,32); L(34,33,32); L(35,33,34); Q(36,34,25,ab(12,13,11),D); N(38,35,37); L(39,35,38); L(40,39,38); L(41,39,40); N(42,40,37); A(42,36); N(43,41,42); L(44,41,43); L(45,44,43); L(46,44,45); Q(47,45,36,ab(12,13,11),D); N(49,46,48); L(50,46,49); L(51,50,49); L(52,50,51); N(53,51,48); A(53,47); N(54,52,53); L(55,52,54); L(56,55,54); L(57,55,56); H(58,47,56,2); N(59,57,58); L(60,57,59); L(61,60,59); A(47,58); A(58,56); N(62,61,58); A(62,47); A(62,4); A(61,5); A(60,5); # #//Ende der Eingabe, weiter mit fedgeo: p(4,6,P1) p(5,6,P2) p(4.5,6.866025403784438,P3) p(5.5,6.866025403784438,P4) p(6,6,P5) p(3.749999999999998,6.968245836551853,P6) p(3.0364745084375784,6.267616567329815,P7) p(2.786474508437576,7.235862403881669,P8) p(2.0729490168751568,6.535233134659631,P9) p(4.249999999999998,7.834271240336292,P10) p(3.2864745084375757,8.101887807666108,P11) p(3.9999999999999956,8.802517076888147,P12) p(2.572949016875156,7.40125853844407,P13) p(1.5729490168751554,7.401258538444068,P14) p(2.0729490168751545,8.267283942228508,P15) p(1.0729490168751545,8.267283942228506,P16) p(3.0364745084375753,8.534900509558327,P17) p(2.036474508437575,8.534900509558327,P18) p(1.3229490168751523,9.23552977878036,P19) p(2.286474508437572,9.503146346110181,P20) p(1.57294901687515,10.203775615332216,P21) p(3.286474508437572,9.503146346110181,P22) p(2.5729490168751497,10.203775615332216,P23) p(2.0729490168751488,11.069801019116655,P24) p(4.499999999999994,9.668542480672587,P25) p(3.5364745084375717,9.936159048002402,P26) p(3.0364745084375704,10.80218445178684,P27) p(2.7864745084375686,11.770430288338693,P28) p(3.74999999999999,11.502813721008877,P29) p(3.499999999999988,12.471059557560729,P30) p(4.249999999999992,10.63678831722444,P31) p(3.999999999999994,11.605034153776295,P32) p(4.4999999999999885,12.471059557560736,P33) p(4.999999999999995,11.605034153776302,P34) p(5.4999999999999885,12.471059557560743,P35) p(5.499999999999994,9.668542480672592,P36) p(5.249999999999995,10.636788317224447,P37) p(5.749999999999987,11.502813721008888,P38) p(6.463525491562409,12.203442990230924,P39) p(6.713525491562407,11.235197153679069,P40) p(7.427050983124831,11.935826422901105,P41) p(6.2135254915624145,10.369171749894626,P42) p(6.927050983124836,11.069801019116664,P43) p(7.927050983124835,11.069801019116667,P44) p(7.42705098312484,10.203775615332228,P45) p(8.42705098312484,10.203775615332233,P46) p(5.9999999999999964,8.802517076888154,P47) p(6.713525491562418,9.503146346110192,P48) p(7.713525491562418,9.503146346110196,P49) p(8.67705098312484,9.235529778780379,P50) p(7.963525491562418,8.53490050955834,P51) p(8.92705098312484,8.267283942228524,P52) p(6.963525491562418,8.534900509558337,P53) p(7.92705098312484,8.26728394222852,P54) p(8.427050983124843,7.401258538444083,P55) p(7.427050983124843,7.40125853844408,P56) p(7.927050983124846,6.535233134659643,P57) p(6.71352549156242,8.101887807666117,P58) p(7.21352549156243,7.235862403881685,P59) p(6.963525491562423,6.267616567329832,P60) p(6.250000000000007,6.9682458365518745,P61) p(5.7499999999999964,7.834271240336307,P62) nolabel() s(P1,P2) s(P1,P3) s(P2,P3) s(P3,P4) s(P2,P4) s(P4,P5) s(P2,P5) s(P1,P6) s(P1,P7) s(P6,P7) s(P7,P8) s(P6,P8) s(P7,P9) s(P8,P9) s(P6,P10) s(P3,P10) s(P8,P11) s(P10,P11) s(P11,P12) s(P10,P12) s(P9,P13) s(P11,P13) s(P9,P14) s(P13,P14) s(P14,P15) s(P13,P15) s(P17,P15) s(P14,P16) s(P15,P16) s(P12,P17) s(P16,P18) s(P17,P18) s(P16,P19) s(P18,P19) s(P19,P20) s(P18,P20) s(P19,P21) s(P20,P21) s(P20,P22) s(P17,P22) s(P12,P22) s(P21,P23) s(P22,P23) s(P26,P23) s(P21,P24) s(P23,P24) s(P26,P25) s(P12,P25) s(P24,P27) s(P26,P27) s(P24,P28) s(P27,P28) s(P28,P29) s(P27,P29) s(P28,P30) s(P29,P30) s(P29,P31) s(P26,P31) s(P25,P31) s(P30,P32) s(P31,P32) s(P30,P33) s(P32,P33) s(P33,P34) s(P32,P34) s(P37,P34) s(P33,P35) s(P34,P35) s(P37,P36) s(P25,P36) s(P35,P38) s(P37,P38) s(P35,P39) s(P38,P39) s(P39,P40) s(P38,P40) s(P39,P41) s(P40,P41) s(P40,P42) s(P37,P42) s(P36,P42) s(P41,P43) s(P42,P43) s(P41,P44) s(P43,P44) s(P44,P45) s(P43,P45) s(P48,P45) s(P44,P46) s(P45,P46) s(P48,P47) s(P36,P47) s(P58,P47) s(P46,P49) s(P48,P49) s(P46,P50) s(P49,P50) s(P50,P51) s(P49,P51) s(P50,P52) s(P51,P52) s(P51,P53) s(P48,P53) s(P47,P53) s(P52,P54) s(P53,P54) s(P52,P55) s(P54,P55) s(P55,P56) s(P54,P56) s(P55,P57) s(P56,P57) s(P56,P58) s(P57,P59) s(P58,P59) s(P57,P60) s(P59,P60) s(P5,P60) s(P60,P61) s(P59,P61) s(P5,P61) s(P61,P62) s(P58,P62) s(P47,P62) s(P4,P62) \geooff \geoprint() \sourceon GAP W60:=[[1/2,-1/2*Sqrt(3)],[1/2*Sqrt(3),1/2]]; Wbl:=[[1/4,-1/4*Sqrt(15)],[1/4*Sqrt(15),1/4]]*W60^-1; P:=[]; P[1]:=[0,0]; P[2]:=[1,0]; P[3]:=P[1]+W60*(P[2]-P[1]); P[4]:=P[3]+(P[2]-P[1]); P[5]:=[2,0]; P[6]:=P[1]+Wbl^-1*W60*(P[3]-P[1]); P[7]:=P[1]+W60*(P[6]-P[1]); P[8]:=P[6]+(P[7]-P[1]); P[9]:=P[7]+(P[7]-P[1]); P[10]:=P[3]+(P[6]-P[1]); P[11]:=P[10]+(P[7]-P[1]); P[12]:=P[10]+(P[10]-P[3]); P[13]:=P[11]+(P[11]-P[12]); P[14]:=P[9]+W60*(P[13]-P[9]); P[15]:=P[13]+(P[14]-P[9]); P[16]:=P[14]+(P[14]-P[9]); P[15]-P[16]; P[17]:=(P[15]+P[12])/2; P[18]:=P[17]+(P[16]-P[15]); P[19]:=P[16]+W60*(P[18]-P[16]); P[20]:=P[18]+(P[19]-P[16]); P[21]:=P[19]+(P[19]-P[16]); P[22]:=P[17]+(P[19]-P[16]); P[23]:=P[22]+(P[22]-P[12]); P[24]:=P[21]+W60*(P[23]-P[21]); P[25]:=P[12]+(P[24]-P[21]); P[26]:=(P[23]+P[25])/2; P[27]:=P[26]+(P[24]-P[23]); P[28]:=P[24]+W60*(P[27]-P[24]); P[29]:=P[27]+(P[28]-P[24]); P[30]:=P[28]+(P[28]-P[24]); P[31]:=P[26]+(P[28]-P[24]); P[32]:=P[31]+(P[31]-P[25]); P[33]:=P[30]+W60*(P[32]-P[30]); P[33]-P[30]; P[34]:=P[32]+(P[33]-P[30]); P[35]:=P[33]+(P[33]-P[30]); P[36]:=P[25]+(P[33]-P[30]); P[37]:=(P[34]+P[36])/2; P[38]:=P[37]+(P[35]-P[34]); P[39]:=P[35]+W60*(P[38]-P[35]); P[40]:=P[38]+(P[39]-P[35]); P[41]:=P[39]+(P[39]-P[35]); P[42]:=P[37]+(P[39]-P[35]); P[43]:=P[42]+(P[41]-P[40]); P[44]:=P[41]+W60*(P[43]-P[41]); P[45]:=P[43]+(P[44]-P[41]); P[46]:=P[44]+(P[44]-P[41]); P[47]:=P[36]+(P[44]-P[41]); P[48]:=(P[47]+P[45])/2; P[49]:=P[48]+(P[46]-P[45]); P[50]:=P[46]+W60*(P[49]-P[46]); P[51]:=P[49]+(P[50]-P[46]); P[52]:=P[50]+(P[50]-P[46]); P[53]:=P[48]+(P[50]-P[46]); P[54]:=P[53]+(P[52]-P[51]); P[55]:=P[52]+W60*(P[54]-P[52]); P[56]:=P[54]+(P[55]-P[52]); P[57]:=P[55]+(P[55]-P[52]); P[58]:=(P[47]+P[56])/2; P[59]:=P[58]+(P[57]-P[56]); P[60]:=P[57]+W60*(P[59]-P[57]); P[61]:=P[59]+(P[60]-P[57]); P[62]:=P[58]+(P[60]-P[57]); (P[5]-P[60])^2; (P[5]-P[61])^2; (P[4]-P[62])^2; Liste_der_Kanten:=[ [ 1, 2 ], [ 1, 3 ], [ 2, 3 ], [ 3, 4 ], [ 2, 4 ], [ 4, 5 ], [ 2, 5 ], [ 1, 6 ], [ 1, 7 ], [ 6, 7 ], [ 7, 8 ], [ 6, 8 ], [ 7, 9 ], [ 8, 9 ], [ 6, 10 ], [ 3, 10 ], [ 8, 11 ], [ 10, 11 ], [ 11, 12 ], [ 10, 12 ], [ 9, 13 ], [ 11, 13 ], [ 9, 14 ], [ 13, 14 ], [ 14, 15 ], [ 13, 15 ], [ 15, 17 ], [ 14, 16 ], [ 15, 16 ], [ 12, 17 ], [ 16, 18 ], [ 17, 18 ], [ 16, 19 ], [ 18, 19 ], [ 19, 20 ], [ 18, 20 ], [ 19, 21 ], [ 20, 21 ], [ 20, 22 ], [ 17, 22 ], [ 12, 22 ], [ 21, 23 ], [ 22, 23 ], [ 23, 26 ], [ 21, 24 ], [ 23, 24 ], [ 25, 26 ], [ 12, 25 ], [ 24, 27 ], [ 26, 27 ], [ 24, 28 ], [ 27, 28 ], [ 28, 29 ], [ 27, 29 ], [ 28, 30 ], [ 29, 30 ], [ 29, 31 ], [ 26, 31 ], [ 25, 31 ], [ 30, 32 ], [ 31, 32 ], [ 30, 33 ], [ 32, 33 ], [ 33, 34 ], [ 32, 34 ], [ 34, 37 ], [ 33, 35 ], [ 34, 35 ], [ 36, 37 ], [ 25, 36 ], [ 35, 38 ], [ 37, 38 ], [ 35, 39 ], [ 38, 39 ], [ 39, 40 ], [ 38, 40 ], [ 39, 41 ], [ 40, 41 ], [ 40, 42 ], [ 37, 42 ], [ 36, 42 ], [ 41, 43 ], [ 42, 43 ], [ 41, 44 ], [ 43, 44 ], [ 44, 45 ], [ 43, 45 ], [ 45, 48 ], [ 44, 46 ], [ 45, 46 ], [ 47, 48 ], [ 36, 47 ], [ 47, 58 ], [ 46, 49 ], [ 48, 49 ], [ 46, 50 ], [ 49, 50 ], [ 50, 51 ], [ 49, 51 ], [ 50, 52 ], [ 51, 52 ], [ 51, 53 ], [ 48, 53 ], [ 47, 53 ], [ 52, 54 ], [ 53, 54 ], [ 52, 55 ], [ 54, 55 ], [ 55, 56 ], [ 54, 56 ], [ 55, 57 ], [ 56, 57 ], [ 56, 58 ], [ 57, 59 ], [ 58, 59 ], [ 57, 60 ], [ 59, 60 ], [ 5, 60 ], [ 60, 61 ], [ 59, 61 ], [ 5, 61 ], [ 61, 62 ], [ 58, 62 ], [ 47, 62 ], [ 4, 62 ] ]; \sourceoff \sourceon GAP-Logfile gap> for Kante in Liste_der_Kanten do Print(" ",(P[Kante[1]]-P[Kante[2]])^2); od; 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 \sourceoff Ebenfalls alles Kanten mit Länge 1. Die nächsten beiden Grapen entstehen durch Umlegen einiger Kanten im Inneren. #375-9 4/6 mit 128 Kanten \geo ebene(417.71,338.55) x(1.07,9.43) y(6,12.77) form(.) #//Eingabe war: #//blauerWinkel=44.47751218593006; gruenerWinkel=0; orangerWinkel=0; #//Figure 6: 63 128 v1 #//blauerWinkel=44.47751218593006; #D=50; P[1]=[0,0]; P[2]=[D,0]; A(2,1); L(3,1,2); L(4,3,2); L(5,4,2); M(6,1,3,blauerWinkel,2); N(10,6,3); N(11,8,10); L(12,11,10); N(13,9,11); L(14,9,13); L(15,14,13); L(16,14,15); H(17,12,15,2); A(15,17); A(17,12); N(18,16,17); L(19,16,18); L(20,19,18); L(21,19,20); N(22,20,17); A(22,12); N(23,21,22); L(24,21,23); Q(25,23,12,ab(12,13,11),D); N(27,24,26); L(28,24,27); L(29,28,27); L(30,28,29); N(31,29,26); A(31,25); N(32,30,31); L(33,30,32); L(34,33,32); L(35,33,34); Q(36,34,25,ab(12,13,11),D); N(38,35,37); L(39,35,38); L(40,39,38); L(41,39,40); N(42,40,37); A(42,36); N(43,41,42); L(44,41,43); L(45,44,43); L(46,44,45); Q(47,45,36,ab(12,13,11),D); N(49,46,48); L(50,46,49); L(51,50,49); L(52,50,51); N(53,51,48); A(53,47); N(54,52,53); L(55,52,54); L(56,55,54); L(57,55,56); H(58,47,56,2); N(59,57,58); L(60,57,59); L(61,60,59); A(47,58); A(58,56); N(62,61,58); A(62,47); A(62,4); A(61,5); A(60,5); A(36,25); L(63,25,12); A(36,63); A(47,63); # #//Ende der Eingabe, weiter mit fedgeo: p(4,6,P1) p(5,6,P2) p(4.5,6.866025403784438,P3) p(5.5,6.866025403784438,P4) p(6,6,P5) p(3.749999999999998,6.968245836551853,P6) p(3.0364745084375784,6.267616567329815,P7) p(2.786474508437576,7.235862403881669,P8) p(2.0729490168751568,6.535233134659631,P9) p(4.249999999999998,7.834271240336292,P10) p(3.2864745084375757,8.101887807666108,P11) p(3.9999999999999956,8.802517076888147,P12) p(2.572949016875156,7.40125853844407,P13) p(1.5729490168751554,7.401258538444068,P14) p(2.0729490168751545,8.267283942228508,P15) p(1.0729490168751545,8.267283942228506,P16) p(3.0364745084375753,8.534900509558327,P17) p(2.036474508437575,8.534900509558327,P18) p(1.3229490168751523,9.23552977878036,P19) p(2.286474508437572,9.503146346110181,P20) p(1.57294901687515,10.203775615332216,P21) p(3.286474508437572,9.503146346110181,P22) p(2.5729490168751497,10.203775615332216,P23) p(2.0729490168751488,11.069801019116655,P24) p(4.499999999999994,9.668542480672587,P25) p(3.5364745084375717,9.936159048002402,P26) p(3.0364745084375704,10.80218445178684,P27) p(2.7864745084375686,11.770430288338693,P28) p(3.74999999999999,11.502813721008877,P29) p(3.499999999999988,12.471059557560729,P30) p(4.249999999999992,10.63678831722444,P31) p(3.999999999999994,11.605034153776295,P32) p(4.4999999999999885,12.471059557560736,P33) p(4.999999999999995,11.605034153776302,P34) p(5.4999999999999885,12.471059557560743,P35) p(5.499999999999994,9.668542480672592,P36) p(5.249999999999995,10.636788317224447,P37) p(5.749999999999987,11.502813721008888,P38) p(6.463525491562409,12.203442990230924,P39) p(6.713525491562407,11.235197153679069,P40) p(7.427050983124831,11.935826422901105,P41) p(6.2135254915624145,10.369171749894626,P42) p(6.927050983124836,11.069801019116664,P43) p(7.927050983124835,11.069801019116667,P44) p(7.42705098312484,10.203775615332228,P45) p(8.42705098312484,10.203775615332233,P46) p(5.9999999999999964,8.802517076888154,P47) p(6.713525491562418,9.503146346110192,P48) p(7.713525491562418,9.503146346110196,P49) p(8.67705098312484,9.235529778780379,P50) p(7.963525491562418,8.53490050955834,P51) p(8.92705098312484,8.267283942228524,P52) p(6.963525491562418,8.534900509558337,P53) p(7.92705098312484,8.26728394222852,P54) p(8.427050983124843,7.401258538444083,P55) p(7.427050983124843,7.40125853844408,P56) p(7.927050983124846,6.535233134659643,P57) p(6.71352549156242,8.101887807666117,P58) p(7.21352549156243,7.235862403881685,P59) p(6.963525491562423,6.267616567329832,P60) p(6.250000000000007,6.9682458365518745,P61) p(5.7499999999999964,7.834271240336307,P62) p(4.999999999999996,8.802517076888147,P63) nolabel() s(P1,P2) s(P1,P3) s(P2,P3) s(P3,P4) s(P2,P4) s(P4,P5) s(P2,P5) s(P1,P6) s(P1,P7) s(P6,P7) s(P7,P8) s(P6,P8) s(P7,P9) s(P8,P9) s(P6,P10) s(P3,P10) s(P8,P11) s(P10,P11) s(P11,P12) s(P10,P12) s(P9,P13) s(P11,P13) s(P9,P14) s(P13,P14) s(P14,P15) s(P13,P15) s(P17,P15) s(P14,P16) s(P15,P16) s(P12,P17) s(P16,P18) s(P17,P18) s(P16,P19) s(P18,P19) s(P19,P20) s(P18,P20) s(P19,P21) s(P20,P21) s(P20,P22) s(P17,P22) s(P12,P22) s(P21,P23) s(P22,P23) s(P26,P23) s(P21,P24) s(P23,P24) s(P26,P25) s(P12,P25) s(P24,P27) s(P26,P27) s(P24,P28) s(P27,P28) s(P28,P29) s(P27,P29) s(P28,P30) s(P29,P30) s(P29,P31) s(P26,P31) s(P25,P31) s(P30,P32) s(P31,P32) s(P30,P33) s(P32,P33) s(P33,P34) s(P32,P34) s(P37,P34) s(P33,P35) s(P34,P35) s(P37,P36) s(P63,P36) s(P35,P38) s(P37,P38) s(P35,P39) s(P38,P39) s(P39,P40) s(P38,P40) s(P39,P41) s(P40,P41) s(P40,P42) s(P37,P42) s(P36,P42) s(P41,P43) s(P42,P43) s(P41,P44) s(P43,P44) s(P44,P45) s(P43,P45) s(P48,P45) s(P44,P46) s(P45,P46) s(P48,P47) s(P36,P47) s(P58,P47) s(P63,P47) s(P46,P49) s(P48,P49) s(P46,P50) s(P49,P50) s(P50,P51) s(P49,P51) s(P50,P52) s(P51,P52) s(P51,P53) s(P48,P53) s(P47,P53) s(P52,P54) s(P53,P54) s(P52,P55) s(P54,P55) s(P55,P56) s(P54,P56) s(P55,P57) s(P56,P57) s(P56,P58) s(P57,P59) s(P58,P59) s(P57,P60) s(P59,P60) s(P5,P60) s(P60,P61) s(P59,P61) s(P5,P61) s(P61,P62) s(P58,P62) s(P47,P62) s(P4,P62) s(P25,P63) s(P12,P63) \geooff \geoprint() \sourceon GAP-Logfile gap> P[63]:=P[12]+(P[2]-P[1]);; gap> (P[63]-P[25])^2; 1 gap> (P[63]-P[36])^2; 1 gap> (P[63]-P[47])^2; 1 \sourceoff Die neuen von P63 ausgehenden Kanten haben alle Länge 1. #375-10 ein weiterer 4/6 mit 128 Kanten \geo ebene(417.71,338.55) x(1.07,9.43) y(6,12.77) form(.) #//Eingabe war: #//blauerWinkel=44.47751218593006; gruenerWinkel=0; orangerWinkel=0; #//blauerWinkel=44.47751218593006; #D=50; P[1]=[0,0]; P[2]=[D,0]; A(2,1); L(3,1,2); L(4,3,2); L(5,4,2); M(6,1,3,blauerWinkel,2); N(10,6,3); N(11,8,10); L(12,11,10); N(13,9,11); L(14,9,13); L(15,14,13); L(16,14,15); H(17,12,15,2); A(15,17); A(17,12); N(18,16,17); L(19,16,18); L(20,19,18); L(21,19,20); N(22,20,17); A(22,12); N(23,21,22); L(24,21,23); Q(25,23,12,ab(12,13,11),D); N(27,24,26); L(28,24,27); L(29,28,27); L(30,28,29); N(31,29,26); A(31,25); N(32,30,31); L(33,30,32); L(34,33,32); L(35,33,34); Q(36,34,25,ab(12,13,11),D); N(38,35,37); L(39,35,38); L(40,39,38); L(41,39,40); N(42,40,37); A(42,36); N(43,41,42); L(44,41,43); L(45,44,43); L(46,44,45); Q(47,45,36,ab(12,13,11),D); N(49,46,48); L(50,46,49); L(51,50,49); L(52,50,51); N(53,51,48); A(53,47); N(54,52,53); L(55,52,54); L(56,55,54); L(57,55,56); H(58,47,56,2); N(59,57,58); L(60,57,59); L(61,60,59); A(47,58); A(58,56); N(62,61,58); A(62,47); A(62,4); A(61,5); A(60,5); A(36,25); L(63,25,12); A(36,63); A(47,63); A(25,31); A(25,36); A(36,37); A(37,31); # #//Ende der Eingabe, weiter mit fedgeo: p(4,6,P1) p(5,6,P2) p(4.5,6.866025403784438,P3) p(5.5,6.866025403784438,P4) p(6,6,P5) p(3.749999999999998,6.968245836551853,P6) p(3.0364745084375784,6.267616567329815,P7) p(2.786474508437576,7.235862403881669,P8) p(2.0729490168751568,6.535233134659631,P9) p(4.249999999999998,7.834271240336292,P10) p(3.2864745084375757,8.101887807666108,P11) p(3.9999999999999956,8.802517076888147,P12) p(2.572949016875156,7.40125853844407,P13) p(1.5729490168751554,7.401258538444068,P14) p(2.0729490168751545,8.267283942228508,P15) p(1.0729490168751545,8.267283942228506,P16) p(3.0364745084375753,8.534900509558327,P17) p(2.036474508437575,8.534900509558327,P18) p(1.3229490168751523,9.23552977878036,P19) p(2.286474508437572,9.503146346110181,P20) p(1.57294901687515,10.203775615332216,P21) p(3.286474508437572,9.503146346110181,P22) p(2.5729490168751497,10.203775615332216,P23) p(2.0729490168751488,11.069801019116655,P24) p(4.499999999999994,9.668542480672587,P25) p(3.5364745084375717,9.936159048002402,P26) p(3.0364745084375704,10.80218445178684,P27) p(2.7864745084375686,11.770430288338693,P28) p(3.74999999999999,11.502813721008877,P29) p(3.499999999999988,12.471059557560729,P30) p(4.249999999999992,10.63678831722444,P31) p(3.999999999999994,11.605034153776295,P32) p(4.4999999999999885,12.471059557560736,P33) p(4.999999999999995,11.605034153776302,P34) p(5.4999999999999885,12.471059557560743,P35) p(5.499999999999994,9.668542480672592,P36) p(5.249999999999995,10.636788317224447,P37) p(5.749999999999987,11.502813721008888,P38) p(6.463525491562409,12.203442990230924,P39) p(6.713525491562407,11.235197153679069,P40) p(7.427050983124831,11.935826422901105,P41) p(6.2135254915624145,10.369171749894626,P42) p(6.927050983124836,11.069801019116664,P43) p(7.927050983124835,11.069801019116667,P44) p(7.42705098312484,10.203775615332228,P45) p(8.42705098312484,10.203775615332233,P46) p(5.9999999999999964,8.802517076888154,P47) p(6.713525491562418,9.503146346110192,P48) p(7.713525491562418,9.503146346110196,P49) p(8.67705098312484,9.235529778780379,P50) p(7.963525491562418,8.53490050955834,P51) p(8.92705098312484,8.267283942228524,P52) p(6.963525491562418,8.534900509558337,P53) p(7.92705098312484,8.26728394222852,P54) p(8.427050983124843,7.401258538444083,P55) p(7.427050983124843,7.40125853844408,P56) p(7.927050983124846,6.535233134659643,P57) p(6.71352549156242,8.101887807666117,P58) p(7.21352549156243,7.235862403881685,P59) p(6.963525491562423,6.267616567329832,P60) p(6.250000000000007,6.9682458365518745,P61) p(5.7499999999999964,7.834271240336307,P62) p(4.999999999999996,8.802517076888147,P63) nolabel() s(P1,P2) s(P1,P3) s(P2,P3) s(P3,P4) s(P2,P4) s(P4,P5) s(P2,P5) s(P1,P6) s(P1,P7) s(P6,P7) s(P7,P8) s(P6,P8) s(P7,P9) s(P8,P9) s(P6,P10) s(P3,P10) s(P8,P11) s(P10,P11) s(P11,P12) s(P10,P12) s(P9,P13) s(P11,P13) s(P9,P14) s(P13,P14) s(P14,P15) s(P13,P15) s(P17,P15) s(P14,P16) s(P15,P16) s(P12,P17) s(P16,P18) s(P17,P18) s(P16,P19) s(P18,P19) s(P19,P20) s(P18,P20) s(P19,P21) s(P20,P21) s(P20,P22) s(P17,P22) s(P12,P22) s(P21,P23) s(P22,P23) s(P26,P23) s(P21,P24) s(P23,P24) s(P26,P25) s(P12,P25) s(P36,P25) s(P24,P27) s(P26,P27) s(P24,P28) s(P27,P28) s(P28,P29) s(P27,P29) s(P28,P30) s(P29,P30) s(P29,P31) s(P26,P31) s(P30,P32) s(P31,P32) s(P30,P33) s(P32,P33) s(P33,P34) s(P32,P34) s(P37,P34) s(P33,P35) s(P34,P35) s(P63,P36) s(P31,P37) s(P35,P38) s(P37,P38) s(P35,P39) s(P38,P39) s(P39,P40) s(P38,P40) s(P39,P41) s(P40,P41) s(P40,P42) s(P37,P42) s(P36,P42) s(P41,P43) s(P42,P43) s(P41,P44) s(P43,P44) s(P44,P45) s(P43,P45) s(P48,P45) s(P44,P46) s(P45,P46) s(P48,P47) s(P36,P47) s(P58,P47) s(P63,P47) s(P46,P49) s(P48,P49) s(P46,P50) s(P49,P50) s(P50,P51) s(P49,P51) s(P50,P52) s(P51,P52) s(P51,P53) s(P48,P53) s(P47,P53) s(P52,P54) s(P53,P54) s(P52,P55) s(P54,P55) s(P55,P56) s(P54,P56) s(P55,P57) s(P56,P57) s(P56,P58) s(P57,P59) s(P58,P59) s(P57,P60) s(P59,P60) s(P5,P60) s(P60,P61) s(P59,P61) s(P5,P61) s(P61,P62) s(P58,P62) s(P47,P62) s(P4,P62) s(P25,P63) s(P12,P63) \geooff \geoprint() Hier kommt nur eine neue Kante hinzu, ebenfalls Länge 1. \sourceon GAP-Logfile gap> (P[31]-P[37])^2; 1 \sourceoff So, an der Stelle endet die Fahrt mit GAP. Bei den anderen Graphen treten Winkel auf, wo das Quadrat der Seitenlänge des betreffenden Dreiecks keine rationale Zahl mehr ist und da weiß GAP nicht weiter. Als Beispiel eine willkürlich ausgewählte Distanz \sourceon GAP-Logfile gap> IsRat((P[4]-P[44])^2); false gap> Sqrt((P[4]-P[44])^2); Error, no method found! ... \sourceoff #350 4/7 mit 185 Kanten, war in Beitrag No.497 gerechnet, #485-2 4/8 mit 176 Kanten in Beitrag No. 488 an vorletzter Stelle #476 4/9 mit 277 Kanten, \geo ebene(657.71,602.65) x(1.96,15.12) y(0.35,12.4) form(.) #//Eingabe war: #//blauerWinkel=87.32759106282208; gruenerWinkel=109.8307284978373; orangerWinkel=0; #//Figure 10: 137 277 #//blauerWinkel=87.32759106282208 109.8307284978373 #D=50; P[1]=[0,0]; P[2]=[D,0]; A(2,1); L(3,1,2); L(4,3,2); L(5,3,4); Q(6,1,5,ab(1,5,[1,5]),ab(1,2,3)); L(11,9,7); A(11,10,ab(11,10,[1,11],"gespiegelt")); L(21,13,15); A(21,10,ab(11,10,[12,21])); A(31,10,ab(10,11,[1,9])); N(41,10,4); Q(42,33,41,D,ab(11,1,7,8,9)); N(46,44,2); L(47,42,43); M(48,35,33,blauerWinkel); M(49,48,35,gruenerWinkel); Q(50,48,49,D,ab(36,33,[1,41],"gespiegelt")); Q(90,89,49,3*D,D); A(90,89); H(91,90,89,3); H(92,89,90,3); A(90,91); A(91,92); A(92,89); L(93,91,90); L(94,92,91); L(95,89,92); A(95,94); A(94,93); N(96,52,95); A(93,47); A(90,47); R(93,47); R(90,47); Q(97,96,46,ab(31,11,[10,31]),ab(11,31,[10,31])); # #//Ende der Eingabe, weiter mit fedgeo: p(4,6,P1) p(5,6,P2) p(4.5,6.866025403784438,P3) p(5.5,6.866025403784438,P4) p(5,7.732050807568877,P5) p(4.036474508437579,7.999667374898695,P6) p(3.1614745084375784,7.515544456622768,P7) p(4.018237254218789,6.999833687449348,P8) p(3.143237254218789,6.51571076917342,P9) p(4.75,8.700296644120732,P10) p(2.2864745084375784,7.031421538346841,P11) p(1.9641265190955735,9.00527355249764,P12) p(2.3350070150988262,9.933954152964983,P13) p(2.953827759103704,9.148421921424323,P14) p(3.3247082551069562,10.077102521891662,P15) p(3.9435289991118334,9.291570290351004,P16) p(3.834706501332249,8.297509093051254,P17) p(3.060590504884914,7.664465315699046,P18) p(2.8994165102139107,8.651391322774447,P19) p(2.125300513766576,8.018347545422241,P20) p(2.7058875111020795,10.862634753432323,P21) p(4.6019792848692465,11.498901981452498,P22) p(5.578294612823271,11.282549536580653,P23) p(4.902770235416367,10.545211882904255,P24) p(5.879085563370391,10.328859438032408,P25) p(5.203561185963488,9.591521784356011,P26) p(4.204956981046642,9.538704723453348,P27) p(3.455422246074361,10.200669738442835,P28) p(4.403468132957944,10.518803352452924,P29) p(3.653933397985663,11.180768367442411,P30) p(6.554609940777294,11.066197091708805,P31) p(6.702630655908051,8.267591754377037,P32) p(7.650676542791632,8.585725368387127,P33) p(6.901141807819352,9.247690383376613,P34) p(7.849187694702934,9.565823997386701,P35) p(7.099652959730653,10.227789012376189,P36) p(6.101048754813808,10.174971951473525,P37) p(5.425524377406902,9.437634297797128,P38) p(6.4018397053609295,9.22128185292528,P39) p(5.726315327954025,8.483944199248883,P40) p(5.25,7.834271240336292,P41) p(7.243438916554276,7.672403127457582,P42) p(6.674988238507902,6.849685784362995,P43) p(5.6782687802307645,6.930619840802349,P44) p(6.246719458277138,7.753337183896938,P45) p(5.999867861013648,5.983743908465064,P46) p(7.67170769678504,6.7687517279236395,P47) p(8.818964744234595,9.321831222490262,P48) p(8.918430563581905,8.326790243041895,P49) p(9.630962600569779,9.905491638577448,P50) p(12.292115981675847,5.3888212846371095,P51) p(11.29713260754567,5.488861702491739,P52) p(11.881261837878078,6.300522371904314,P53) nolabel() p(10.886278463747903,6.400562789758943,P54) p(11.470407694080311,7.2122234591715175,P55) p(12.455872011956023,7.382106001516984,P56) p(13.2780506052826,6.812876381174252,P57) p(12.373993996815935,6.385463643077046,P58) p(13.196172590142513,5.816234022734314,P59) p(11.816017255687507,8.15060186414772,P60) p(14.100229198609181,6.243646760831523,P61) p(14.61842506896761,8.175348870356554,P62) p(14.342310736979462,9.13647366749309,P63) p(13.648009412446136,8.416789243074117,P64) p(13.371895080457987,9.377914040210648,P65) p(12.677593755924661,8.658229615791674,P66) p(12.686424034395728,7.65826860346063,P67) p(13.393326616502453,6.9509576821460755,P68) p(13.652424551681671,7.916808736908595,P69) p(14.3593271337884,7.2094978155940375,P70) p(14.066196404991313,10.09759846462962,P71) p(12.243269053626333,10.920359591351982,P72) p(11.250207545414778,10.802763499118479,P73) p(11.848579502780545,10.001545051603532,P74) p(10.855517994568991,9.88394895937003,P75) p(11.453889951934759,9.082730511855086,P76) p(12.442200692320947,8.930277632455244,P77) p(13.254198548656131,9.513938048542432,P78) p(12.342734872973642,9.925318611903613,P79) p(13.154732729308824,10.508979027990799,P80) p(10.257146037203222,10.685167406884975,P81) p(9.829894239264396,7.915409679680712,P82) p(9.730428419917088,8.910450659129081,P83) p(8.818964744234597,9.321831222490262,P84) p(10.619273340955967,9.753038759177608,P85) p(11.217645298321738,8.951820311662663,P86) p(10.22458379011018,8.83422421942916,P87) p(10.82295574747595,8.033005771914215,P88) p(11.231888025355097,7.338941194735145,P89) label() p(8.242404245380264,7.589912765370922,P90) p(9.238898838705207,7.506255575158996,P91) p(10.235393432030154,7.4225983849470705,P92) p(8.668202290109981,6.6850945377117155,P93) p(9.664696883434926,6.60143734749979,P94) p(10.661191476759871,6.517780157287863,P95) p(10.301728085338357,5.584620969245574,P96) p(7.6462339013046545,0.34584778524874693,P97) p(8.546211335218056,3.18206755541754,P98) p(11.271495770281508,3.835463847303692,P99) nolabel() p(11.235896600161485,2.8360976986440694,P100) p(10.388219712800046,3.3666105586514616,P101) p(10.352620542680032,2.367244409991839,P102) p(9.50494365531859,2.897757269999228,P103) p(9.271797424997786,3.8701989573446425,P104) p(9.78676275516808,4.727409963295103,P105) p(10.271646597639648,3.852831402324165,P106) p(10.786611927809929,4.710042408274637,P107) p(11.20029743004147,1.8367315499844468,P108) p(9.630310107621007,0.5977239602421456,P109) p(8.63827200446283,0.47178587274544626,P110) p(9.025225472965749,1.3938851153509049,P111) p(8.033187369807573,1.2679470278542047,P112) p(8.420140838310491,2.1900462704596624,P113) p(9.342291720632677,2.5768766599489252,P114) p(10.271294575337071,2.2068041049666878,P115) p(9.48630091412684,1.5873003100955367,P116) p(10.415303768831238,1.2172277551132975,P117) p(7.283410742589728,3.299229122250423,P118) p(5.742362747880804,0.9584444153084801,P119) p(5.084741149010852,1.7117928291912783,P120) p(6.065970812769042,1.9046356329485983,P121) p(5.408349213899088,2.657984046831394,P122) p(6.389578877657286,2.850826850588719,P123) p(7.22482256849719,2.3009468846760455,P124) p(7.435528234900923,1.3233973349623964,P125) p(6.483592658188999,1.6296956499922635,P126) p(6.694298324592729,0.6521461002786131,P127) p(4.427119550140899,2.4651412430740733,P128) p(4.7248525770573835,4.44285584449743,P129) p(5.362360219035519,5.213299876481248,P130) p(5.710830501938547,4.275980047429564,P131) p(6.3483381439165605,5.046424079413349,P132) p(6.696808426819708,4.109104250361696,P133) p(6.288737149867185,3.19615417893044,P134) p(5.35792835000404,2.8306477110022557,P135) p(5.506794863462286,3.819505011713935,P136) p(4.575986063599143,3.4539985437857528,P137) nolabel() s(P8,P1) s(P9,P1) s(P1,P2) s(P1,P3) s(P2,P3) s(P3,P4) s(P2,P4) s(P3,P5) s(P4,P5) s(P6,P5) s(P6,P7) s(P6,P8) s(P7,P8) s(P7,P9) s(P8,P9) s(P6,P10) s(P5,P10) s(P16,P10) s(P17,P10) s(P26,P10) s(P27,P10) s(P38,P10) s(P40,P10) s(P9,P11) s(P7,P11) s(P18,P11) s(P20,P11) s(P19,P12) s(P20,P12) s(P12,P13) s(P12,P14) s(P13,P14) s(P13,P15) s(P14,P15) s(P14,P16) s(P15,P16) s(P17,P16) s(P17,P18) s(P17,P19) s(P18,P19) s(P18,P20) s(P19,P20) s(P13,P21) s(P15,P21) s(P28,P21) s(P30,P21) s(P29,P22) s(P30,P22) s(P22,P23) s(P22,P24) s(P23,P24) s(P23,P25) s(P24,P25) s(P24,P26) s(P25,P26) s(P27,P26) s(P27,P28) s(P27,P29) s(P28,P29) s(P28,P30) s(P29,P30) s(P23,P31) s(P25,P31) s(P36,P31) s(P37,P31) s(P39,P32) s(P40,P32) s(P32,P33) s(P32,P34) s(P33,P34) s(P33,P35) s(P34,P35) s(P34,P36) s(P35,P36) s(P37,P36) s(P37,P38) s(P37,P39) s(P38,P39) s(P38,P40) s(P39,P40) s(P10,P41) s(P4,P41) s(P44,P41) s(P45,P41) s(P33,P42) s(P43,P42) s(P45,P42) s(P43,P44) s(P43,P45) s(P44,P45) s(P44,P46) s(P2,P46) s(P130,P46) s(P132,P46) s(P42,P47) s(P43,P47) s(P35,P48) s(P48,P49) s(P82,P49) s(P48,P50) s(P83,P50) s(P84,P50) s(P85,P50) s(P58,P51) s(P59,P51) s(P51,P52) s(P51,P53) s(P52,P53) s(P52,P54) s(P53,P54) s(P53,P55) s(P54,P55) s(P56,P55) s(P56,P57) s(P56,P58) s(P57,P58) s(P57,P59) s(P58,P59) s(P55,P60) s(P56,P60) s(P66,P60) s(P67,P60) s(P76,P60) s(P77,P60) s(P86,P60) s(P88,P60) s(P57,P61) s(P59,P61) s(P68,P61) s(P70,P61) s(P69,P62) s(P70,P62) s(P62,P63) s(P62,P64) s(P63,P64) s(P63,P65) s(P64,P65) s(P64,P66) s(P65,P66) s(P67,P66) s(P67,P68) s(P67,P69) s(P68,P69) s(P68,P70) s(P69,P70) s(P63,P71) s(P65,P71) s(P78,P71) s(P80,P71) s(P79,P72) s(P80,P72) s(P72,P73) s(P72,P74) s(P73,P74) s(P73,P75) s(P74,P75) s(P74,P76) s(P75,P76) s(P77,P76) s(P77,P78) s(P77,P79) s(P78,P79) s(P78,P80) s(P79,P80) s(P73,P81) s(P75,P81) s(P50,P81) s(P85,P81) s(P87,P82) s(P88,P82) s(P82,P83) s(P49,P83) s(P49,P84) s(P83,P84) s(P85,P86) s(P85,P87) s(P86,P87) s(P86,P88) s(P87,P88) s(P54,P89) s(P60,P89) s(P49,P90) s(P91,P90) s(P47,P90) s(P92,P91) s(P89,P92) s(P91,P93) s(P90,P93) s(P47,P93) s(P92,P94) s(P91,P94) s(P93,P94) s(P89,P95) s(P92,P95) s(P94,P95) s(P52,P96) s(P95,P96) s(P105,P96) s(P107,P96) s(P110,P97) s(P112,P97) s(P125,P97) s(P127,P97) s(P103,P98) s(P104,P98) s(P113,P98) s(P114,P98) s(P106,P99) s(P107,P99) s(P99,P100) s(P99,P101) s(P100,P101) s(P100,P102) s(P101,P102) s(P101,P103) s(P102,P103) s(P104,P103) s(P104,P105) s(P104,P106) s(P105,P106) s(P105,P107) s(P106,P107) s(P100,P108) s(P102,P108) s(P115,P108) s(P117,P108) s(P116,P109) s(P117,P109) s(P109,P110) s(P109,P111) s(P110,P111) s(P110,P112) s(P111,P112) s(P111,P113) s(P112,P113) s(P114,P113) s(P114,P115) s(P114,P116) s(P115,P116) s(P115,P117) s(P116,P117) s(P123,P118) s(P124,P118) s(P133,P118) s(P134,P118) s(P126,P119) s(P127,P119) s(P119,P120) s(P119,P121) s(P120,P121) s(P120,P122) s(P121,P122) s(P121,P123) s(P122,P123) s(P124,P123) s(P124,P125) s(P124,P126) s(P125,P126) s(P125,P127) s(P126,P127) s(P120,P128) s(P122,P128) s(P135,P128) s(P137,P128) s(P136,P129) s(P137,P129) s(P129,P130) s(P129,P131) s(P130,P131) s(P130,P132) s(P131,P132) s(P131,P133) s(P132,P133) s(P134,P133) s(P134,P135) s(P134,P136) s(P135,P136) s(P135,P137) s(P136,P137) color(blue) pen(2) m(P33,P35,MA10) m(P35,P48,MB10) f(P35,MA10,MB10) color(maroon) pen(2) m(P35,P48,MA20) m(P48,P49,MB20) f(P48,MA20,MB20) #color(gold) pen(2) #m(P1,P6,MA30) m(P6,P8,MB30) f(P6,MA30,MB30) #m(P41,P42,MA31) m(P42,P45,MB31) f(P42,MA31,MB31) pen(2) color(red) s(P93,P47) abstand(P93,P47,A0) print(abs(P93,P47):,1.96,12.399) print(A0,3.26,12.399) color(red) s(P90,P47) abstand(P90,P47,A1) print(abs(P90,P47):,1.96,12.099) print(A1,3.26,12.099) \geooff \geoprint() #128 4/10 mit 231 Kanten \geo ebene(478.83,622.21) x(2.1,11.68) y(-3.44,9) form(.) #//Eingabe war: #//blauerWinkel=39.600593591737876; gruenerWinkel=32.882386539360276; orangerWinkel=91.10459772745415; #//Figure 11: 114 231 #//blauerWinkel= #D=50; P[1]=[0,0]; P[2]=[D,0]; A(2,1); L(3,1,2); L(4,3,2); L(5,3,4); L(6,4,2); Q(7,5,6,ab(5,6,[1,6]),ab(3,1,2)); A(8,12,ab(1,12,[1,12])); A(12,1,ab(1,12,[1,12])); A(12,19,ab(8,12,[1,12])); Q(43,12,29,ab(19,1,[1,22]),ab(12,8,[1,12])); Q(74,33,64,ab(19,1,[1,22]),ab(1,19,[1,22])); # #//Ende der Eingabe, weiter mit fedgeo: p(4,6,P1) p(5,6,P2) p(4.5,6.866025403784438,P3) p(5.5,6.866025403784438,P4) p(5,7.732050807568877,P5) p(6,6,P6) p(6.713525491562422,6.700629269222037,P7) p(6.75,8.700296644120732,P8) p(5.875,8.216173725844804,P9) p(6.731762745781211,7.700462956671384,P10) p(5.85676274578121,7.216340038395456,P11) p(6.963525491562422,5.732383432670183,P12) p(6.911173994671003,7.713370637045331,P13) p(7.685289991118337,8.346414414397538,P14) p(7.84646398578934,7.359488407322138,P15) p(8.620579982236675,7.992532184674345,P16) p(7.072347989342006,6.726444629969932,P17) p(7.878818990230171,6.135170983739661,P18) p(9.858221470246434,6.421467721593025,P19) p(9.239400726241554,7.206999953133685,P20) p(8.8685202302383,6.278319352666344,P21) p(8.249699486233421,7.063851584207002,P22) p(5.963525491562421,5.732383432670183,P23) p(6.46352549156242,4.866358028885744,P24) p(5.46352549156242,4.866358028885745,P25) p(5.96352549156242,4.000332625101306,P26) p(4.963525491562421,5.732383432670183,P27) p(4.249999999999999,5.0317541634481495,P28) p(4.213525491562422,3.0320867885494516,P29) p(5.088525491562421,3.5162097068253786,P30) p(4.231762745781211,4.0319204759988,P31) p(5.10676274578121,4.516043394274727,P32) p(10.071746961808852,3.453554510142476,P33) p(9.910572967137849,4.440480517217875,P34) p(9.136456970690517,3.80743673986567,P35) p(8.975282976019512,4.7943627469410695,P36) p(8.201166979572177,4.161318969588863,P37) p(9.749398972466846,5.427406524293275,P38) p(8.94292797157868,6.018680170523543,P39) p(7.582346235567298,4.9468512011295225,P40) p(7.953226731570551,5.875531801596863,P41) p(8.57204747557543,5.089999570056204,P42) p(5.054670341628569,0.1778658252291816,P43) p(6.571497670676294,4.812430070998373,P44) p(7.564214562623971,4.932900699956584,P45) p(7.172186741737763,4.0129473382848015,P46) p(8.164903633685526,4.133417967242979,P47) p(6.17946984979003,3.8924767093266133,P48) p(6.544294257692487,2.9614003690630484,P49) p(8.369595959395248,2.1439202789317973,P50) p(8.267249796540387,3.1386691230873875,P51) p(7.456945108543868,2.5526603239974235,P52) p(7.3545989456890055,3.547409168153015,P53) p(5.555546290210353,3.110991334030669,P54) p(7.398485371550526,2.382550172649833,P55) p(7.677381115410689,1.4222287868332453,P56) p(6.706270527565968,1.6608586805512813,P57) p(6.985166271426129,0.700537294734696,P58) p(6.427374783705806,2.621180066367866,P59) p(5.567271536102235,2.111060077089087,P60) p(6.019918306527349,0.43920155998193877,P61) p(5.310970938865401,1.1444629511591362,P62) p(6.27621890376418,1.4057986859118925,P63) p(2.1021947674058943,-0.1922557086865906,P64) p(3.079220557937541,0.02086539452941949,P65) p(2.4061393732040863,0.7604339976743946,P66) p(3.383165163735734,0.9735551008904046,P67) p(2.7100839790022793,1.713123704035378,P68) p(4.056246348469188,0.23398649774543046,P69) p(4.604060273125417,1.0705867033112302,P70) p(3.4618047352823513,2.372605246292415,P71) p(4.4087928823439215,2.05133674593034,P72) p(3.6570721260638486,1.3918552036733054,P73) p(7.713911349934026,-1.9257581840756197,P74) p(9.605613314716136,2.568840192948489,P75) p(10.604865212044222,2.607513771604449,P76) p(10.138731564951424,1.7227994544104916,P77) p(11.137983462279596,1.7614730330664168,P78) p(9.139479667623284,1.6841258757545532,P79) p(9.426738173473463,0.7262727811640035,P80) p(11.17887053402807,-0.23810898509733658,P81) p(11.158426998153832,0.7616820239845401,P82) p(10.302804353750766,0.2440818980333317,P83) p(10.28236081787653,1.2438729071152128,P84) p(8.453583807539403,0.956426164939848,P85) p(10.230594343604889,0.07933749334667173,P86) p(10.429815724142056,-0.9006170165857359,P87) p(9.481539533718879,-0.5831705381417285,P88) p(9.680760914256048,-1.563125048074136,P89) p(9.28231815318171,0.3967839717906756,P90) p(8.38328662406374,-0.04109992794965045,P91) p(8.697336132095037,-1.7444416160748775,P92) p(8.048598986998883,-0.9834290560126338,P93) p(9.032023769159892,-0.8021124880118915,P94) p(6.782101973453689,-1.5628101355847575,P95) p(6.933684431446784,-2.5512547513466988,P96) p(6.0018750549664475,-2.1883067028558347,P97) p(6.153457512959542,-3.176751318617777,P98) p(5.850292596973352,-1.1998620870938943,P99) p(4.931130827598031,-1.5937423248804858,P100) p(4.171368167283053,-3.4438127829958347,P101) p(5.162412840121298,-3.310282050806805,P102) p(4.5512494974405415,-2.518777553938161,P103) p(5.542294170278786,-2.385246821749135,P104) p(5.049601420313842,-0.6007847635207133,P105) p(4.379387596076716,-2.465688088877359,P106) p(3.4282970485044046,-2.774600326120554,P107) p(3.6363164772980694,-1.7964756320020827,P108) p(2.6852259297257532,-2.1053878692452788,P109) p(4.587407024870382,-1.4875633947588813,P110) p(4.050531400406652,-0.6439019911989927,P111) p(2.3937103485658247,-1.1488217889659325,P112) p(3.076363083906263,-0.4180788499428276,P113) p(3.3678786650662063,-1.374644930222125,P114) nolabel() s(P27,P1) s(P1,P2) s(P1,P3) s(P2,P3) s(P3,P4) s(P2,P4) s(P3,P5) s(P4,P5) s(P9,P5) s(P11,P5) s(P4,P6) s(P2,P6) s(P10,P7) s(P11,P7) s(P6,P7) s(P12,P7) s(P8,P9) s(P8,P10) s(P9,P10) s(P9,P11) s(P10,P11) s(P6,P12) s(P17,P12) s(P8,P13) s(P8,P14) s(P13,P14) s(P13,P15) s(P14,P15) s(P14,P16) s(P15,P16) s(P20,P16) s(P22,P16) s(P13,P17) s(P15,P17) s(P17,P18) s(P21,P18) s(P22,P18) s(P12,P18) s(P38,P19) s(P19,P20) s(P19,P21) s(P20,P21) s(P20,P22) s(P21,P22) s(P12,P23) s(P12,P24) s(P23,P24) s(P23,P25) s(P24,P25) s(P24,P26) s(P25,P26) s(P30,P26) s(P32,P26) s(P23,P27) s(P25,P27) s(P27,P28) s(P31,P28) s(P32,P28) s(P1,P28) s(P29,P30) s(P29,P31) s(P30,P31) s(P30,P32) s(P31,P32) s(P33,P34) s(P33,P35) s(P34,P35) s(P34,P36) s(P35,P36) s(P35,P37) s(P36,P37) s(P40,P37) s(P42,P37) s(P34,P38) s(P36,P38) s(P38,P39) s(P41,P39) s(P42,P39) s(P19,P39) s(P12,P40) s(P12,P41) s(P40,P41) s(P40,P42) s(P41,P42) s(P69,P43) s(P12,P44) s(P12,P45) s(P44,P45) s(P44,P46) s(P45,P46) s(P45,P47) s(P46,P47) s(P51,P47) s(P53,P47) s(P44,P48) s(P46,P48) s(P48,P49) s(P52,P49) s(P53,P49) s(P54,P49) s(P50,P51) s(P50,P52) s(P51,P52) s(P51,P53) s(P52,P53) s(P48,P54) s(P59,P54) s(P50,P55) s(P50,P56) s(P55,P56) s(P55,P57) s(P56,P57) s(P56,P58) s(P57,P58) s(P61,P58) s(P63,P58) s(P55,P59) s(P57,P59) s(P54,P60) s(P59,P60) s(P62,P60) s(P63,P60) s(P43,P61) s(P43,P62) s(P61,P62) s(P61,P63) s(P62,P63) s(P64,P65) s(P64,P66) s(P65,P66) s(P65,P67) s(P66,P67) s(P66,P68) s(P67,P68) s(P71,P68) s(P73,P68) s(P65,P69) s(P67,P69) s(P69,P70) s(P72,P70) s(P73,P70) s(P43,P70) s(P29,P71) s(P29,P72) s(P71,P72) s(P71,P73) s(P72,P73) s(P33,P75) s(P33,P76) s(P75,P76) s(P75,P77) s(P76,P77) s(P76,P78) s(P77,P78) s(P82,P78) s(P84,P78) s(P75,P79) s(P77,P79) s(P79,P80) s(P83,P80) s(P84,P80) s(P85,P80) s(P81,P82) s(P81,P83) s(P82,P83) s(P82,P84) s(P83,P84) s(P79,P85) s(P90,P85) s(P81,P86) s(P81,P87) s(P86,P87) s(P86,P88) s(P87,P88) s(P87,P89) s(P88,P89) s(P92,P89) s(P94,P89) s(P86,P90) s(P88,P90) s(P85,P91) s(P90,P91) s(P93,P91) s(P94,P91) s(P74,P92) s(P74,P93) s(P92,P93) s(P92,P94) s(P93,P94) s(P74,P95) s(P74,P96) s(P95,P96) s(P95,P97) s(P96,P97) s(P96,P98) s(P97,P98) s(P102,P98) s(P104,P98) s(P95,P99) s(P97,P99) s(P99,P100) s(P103,P100) s(P104,P100) s(P105,P100) s(P101,P102) s(P101,P103) s(P102,P103) s(P102,P104) s(P103,P104) s(P99,P105) s(P110,P105) s(P101,P106) s(P101,P107) s(P106,P107) s(P106,P108) s(P107,P108) s(P107,P109) s(P108,P109) s(P112,P109) s(P114,P109) s(P106,P110) s(P108,P110) s(P105,P111) s(P110,P111) s(P113,P111) s(P114,P111) s(P64,P112) s(P64,P113) s(P112,P113) s(P112,P114) s(P113,P114) color(blue) pen(2) color(maroon) pen(2) color(gold) pen(2) pen(2) \geooff \geoprint() #491 4/11 mit 817 Kanten hierzu nochmal der Kern \geo ebene(551.54,563.19) x(-0.26,10.77) y(1.52,12.78) form(.) #//Eingabe war: #//blauerWinkel=39.600593591737876; gruenerWinkel=32.882386539359686; orangerWinkel=5; #//Eingabe war: # #//blauerWinkel=39.600593591737876; gruenerWinkel=32.882386539359686; orangerWinkel=5; #//No.313-3: #//blauerWinkel=39.600593591737876; #//gruenerWinkel=32.882386539359686; #D=50; P[1]=[0,0]; P[2]=[D,0]; A(2,1); #M(3,1,2,gruenerWinkel); N(4,3,2); L(5,3,4); #M(6,1,3,blauerWinkel); N(7,6,3); N(8,7,5); L(9,8,5); L(10,8,9); L(11,10,9); L(12,6,7); #Q(13,12,10,2*D,D); A(13,12); H(14,12,13,2); A(12,14); A(14,13); L(15,12,14); L(16,14,13); A(15,16); L(17,16,13); N(18,6,15); N(19,1,18); L(20,19,18); #Q(21,20,17,2*D,2*D); A(20,21); H(22,20,21,2); A(20,22); A(22,21); L(23,20,22); L(24,22,21); A(23,24); N(25,19,23); N(26,1,25); L(27,26,25); #Q(28,27,24,2*D,D); A(27,28); H(29,27,28,2); A(27,29); A(29,28); L(30,27,29); L(31,29,28); A(30,31); L(32,31,28); N(33,26,30); N(34,1,33); L(35,34,33); #Q(36,35,32,2*D,2*D); A(35,36); H(37,35,36,2); A(35,37); A(37,36); L(38,35,37); L(39,37,36); A(38,39); N(40,34,38); N(41,1,40); L(42,41,40); #Q(43,42,39,2*D,D); A(42,43); H(44,42,43,2); A(42,44); A(44,43); L(45,42,44); L(46,44,43); A(45,46); L(47,46,43); N(48,41,45); N(49,1,48); L(50,49,48); #Q(51,50,47,2*D,2*D); A(50,51); H(52,50,51,2); A(50,52); A(52,51); L(53,50,52); L(54,52,51); A(53,54); N(55,49,53); N(56,1,55); L(57,56,55); #Q(58,57,54,2*D,D); A(57,58); H(59,57,58,2); A(57,59); A(59,58); L(60,57,59); L(61,59,58); A(60,61); L(62,61,58); N(63,56,60); N(64,1,63); L(65,64,63); #Q(66,65,62,2*D,2*D); A(65,66); H(67,65,66,2); A(65,67); A(67,66); L(68,65,67); L(69,67,66); A(68,69); N(70,64,68); N(71,1,70); L(72,71,70); N(73,2,71); N(74,73,72); L(75,74,72); L(76,74,75); L(77,76,75); L(78,76,77); L(79,2,73); N(80,4,79); L(81,80,79); L(82,80,81); L(83,82,81); L(84,82,83); L(85,84,83); L(86,84,85); L(87,86,85); L(88,86,87); # #//Justieren #A(69,77); R(69,77); # #//weiter #L(89,21,17); Q(90,80,88,ab(78,87),ab(78,79)); A(90,80); A(90,88); A(90,11); R(90,11); L(91,11,90); # #R(18,25); # #alert( #"Winkel(P3,P1,P2)="+winkel(3,1,2)+"\n"+ #"Winkel(P6,P1,P3)="+winkel(6,1,3)+"\n"+ #"Winkel(P19,P1,P6)="+winkel(19,1,6)+"\n"+ #"Winkel(P26,P1,P19)="+winkel(26,1,19)+"\n"+ #"Winkel(P34,P1,P26)="+winkel(34,1,26)+"\n"+ #"Winkel(P41,P1,P34)="+winkel(41,1,34)+"\n"+ #"Winkel(P49,P1,P41)="+winkel(49,1,41)+"\n"+ #"Winkel(P56,P1,P49)="+winkel(56,1,49)+"\n"+ #"Winkel(P64,P1,P56)="+winkel(64,1,56)+"\n"+ #"Winkel(P71,P1,P64)="+winkel(71,1,64)+"\n"+ #"Winkel(P2,P1,P71)="+winkel(2,1,71)+"\n" #); # # # #//Ende der Eingabe, weiter mit fedgeo: p(4,6,P1) p(5,6,P2) p(4.83978680368108,6.542916314327646,P3) p(5.83978680368108,6.542916314327646,P4) p(5.33978680368108,7.408941718112084,P5) p(4.300989090476435,6.953627583186522,P6) p(5.140775894157516,7.496543897514169,P7) p(5.640775894157515,8.362569301298606,P8) p(6.316147061708384,7.62509131109078,P9) p(6.617136152184819,8.578718894277303,P10) p(7.292507319735688,7.841240904069476,P11) p(4.250703171980216,7.952362446101096,P12) p(5.82376777388737,9.187460724873555,P13) p(5.037235472933793,8.569911585487326,P14) p(4.109156079663314,8.942293969317037,P15) p(4.895688380616891,9.559843108703264,P16) p(5.682220681570467,10.177392248089493,P17) p(4.159441998159538,7.943559106402462,P18) p(3.858452907683103,6.98993152321594,P19) p(3.183081740132234,7.727409513423767,P20) p(3.754660921776905,9.64399429868906,P21) p(3.4688713309545696,8.685701906056414,P22) p(2.4960709792701588,8.454056755529393,P23) p(2.7818605700924937,9.41234914816204,P24) p(3.1714421468210303,7.716578765321569,P25) p(3.312989239137927,6.726647242105629,P26) p(2.3849098458674494,7.099029625935345,P27) p(1.858464789584191,9.02849991664078,P28) p(2.1216873177258204,8.063764771288062,P29) p(1.4178134379975087,7.353439802392688,P30) p(1.1545909098558793,8.318174947745407,P31) p(0.8913683817142499,9.282910093098124,P32) nolabel() p(2.3458928312679865,6.981057418562973,P33) p(3.032903592130059,6.254410176457345,P34) p(2.060103240445647,6.022765025930328,P35) p(0.5337482643676528,7.315142868127394,P36) p(1.2969257524066493,6.668953947028861,P37) p(1.1188984751107602,5.684928394241428,P38) p(0.35572098707176325,6.331117315339962,P39) p(2.091698826795172,5.916573544768446,P40) p(3.058795234665113,5.662163368311102,P41) p(2.354921354936801,4.9518383994157285,P42) p(0.3913364065943399,5.331751745644752,P43) p(1.3731288807655706,5.141795072530241,P44) p(1.6995178133156421,4.1965595120963215,P45) p(0.717725339144411,4.386516185210834,P46) p(-0.2640671350268189,4.576472858325345,P47) p(2.403391693043959,4.906884480991691,P48) p(3.3445964583788466,5.244721112680588,P49) p(3.1665691810829553,4.260695559893156,P50) p(1.3581031806081576,3.406616684655811,P51) p(2.2623361808455567,3.8336561222744834,P52) p(3.0842796823598464,3.264087091938012,P53) p(2.1800466821224473,2.8370476543193393,P54) p(3.2623069596557404,4.248112644725444,P55) p(3.9177105012768942,5.003391532044856,P56) p(4.244099433826972,4.0581559716109386,P57) p(3.090826159698185,2.4241545165380654,P58) p(3.6674627967625786,3.241155244074502,P59) p(4.663324500251698,3.1502736313921282,P60) label() p(4.086687863187304,2.3332729038556916,P61) p(3.510051226122911,1.516272176319255,P62) p(4.336935567701615,4.095509191826043,P63) p(4.41922506642472,5.092117659781187,P64) p(5.241168567939012,4.522548629444718,P65) p(5.238462061052605,2.5225504607404385,P66) p(5.239815314495809,3.5225495450925783,P67) p(6.106516552027541,4.021377135409075,P68) p(6.105163298584338,3.0213780510569355,P69) p(5.284573050513252,4.590946165745548,P70) p(4.865347984088531,5.498828505964362,P71) p(5.8612096875776505,5.407946893281981,P72) p(5.865347984088531,5.498828505964362,P73) p(6.8612096875776505,5.407946893281979,P74) p(6.361209687577649,4.5419214894975415,P75) p(7.36120968757765,4.54192148949754,P76) p(6.861209687577648,3.675896085713102,P77) p(7.861209687577649,3.6758960857131,P78) p(5.86670123753173,6.498827590316501,P79) p(6.706488041212809,7.041743904644149,P80) p(6.7567739597090295,6.043009041729576,P81) p(7.596560763390109,6.585925356057223,P82) p(7.646846681886329,5.58719049314265,P83) p(8.486633485567406,6.130106807470297,P84) p(8.536919404063628,5.131371944555725,P85) p(9.376706207744707,5.674288258883371,P86) p(9.426992126240926,4.675553395968798,P87) p(10.266778929922005,5.218469710296445,P88) p(4.256504627166384,11.580008992683133,P89) p(8.272270479876088,8.041401214899846,P90) p(7.6090449857973965,8.789820845858369,P91) nolabel() s(P1,P2) s(P1,P3) s(P3,P4) s(P2,P4) s(P3,P5) s(P4,P5) s(P1,P6) s(P6,P7) s(P3,P7) s(P7,P8) s(P5,P8) s(P8,P9) s(P5,P9) s(P8,P10) s(P9,P10) s(P10,P11) s(P9,P11) s(P6,P12) s(P7,P12) s(P14,P12) s(P10,P13) s(P13,P14) s(P12,P15) s(P14,P15) s(P16,P15) s(P14,P16) s(P13,P16) s(P16,P17) s(P13,P17) s(P6,P18) s(P15,P18) s(P1,P19) s(P18,P19) s(P19,P20) s(P18,P20) s(P22,P20) s(P17,P21) s(P21,P22) s(P20,P23) s(P22,P23) s(P24,P23) s(P22,P24) s(P21,P24) s(P19,P25) s(P23,P25) s(P1,P26) s(P25,P26) s(P26,P27) s(P25,P27) s(P29,P27) s(P24,P28) s(P28,P29) s(P27,P30) s(P29,P30) s(P31,P30) s(P29,P31) s(P28,P31) s(P31,P32) s(P28,P32) s(P26,P33) s(P30,P33) s(P1,P34) s(P33,P34) s(P34,P35) s(P33,P35) s(P37,P35) s(P32,P36) s(P36,P37) s(P35,P38) s(P37,P38) s(P39,P38) s(P37,P39) s(P36,P39) s(P34,P40) s(P38,P40) s(P1,P41) s(P40,P41) s(P41,P42) s(P40,P42) s(P44,P42) s(P39,P43) s(P43,P44) s(P42,P45) s(P44,P45) s(P46,P45) s(P44,P46) s(P43,P46) s(P46,P47) s(P43,P47) s(P41,P48) s(P45,P48) s(P1,P49) s(P48,P49) s(P49,P50) s(P48,P50) s(P52,P50) s(P47,P51) s(P51,P52) s(P50,P53) s(P52,P53) s(P54,P53) s(P52,P54) s(P51,P54) s(P49,P55) s(P53,P55) s(P1,P56) s(P55,P56) s(P56,P57) s(P55,P57) s(P59,P57) s(P54,P58) s(P58,P59) s(P57,P60) s(P59,P60) s(P61,P60) s(P59,P61) s(P58,P61) s(P61,P62) s(P58,P62) s(P56,P63) s(P60,P63) s(P1,P64) s(P63,P64) s(P64,P65) s(P63,P65) s(P67,P65) s(P62,P66) s(P66,P67) s(P65,P68) s(P67,P68) s(P69,P68) s(P67,P69) s(P66,P69) s(P77,P69) s(P64,P70) s(P68,P70) s(P1,P71) s(P70,P71) s(P71,P72) s(P70,P72) s(P2,P73) s(P71,P73) s(P73,P74) s(P72,P74) s(P74,P75) s(P72,P75) s(P74,P76) s(P75,P76) s(P76,P77) s(P75,P77) s(P76,P78) s(P77,P78) s(P2,P79) s(P73,P79) s(P4,P80) s(P79,P80) s(P80,P81) s(P79,P81) s(P80,P82) s(P81,P82) s(P82,P83) s(P81,P83) s(P82,P84) s(P83,P84) s(P84,P85) s(P83,P85) s(P84,P86) s(P85,P86) s(P86,P87) s(P85,P87) s(P86,P88) s(P87,P88) s(P21,P89) s(P17,P89) s(P11,P90) s(P11,P91) s(P90,P91) color(blue) pen(2) m(P3,P1,MA10) m(P1,P6,MB10) f(P1,MA10,MB10) color(maroon) pen(2) m(P2,P1,MA20) m(P1,P3,MB20) f(P1,MA20,MB20) color(gold) pen(2) pen(2) color(red) s(P69,P77) abstand(P69,P77,A0) print(abs(P69,P77):,-0.26,12.78) print(A0,1.04,12.78) color(red) s(P90,P11) abstand(P90,P11,A1) print(abs(P90,P11):,-0.26,12.48) print(A1,1.04,12.48) color(red) s(P18,P25) abstand(P18,P25,A2) print(abs(P18,P25):,-0.26,12.18) print(A2,1.04,12.18) \geooff \geoprint() Der Abstand P18-P25=1.013 ist keine Kante, damit stelle ich nur fest, ob der Winkel in P19 tatsächlich größer 0 ist.


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  Beitrag No.501, vom Themenstarter, eingetragen 2016-09-04

Perfekt! Jetzt können wir was die Beweise angeht einfach auf den Thread und spezielle Beiträge darin verweisen. Wer es dann genauer wissen will, kann ja dann beim Graphen-Team (das sind wir ;-) ) nachfragen.


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haribo
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  Beitrag No.502, eingetragen 2016-09-05

guter plan, evtl finden wir noch nen tollen namen!!!


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haribo
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  Beitrag No.503, eingetragen 2016-09-17

hallo, wiso diskutieren wir die beweglichkeit des 4/12 unendlich nicht hier? ich hab in einer ecke meines zeichenplatzes noch diesen 4/13 gefunden http://www.matheplanet.com/matheplanet/nuke/html/uploads/a/35059_st4-13-beweglich.png ich hatte damals (11.april 2016) beschlossen das eine winkeländerung möglich ist, aber eben nicht überschneidungsfrei wieder zusammengeführt werden kann, also auf diese weise kein zweiter 13er knoten generiert werden kann http://www.matheplanet.com/matheplanet/nuke/html/uploads/a/35059_st4-13-beweglich-detail.png dieser schluss muss aber nicht richtig sein..... ansonsten ging es meines wissens damals (noch) nicht um starr nachtrag: wir haben wohl nur zwei beiträge zu den 4/unendlich-infiniten graphen geschrieben #138 und #162 beide anfang april 2016


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haribo
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  Beitrag No.504, eingetragen 2016-09-17

man kann an jedem (?, na jedenfals an vielen) knoten des unendlich/4 graphen wiederum einen neuen unendlichen sektor starten! er bleibt aber ein unendlicher also so ungefähr sieht ein 4-13-13-infinite in seinen wesentlichen bestandteilen aus (is diesmal der einfachheithalber nur ein 4-13-11 aber das ändert nichts am prinzip): http://www.matheplanet.com/matheplanet/nuke/html/uploads/a/35059_st4-13-13-infinite.png


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Slash
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  Beitrag No.505, vom Themenstarter, eingetragen 2016-09-17

\quoteon(2016-09-17 18:12 - haribo in Beitrag No. 503) hallo, wiso diskutieren wir die beweglichkeit des 4/12 unendlich nicht hier? \quoteoff Klar sollten wir das tun. Dieser Beitrag ist also eigentlich von Stefan. :-) Hallo, im letzten Satz des PDF ist mir noch etwas aufgefallen. "rigid" heißt doch starr, aber nach gründlichen Überlegungen müsste der unendliche 4/12 eigentlich beweglich sein. Sehr beweglich sogar, wie eine quicklebendige, gaaanz langsam im Meer dahinschwebende (nicht gleich erschrecken, ist harmlos) Qualle. Im ersten Bild gebe ich die blauen Winkel als 30°-Winkel ein, alle anderen Winkel ergeben sich danach zwansläufig, da ist keine Variationsmöglichkeit mehr. http://www.matheplanet.de/matheplanet/nuke/html/uploads/a/8038_4_12_stefan_a.png Nun kann ich aber jeden blauen Winkel etwas variieren. Als Beispiel verändere ich den bei Punkt P2 beginnenden blauen Winkel von 30° auf 46°. http://www.matheplanet.de/matheplanet/nuke/html/uploads/a/8038_4_12_stefan_b.png Der von P26 nach rechts ausgehende Keil bleibt in sich unverändert, verschiebt sich aber nach oben und dabei drehen sich alle grünen Kante um den gleichen Winkel. Das geht, weil die grünen Kanten alle parallel sind und es ist auch vorstellbar, dass sich dies nach rechts unendlich fortsetzen lässt. Die zu P2-P26 parallelen Kanten sollen die grünen Kanten sein, das nochmal neu einzugeben lasse ich jetzt weg. Nun noch ein Beispiel, wo mehrere blaue Winkel unterschiedlich verändert wurden. Mehr Kanten zeichnen hat der Formeleditor fedgeo nicht mitgemacht. http://www.matheplanet.de/matheplanet/nuke/html/uploads/a/8038_4_12_stefan_c.png Schaut euch das am besten im Streichholzprogramm an, da werden noch mehr Kanten gezeichnet und es ist besser erkennbar, dass sich das Muster periodisch unendlich fortsetzt. Wichtig: Diese Eingabe funktioniert nur in älteren Versionen des Streichholzprogramms, etwa Streichholzgraph-195.htm, die neueren Versionen sind alle verbastelt, das passt alles nicht mehr richtig zusammen. Der Bildaufbau dauert länger als sonst. Es müsste auch möglich sein, einen 4/12 mit mehreren 12-er Knoten zu zeichnen. Doch da ist die Formulierung im PDF nicht eindeutig genug, ob tatsächlich nur 4/12 mit einem 12-er Knoten betrachtet werden oder ob behauptet wird, dass es keine anderen gibt. Viele Grüße, Stefan


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  Beitrag No.506, vom Themenstarter, eingetragen 2016-09-17

Hi Stefan, super Leistung, dass dir der Fehler mit der Starrheit aufgefallen ist. Das letzte Bild ist wirklich der Hammer. Das hätte ich nicht gedacht, dass der Graph sooo beweglich ist. Ich hatte das schon immer im Hinterkopf, da ich die Beweglichkeit nie am Modell gepfrüft hatte, war mir aber nie ganz sicher, ob die Unendlichkeit eine Prüfung überhaupt zulässt. Das hast du ja jetzt herausgefunden. Die Formulierung (eigentlich nur eine Vermutung) im Paper war so gemeint, dass es immer nur einen Knoten höheren Grades als 11 geben kann. Lässt sich diese Beweglichkeit des 4/12 auf alle 4/n mit n>12 übertragen? Das wäre noch sehr wichtig zu wissen. Und es sind dann auch immer unendlich viele Knoten n-ten Grades möglich? Viele Grüße und nochmals Danke für das Finden dieses Fehlers. Auch haribo danke ich für seine beiden Beiträge dazu. Mike


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haribo
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  Beitrag No.507, eingetragen 2016-09-17

nochmal nen ordentlicheren 4-12-12-unendlich http://www.matheplanet.com/matheplanet/nuke/html/uploads/a/35059_st4-12-12unendlich.png das blaue rautenfeld könnte man evtl. auch noch runterzerren bis sich alle unter 60 grad schneiden... könnte noch was bringen


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haribo
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  Beitrag No.508, eingetragen 2016-09-18

zur beweglichkeit, sie ist einerseits noch freier als stefan sie hier darstellt, da keine punktsymetrie erforderlich ist, andrerseits ist jeder ursprungsstrang durch seine nachbar-ursprungs-strang-richtungen in seiner beweglichkeit eingeschränkt: http://www.matheplanet.com/matheplanet/nuke/html/uploads/a/35059_st4-unendlich-beweglich.png beachte die ursprungs radialen, hier links unten am ursprung rot,grün,blau den grünen radialen strang habe ich zur unterscheidung gelb fortgesetzt, und dieser gelbe strang kann in jedem neuen abstand seine richtung frei im bereich zwischen der roten und blauen richtung wählen, allerdings geht jeder rechtseitige ast von diesem gelben strang als paralelle zu rot los, und jeder linksseitige ast vom gelben strang als paralelle zu blau man kann also, im rahmen der ursprünglichen nachbar-radialen richtungen, jeden strang einzeln frei herumvagabundieren lassen, muss in der beweglichkeit also keine punktsymetrie zum ursprung einhalten der blaue ursprungsstrang könnte also, in dem rahmen, eine ganz andere linie verfolgen, der rote auch und die bereiche dazwischen würden sich dann mit paralellogrammen immer wieder 4/4 füllen lassen


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Slash
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  Beitrag No.509, vom Themenstarter, eingetragen 2016-09-18

Sehr schön! Wer hätte gedacht, dass die Unendlichen soviel Forschungspotenzial besitzen. Mal wieder ein gutes Beispiel dafür, was es noch Neues zu entdecken gibt, wenn einer ein Thema anstößt, das ein anderer schon für erledigt hielt. Der 4/11 war auch so ein Ding - Beweglichkeit des Kerns und Minimierung. Ein starrer 4/7, ein symmetrischer 4/10 und ein 4/9 ohne Klammer - natürlich alle minimal - müssen auch noch entdeckt werden. ;-)


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haribo
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  Beitrag No.510, eingetragen 2016-09-18

12-12-4-ziemlich einfach http://www.matheplanet.com/matheplanet/nuke/html/uploads/a/35059_st4-12-12-unendlich-einfach.png [Die Antwort wurde nach Beitrag No.508 begonnen.]


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haribo
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  Beitrag No.511, eingetragen 2016-09-18

\quoteon(2016-09-18 00:51 - Slash in Beitrag No. 509) Ein starrer 4/7, ein symmetrischer 4/10 und ein 4/9 ohne Klammer - natürlich alle minimal - müssen auch noch entdeckt werden. ;-) \quoteoff immer willst du den schönen 4/10er angreifen, das finde ich nicht in ordnung lass uns lieber kollektiv euer 4/11er monster mit seinen fünf klammern verbessern hier mein strategie vorschlag: endliche, kleine 11er kugeln am schwarzen strich in den pfelirichtungen aufknacken und verändern bis sie erstens zu zehn elfteln glatt geschlossen sind und zweitens zwei stück davon gespiegelt wieder zusammengesetzt werden können.... das hat gutes potential meine ich, evtl braucht man dazu dann nur noch eine klammer, oder im besten fall gar keine mehr diese elfer-fast-kugeln sind innerhalb der letzten zwei stunden als spinn-off entstanden... die roten linien passen noch nicht, (eben nur fast) http://www.matheplanet.com/matheplanet/nuke/html/uploads/a/35059_st4-11strategie.png


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Slash
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  Beitrag No.512, vom Themenstarter, eingetragen 2016-09-18

Du haust ja heute richtig was an Ideen raus, haribo! Bei den 4/11er Kugeln entstehen aber 5er Knoten, wenn die roten Kanten passen würden, oder?


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haribo
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  Beitrag No.513, eingetragen 2016-09-18

Ach echt 5er? Wie kleinlich ist dassdenn. Dann fangen wir innen eben vorerst auch mit zwei 5er Kernen an, oder? Da reicht dann ein Rad , das hat dann paar mal 5er und Rest besteht aus 4er n na ja ob das dann was neues ist? http://www.matheplanet.com/matheplanet/nuke/html/uploads/a/35059_st4-5-unsym.png


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  Beitrag No.514, vom Themenstarter, eingetragen 2016-09-18

Ich fasse zusammen: Für alle n>11 existieren nur unendliche (4,n)-reguläre Streichholzgraphen mit einer unendlichen Anzahl an Knoten und Kanten. Die Anzahl der Knoten vom Grad n ist dabei nicht begrenzt und kann von 1 bis Unendlich reichen. Jeder dieser Graphen ist flexibel und kann sowohl symmetrisch als auch asymmetrisch konstruiert werden. Aufgrund der Unendlichkeit gibt es es unendliche viele Variationsmöglichkeiten zur Konstruktion eines jeden solchen Graphen.


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haribo
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  Beitrag No.515, eingetragen 2016-09-18

es tauchen wiedersprüche auf zu den beweglichkeitsüberlegungen aus #508 es können überschneidungen in den rautenbereichen entstehen http://www.matheplanet.com/matheplanet/nuke/html/uploads/a/35059_st4-12_mit_berschneidung.png


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  Beitrag No.516, vom Themenstarter, eingetragen 2016-09-18

Macht ja nichts. Man kann den Graphen ja so verformen, dass keine Überschneidungen stattfinden. Es bleiben ja trotzdem unendlich viele Möglichkeiten im Sinne der rellen Zahlen und der Verformungen wie wir sie schon hatten. Wir können im Paper ja ein paar Beispiele angeben. Daraus könnte man sogar ein eigenes Paper/Kapitel machen. Der 4/7 lässt sich ja auch mit Überschneidungen verformen. Darauf muss man wohl nicht extra hinweisen.


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haribo
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  Beitrag No.517, eingetragen 2016-09-18

die beschreibung in #508 ist dann aber noch nicht korrekt


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StefanVogel
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  Beitrag No.518, eingetragen 2016-09-24

Die Beschreibung stimmt, man muss nur in der Skizze den rot und blau beginnenden Radialstrang ebenfalls komplett rot und blau durchzeichnen. Dann gibt es zu jeder gelben und blauen Kante irgendwo innerhalb des Sektors eine Raute, die aus diesen beiden Kanten gebildet wird. Man muss nur von der ausgewählten gelben Kante in Richtung der blauen Kanten gehen und von der ausgewählten blauen Kante in Richtung der gelben Kanten. Am Treffpunkt beider Wege befindet sich diese Raute. Daraus ergibt sich die Bedingung, dass jede gelbe Kante einen kleineren Anstieg haben muss als jede blaue Kante und jede rote Kante einen kleineren Anstieg als jede gelbe Kante. Im Graph #515 hat vom Mittelpunkt aus gezählt die dritte gelbe Kante einen größeren Anstieg als die zweite grüne, das führt dann zur Überschneidung, ebenso die dritte grüne und zweite weiße Kante. Wenn man sich anfangs für die gelben Kanten einen Bereich von 0° bis 30° vorgibt und für die blauen Kanten einen Bereich von 30° bis 60°, dann kann keine Überschneidung auftreten und es ist immer noch genügend Spielraum, um unendlich viele Fortsetzungen zu finden. Als Beispiel dieser Sektor, in dem die Radialstränge gegenläufig aufeinander zusteuern, die sich anbahnende Überschneidung sich aber wieder auflöst. \geo ebene(904.08,450.99) x(4,34.14) y(8,23.03) form(.) #//Eingabe war: #//blauerWinkel=40.49207000332465; gruenerWinkel=32.36251966007222; orangerWinkel=0; #//Sektor aus unendlich 4/n #D=30; P[1]=[0,2*D]; P[2]=[D,2*D]; A(2,1); M(3,1,2,30); #var p=4;//nächste Knotennummer # #var par=13;//Wellenamplitude #var T=7;//Wellenlänge # #for (var k=1;k<30;k++) { # for (var i=0;iBeitrag No. 511) lass uns lieber kollektiv euer 4/11er monster mit seinen fünf klammern verbessern \quoteoff Das wäre mir sehr recht, weil bei diesem Graph eigentlich noch eine Überprüfung mit noch mehr Nachkommastellen erforderlich ist. Deshalb habe ich einen weiteren 11-er Kern ausprobiert, kann sein, dass der schonmal da war. \geo ebene(491.21,612.64) x(-0.99,8.83) y(0.52,12.78) form(.) #//Eingabe war: #//blauerWinkel=40.49207000332465; gruenerWinkel=32.36251966007222; orangerWinkel=0; #//Bodybilder No.323-4 mit Kern 313-3: mit senkrechtem R(162,78) #//blauerWinkel=40.49207000332465; gruenerWinkel=32.36251966007222 #D=50; P[1]=[0,0]; P[2]=[D,0]; A(2,1); #M(3,1,2,gruenerWinkel); N(4,3,2); L(5,3,4); #M(6,1,3,blauerWinkel); N(7,6,3); N(8,7,5); L(9,8,5); L(10,8,9); L(11,10,9); L(12,6,7); #Q(13,12,10,ab(11,5,8,9,10),D); L(17,16,13); #N(18,6,14); N(19,1,18); L(20,19,18); #Q(21,20,17,ab(11,5,[8,10]),ab(5,11,[8,10])); L(28,25,27); #N(29,19,22); N(30,1,29); L(31,30,29); #Q(32,31,24,ab(13,12,[14,17]),D); #N(37,30,33); N(38,1,37); L(39,38,37); #Q(40,39,36,ab(21,20,[22,24]),ab(21,17,[25,28])); #N(48,38,41); N(49,1,48); L(50,49,48); #Q(51,50,43,ab(13,12,[14,17]),D); #N(56,49,52); N(57,1,56); L(58,57,56); #Q(59,58,55,ab(21,20,[22,24]),ab(21,17,[25,28])); #N(67,57,60); N(68,1,67); L(69,68,67); #Q(70,69,62,ab(13,12,[14,17]),D); #N(75,68,71); N(76,1,75); L(77,76,75); #Q(78,77,74,ab(21,20,[22,24]),ab(21,17,[25,28])); #N(86,76,79); N(87,1,86); L(88,87,86); # #N(89,2,87); #Q(90,89,88,D,ab(71,69,[70,74])); #L(95,2,89); N(96,4,95); L(97,96,95); N(98,11,97); L(99,98,97); L(100,98,99); # #A(81,91); R(81,91); #A(11,96); R(11,96); #R(18,29); #/* #A(99,100); A(100,99,ab(99,100,[1,100])); A(99,100); # #Q(199,28,194,5.87336307704547344599*D,6.20985554572319298217*D); #A(199,28); A(199,194); #Q(200,28,199,3.85410196624968426349*D,3.85410196624968426349*D); #A(200,28); A(200,199); #Q(201,28,200,ab(21,17,[25,28]),ab(17,21,[25,28])); #A(205,209); L(210,209,205); #A(200,199,ab(28,200,[201,209])); A(210,215); A(210,219); #Q(220,199,194,ab(199,200,[211,219]),ab(210,200,[210,219],199)); #A(225,239); A(229,239); # #Q(240,94,85,ab(199,194,[220,239],"gespiegelt"),ab(28,199,[200,219])); # #Q(281,66,47,ab(240,94,[241,260]),ab(240,85,[261,280])); #Q(322,185,166,ab(240,94,[241,260]),ab(240,85,[261,280])); #Q(363,147,128,ab(240,94,[241,260]),ab(240,85,[261,280])); # #function W(k,i,j) { # var Winkel=Math.acos( # ((P[k][0]-P[i][0])*(P[j][0]-P[i][0]) # +(P[k][1]-P[i][1])*(P[j][1]-P[i][1]))/ab(k,i)/ab(i,j)) # *180/Math.PI; # alert(Winkel); # } # #//für Ausgabe der Winkel in der nächsten Zeile "//" entfernen: #//W(3,1,2); W(6,1,3); W(19,1,6); W(30,1,19); W(38,1,30); W(49,1,38); W(57,1,49); W(68,1,57); W(76,1,68); W(87,1,76); W(2,1,87); # #*/ # #//Ende der Eingabe, weiter mit fedgeo: p(4,6,P1) p(5,6,P2) p(4.844678258782334,6.535274358754876,P3) p(5.844678258782334,6.535274358754876,P4) p(5.344678258782334,7.401299762539314,P5) p(4.29479775600703,6.955559670064209,P6) p(5.1394760147893646,7.4908340288190844,P7) p(5.639476014789365,8.356859432603523,P8) p(6.3196160858933315,7.623777251890683,P9) p(6.614413841900362,8.579336921954893,P10) p(7.294553913004329,7.846254741242053,P11) p(4.25357569272205,7.954709679571554,P12) p(5.824489948800048,9.192541816838522,P13) p(4.110307218494558,8.944393540353637,P14) p(5.039032820761049,8.573625748205039,P15) p(4.895764346533558,9.56330960898712,P16) p(5.681221474572558,10.182225677620604,P17) p(4.151529281779548,7.945243530846292,P18,nolabel) print(\P18,3.75,8.2) p(3.856731525772518,6.989683860782083,P19) p(3.176591454668552,7.722766041494922,P20) p(3.757065806355596,9.636675529175442,P21) p(2.492962924152617,8.452596180818194,P22) p(3.466828630512074,8.679720785335181,P23) p(2.7832000999961393,9.409550924658454,P24) p(4.001874579613895,10.606246911042588,P25) p(4.719143640464077,9.909450603398025,P26) p(4.963952413722375,10.879021985265169,P27) p(4.246683352872193,11.575818292909734,P28) p(3.1731029952567824,7.71951400010554,P29,nolabel) print(\P29,2.77,7.85) nolabel() p(3.316371469484264,6.7298301393234565,P30) p(2.3876458672177776,7.100597931472063,P31) p(1.8583244952593039,9.029281131271345,P32) p(1.4201712007889404,7.3535658539808475,P33) p(2.1229851812385405,8.064939531371703,P34) p(1.1555105148097033,8.31790745388049,P35) p(0.8908498288304658,9.28224905378013,P36) p(2.3488968030554283,6.982798061832245,P37) p(3.032525333571164,6.252967922508789,P38) p(2.0586596272116466,6.025843317992064,P39) p(0.5296911898032395,7.315128204046692,P40) p(1.1181407858402288,5.686101785315582,P41) p(1.294175408507444,6.670485761019378,P42) p(0.35365656713602434,6.330744228342896,P43) p(-0.23180746453154732,7.963294694576947,P44) p(0.7102705093168526,8.29868862891341,P45) p(-0.05122814501793638,8.946855119443667,P46) p(-0.993306118866335,8.611461185107203,P47) p(2.0920064921997454,5.9132263898323085,P48) p(3.0594811586285813,5.660258467323519,P49) p(2.3566671781789785,4.9488847899326665,P50) p(0.3936152752706903,5.331542896456169,P51) p(1.7002083818452043,4.194522908130561,P52) p(1.3751412267248342,5.1402138431944175,P53) p(0.71868243039106,4.385851961392312,P54) p(-0.2628435210630844,4.577181014654064,P55) p(2.403022362294803,4.905896585521418,P56) p(3.3435412036662218,5.245638118197899,P57) p(3.1675065809990053,4.261254142494104,P58) p(1.3591111439145358,3.407025869061251,P59) p(3.085299414439773,3.2646388798343833,P60) p(2.2633088624567708,3.834140005777677,P61) p(2.1811016958975387,2.8375247431179558,P62) p(0.4469304364439033,2.997237683630806,P63) p(0.5481338114257261,3.9921034418576573,P64) p(-0.3640468960449068,3.5823152564272105,P65) p(-0.4652502710267292,2.587449498200361,P66) p(3.261334037106984,4.24902285553818,P67) p(3.9177928334407626,5.00338473734028,P68) p(4.2428599885611264,4.057693802276423,P69) p(3.091000831407571,2.4226951839034574,P70) p(4.662870368604461,3.150174501844825,P71) p(3.666930409984349,3.2401944930899402,P72) p(4.0869407900276835,2.332675192658343,P73) p(3.5110112114509056,1.5151758834718603,P74) p(4.337803213484089,4.095865436908681,P75) p(4.420010380043326,5.0924806995684,P76) p(5.242000932026325,4.522979573625102,P77) p(5.238531299888241,2.522982583214159,P78) p(6.107157624585954,4.021477931235683,P79) p(5.240266115957283,3.522981078419631,P80) label() p(6.105422808516913,3.021479436030211,P81) p(5.243044379819401,1.5229927672112487,P82) p(4.3747712556695735,2.0190792333430103,P83) p(4.379284335600735,1.0190894173400986,P84) p(5.247557459750561,0.5230029512083378,P85) p(5.285167072602956,4.590979057178983,P86) p(4.86515669255963,5.498498357610584,P87) p(5.861096651179741,5.40847836636546,P88) p(5.86515669255963,5.498498357610584,P89) p(6.861096651179742,5.408478366365474,P90) p(6.861096651179764,3.676427558796596,P91) p(6.3610966511797535,4.542452962581028,P92) p(7.3610966511797535,4.542452962581042,P93) p(7.861096651179766,3.6764275587966093,P94) p(5.866891508628668,6.498496852816055,P95) p(6.711569767411,7.033771211570935,P96) p(6.752791830695985,6.034621202063589,P97) p(7.3357759762892965,6.8471047317347065,P98) p(7.747915280344276,5.9359838868117745,P99) p(8.330899425937588,6.748467416482891,P100) nolabel() s(P1,P2) s(P1,P3) s(P3,P4) s(P2,P4) s(P3,P5) s(P4,P5) s(P1,P6) s(P6,P7) s(P3,P7) s(P7,P8) s(P5,P8) s(P8,P9) s(P5,P9) s(P8,P10) s(P9,P10) s(P10,P11) s(P9,P11) s(P96,P11) s(P6,P12) s(P7,P12) s(P15,P13) s(P16,P13) s(P10,P13) s(P12,P14) s(P12,P15) s(P14,P15) s(P14,P16) s(P15,P16) s(P16,P17) s(P13,P17) s(P26,P17) s(P27,P17) s(P6,P18) s(P14,P18) s(P1,P19) s(P18,P19) s(P19,P20) s(P18,P20) s(P23,P21) s(P24,P21) s(P20,P22) s(P20,P23) s(P22,P23) s(P22,P24) s(P23,P24) s(P21,P25) s(P21,P26) s(P25,P26) s(P25,P27) s(P26,P27) s(P25,P28) s(P27,P28) s(P19,P29) s(P22,P29) s(P1,P30) s(P29,P30) s(P30,P31) s(P29,P31) s(P34,P32) s(P35,P32) s(P24,P32) s(P31,P33) s(P31,P34) s(P33,P34) s(P33,P35) s(P34,P35) s(P32,P36) s(P35,P36) s(P45,P36) s(P46,P36) s(P30,P37) s(P33,P37) s(P1,P38) s(P37,P38) s(P38,P39) s(P37,P39) s(P42,P40) s(P43,P40) s(P39,P41) s(P39,P42) s(P41,P42) s(P41,P43) s(P42,P43) s(P40,P44) s(P40,P45) s(P44,P45) s(P44,P46) s(P45,P46) s(P44,P47) s(P46,P47) s(P38,P48) s(P41,P48) s(P1,P49) s(P48,P49) s(P49,P50) s(P48,P50) s(P53,P51) s(P54,P51) s(P43,P51) s(P50,P52) s(P50,P53) s(P52,P53) s(P52,P54) s(P53,P54) s(P51,P55) s(P54,P55) s(P64,P55) s(P65,P55) s(P49,P56) s(P52,P56) s(P1,P57) s(P56,P57) s(P57,P58) s(P56,P58) s(P61,P59) s(P62,P59) s(P58,P60) s(P58,P61) s(P60,P61) s(P60,P62) s(P61,P62) s(P59,P63) s(P59,P64) s(P63,P64) s(P63,P65) s(P64,P65) s(P63,P66) s(P65,P66) s(P57,P67) s(P60,P67) s(P1,P68) s(P67,P68) s(P68,P69) s(P67,P69) s(P72,P70) s(P73,P70) s(P62,P70) s(P69,P71) s(P69,P72) s(P71,P72) s(P71,P73) s(P72,P73) s(P70,P74) s(P73,P74) s(P83,P74) s(P84,P74) s(P68,P75) s(P71,P75) s(P1,P76) s(P75,P76) s(P76,P77) s(P75,P77) s(P80,P78) s(P81,P78) s(P77,P79) s(P77,P80) s(P79,P80) s(P79,P81) s(P80,P81) s(P91,P81) s(P78,P82) s(P78,P83) s(P82,P83) s(P82,P84) s(P83,P84) s(P82,P85) s(P84,P85) s(P76,P86) s(P79,P86) s(P1,P87) s(P86,P87) s(P87,P88) s(P86,P88) s(P2,P89) s(P87,P89) s(P89,P90) s(P88,P90) s(P92,P91) s(P93,P91) s(P88,P92) s(P90,P92) s(P90,P93) s(P92,P93) s(P91,P94) s(P93,P94) s(P2,P95) s(P89,P95) s(P4,P96) s(P95,P96) s(P96,P97) s(P95,P97) s(P11,P98) s(P97,P98) s(P98,P99) s(P97,P99) s(P98,P100) s(P99,P100) color(blue) pen(2) m(P3,P1,MA10) m(P1,P6,MB10) f(P1,MA10,MB10) color(maroon) pen(2) m(P2,P1,MA20) m(P1,P3,MB20) f(P1,MA20,MB20) pen(2) color(red) s(P81,P91) abstand(P81,P91,A0) print(abs(P81,P91):,-0.99,12.776) print(A0,0.31,12.776) color(red) s(P11,P96) abstand(P11,P96,A1) print(abs(P11,P96):,-0.99,12.476) print(A1,0.31,12.476) color(red) s(P18,P29) abstand(P18,P29,A2) print(abs(P18,P29):,-0.99,12.176) print(A2,0.31,12.176) \geooff \geoprint() Die Winkel sind von P1-P2 ausgehend entgegen dem Uhrzeigersinn 32,36251966007221 40,49207000332465 25,382433534610843 34,89082087676045 32,2189476094507 34,51433594736363 29,108515978283318 36,31491131809427 29,550687898877964 35,06535948431688 30,09939768884507 Grad. Im Vergleich zum bisherigen Kern wird Kante P11-P96 auf Länge 1 justiert anstelle von Kante P93-P99. Die Strecke P18-P29 ist keine Kante sondern nur die darunterliegende Strecke P18-P20 ist eine Kante. Mit Abstand P18-P29 überprüfe ich nur, ob die schmale Raute einen Innenwinkel größer Null hat. Der Abstand 1,004 ist ein deutlich besserer Wert als im vorhergehenden Kern. Beim Zusammensetzen habe ich dann aber nur einen neuen asymmetrischen Graph 4/11 mit 403 Knoten und 813 Kanten gefunden, habe also den falschen Rekord erwischt :-?


   Profil
StefanVogel
Senior Letzter Besuch: in der letzten Woche
Dabei seit: 26.11.2005
Mitteilungen: 3905
Wohnort: Raun
  Beitrag No.519, eingetragen 2016-09-24

\geo ebene(752.85,602.43) x(-5.96,19.13) y(-2.96,17.12) form(.) #//Eingabe war: #//blauerWinkel=40.49207000332465; gruenerWinkel=32.36251966007222; orangerWinkel=0; #//Bodybilder No.323-4 mit Kern 313-3: mit senkrechtem R(162,78) #//blauerWinkel=40.49207000332465; gruenerWinkel=32.36251966007222 #D=30; P[1]=[0,0]; P[2]=[D,0]; A(2,1); #M(3,1,2,gruenerWinkel); N(4,3,2); L(5,3,4); #M(6,1,3,blauerWinkel); N(7,6,3); N(8,7,5); L(9,8,5); L(10,8,9); L(11,10,9); L(12,6,7); #Q(13,12,10,ab(11,5,8,9,10),D); L(17,16,13); #N(18,6,14); N(19,1,18); L(20,19,18); #Q(21,20,17,ab(11,5,[8,10]),ab(5,11,[8,10])); L(28,25,27); #N(29,19,22); N(30,1,29); L(31,30,29); #Q(32,31,24,ab(13,12,[14,17]),D); #N(37,30,33); N(38,1,37); L(39,38,37); #Q(40,39,36,ab(21,20,[22,24]),ab(21,17,[25,28])); #N(48,38,41); N(49,1,48); L(50,49,48); #Q(51,50,43,ab(13,12,[14,17]),D); #N(56,49,52); N(57,1,56); L(58,57,56); #Q(59,58,55,ab(21,20,[22,24]),ab(21,17,[25,28])); #N(67,57,60); N(68,1,67); L(69,68,67); #Q(70,69,62,ab(13,12,[14,17]),D); #N(75,68,71); N(76,1,75); L(77,76,75); #Q(78,77,74,ab(21,20,[22,24]),ab(21,17,[25,28])); #N(86,76,79); N(87,1,86); L(88,87,86); # #N(89,2,87); #Q(90,89,88,D,ab(71,69,[70,74])); #L(95,2,89); N(96,4,95); L(97,96,95); N(98,11,97); L(99,98,97); L(100,98,99); # #A(81,91); R(81,91); #A(11,96); R(11,96); #R(18,29); # #A(99,100); A(100,99,ab(99,100,[1,100])); A(99,100); # #Q(199,28,194,5.87336307704547344599*D,6.20985554572319298217*D); #A(199,28); A(199,194); #Q(200,28,199,3.85410196624968426349*D,3.85410196624968426349*D); #A(200,28); A(200,199); #Q(201,28,200,ab(21,17,[25,28]),ab(17,21,[25,28])); #A(205,209); L(210,209,205); #A(200,199,ab(28,200,[201,209])); A(210,215); A(210,219); #Q(220,199,194,ab(199,200,[211,219]),ab(210,200,[210,219],199)); #A(225,239); A(229,239); # #Q(240,94,85,ab(199,194,[220,239],"gespiegelt"),ab(28,199,[200,219])); # #Q(281,66,47,ab(240,94,[241,260]),ab(240,85,[261,280])); #Q(322,185,166,ab(240,94,[241,260]),ab(240,85,[261,280])); #Q(363,147,128,ab(240,94,[241,260]),ab(240,85,[261,280])); # #function W(k,i,j) { # var Winkel=Math.acos( # ((P[k][0]-P[i][0])*(P[j][0]-P[i][0]) # +(P[k][1]-P[i][1])*(P[j][1]-P[i][1]))/ab(k,i)/ab(i,j)) # *180/Math.PI; # alert(Winkel); # } # #//für Ausgabe der Winkel in der nächsten Zeile "//" entfernen: #//W(3,1,2); W(6,1,3); W(19,1,6); W(30,1,19); W(38,1,30); W(49,1,38); W(57,1,49); W(68,1,57); W(76,1,68); W(87,1,76); W(2,1,87); # # # #//Ende der Eingabe, weiter mit fedgeo: nolabel() p(4,6,P1) p(5,6,P2) p(4.844678258782334,6.535274358754876,P3) p(5.844678258782334,6.535274358754876,P4) p(5.344678258782334,7.401299762539314,P5) p(4.29479775600703,6.955559670064209,P6) p(5.1394760147893646,7.4908340288190844,P7) p(5.6394760147893646,8.356859432603523,P8) p(6.3196160858933315,7.623777251890684,P9) p(6.614413841900362,8.579336921954893,P10) p(7.294553913004328,7.846254741242054,P11) p(4.253575692722049,7.954709679571554,P12) p(5.824489948800047,9.192541816838522,P13) 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p(7.198296676996272,11.726080226064568,P236) p(8.062104306624011,11.222258453016885,P237) p(8.93033057587689,11.718426917733485,P238) p(7.202715316621416,12.726070463828846,P239) p(10.59908381544183,-1.8972366028734795,P240) p(10.28009566116734,1.9436420106317982,P241) p(10.972986497953372,0.0675017471392323,P242) p(10.028754165875217,-0.26177822956487606,P243) p(10.7860351566976,-0.914867427867124,P244) p(9.841802824619451,-1.2441474045712315,P245) p(9.08452183379707,-0.5910582062689782,P246) p(9.640925805740148,1.1745764114055781,P247) p(10.626541079560356,1.005571878885517,P248) p(9.987371224133167,0.23650627965929516,P249) p(9.00175595031296,0.40551081217935536,P250) p(7.487193968668194,1.711689208783877,P251) p(8.431426300746349,2.04096918548797,P252) p(7.674145309923974,2.694058383790226,P253) p(8.618377642002125,3.0233383604943165,P254) p(9.3756586328245,2.3702491621920623,P255) p(8.819254660881402,0.6046145445175135,P256) p(7.8336393870611944,0.7736190770375853,P257) p(8.472809242488395,1.5426846762638036,P258) p(9.458424516308597,1.3736801437437256,P259) p(8.180084805454204,-0.1644510547086977,P260) p(6.894793745744498,-2.9613498702428025,P261) p(8.894716053928049,-2.943721449162476,P262) p(8.86766676352563,-1.94408734815915,P263) p(9.746899934684937,-2.420479026017979,P264) p(9.71985064428252,-1.420844925014654,P265) p(8.840617473123212,-0.9444532471558285,P266) p(7.387140992548297,-2.0909510027316376,P267) p(7.894754899836274,-2.95253565970264,P268) p(8.387102146640073,-2.0821367921914753,P269) p(7.879488239352099,-1.2205521352204727,P270) p(8.120944205217032,-0.25014035842249527,P271) p(5.587290874419931,-1.4479311438230402,P272) p(6.569496124072378,-1.2601204743838927,P273) p(6.2410423100822126,-2.2046405070329165,P274) p(7.223247559734659,-2.0168298375937788,P275) p(7.551701373724823,-1.0723098049447497,P276) p(6.185930311158849,0.1773783112595151,P277) p(5.41742416708521,-0.46246409630736185,P278) p(6.3557970184935915,-0.8080887362561073,P279) p(7.124303162567246,-0.16824632868919842,P280) p(-5.961178784504602,5.4783102131933346,P281) p(-3.440730704320507,2.5625867281306705,P282) p(-5.105871852049274,3.6704246937829215,P283) p(-4.536861191691383,4.492754839405154,P284) p(-5.533525318276938,4.574367453488129,P285) p(-4.96451465791905,5.396697599110359,P286) p(-3.967850531333494,5.315084985027382,P287) p(-3.377308080486835,3.56057348695368,P288) p(-4.27330127818489,3.1165057109567944,P289) p(-4.209878654351222,4.114492469779801,P290) p(-3.313885456653166,4.558560245776688,P291) p(-1.320557203482041,4.395335017610721,P292) p(-1.8895678638399405,3.573004871988502,P293) p(-0.892903737254386,3.491392257905517,P294) p(-1.4619143976122881,2.669062112283299,P295) p(-2.458578524197838,2.75067472636628,P296) p(-3.04912097504448,4.50518622443999,P297) p(-2.1531277773464126,4.949254000436866,P298) p(-2.2165504011800943,3.951267241613854,P299) p(-3.112543598878159,3.5071994656169867,P300) p(-2.9856983512107966,5.503172983262996,P301) p(-4.808734627908077,9.156077801306566,P302) p(-5.895701645487467,7.4772381119095765,P303) p(-5.046509759930894,6.949153704352536,P304) p(-5.928440214996035,6.477774162551457,P305) p(-5.079248329439462,5.949689754994415,P306) p(-4.197317874374322,6.421069296795492,P307) p(-4.353517472353239,8.265697353807541,P308) p(-5.3522181366977755,8.31665795660807,P309) p(-4.89700098114294,7.426277509109047,P310) p(-3.8983003167984034,7.375316906308516,P311) p(-3.2214064242475127,6.63923630051369,P312) p(-2.825387486341417,9.413631904437079,P313) p(-3.209700073653111,8.490428874094457,P314) p(-3.817061057124744,9.28485485287182,P315) p(-4.201373644436448,8.361651822529204,P316) p(-3.5940126609648093,7.5672258437518405,P317) p(-1.7986765712909527,8.018689361922844,P318) p(-1.9093468026038298,9.012546544772102,P319) p(-2.714717255028507,8.419774721587771,P320) p(-2.6040470237156113,7.425917538738494,P321) p(15.774681624096115,15.919753997193933,P322) p(12.066745674161847,14.868415346979477,P323) p(13.77471043326423,15.909019201318074,P324) p(14.27935153393867,15.045689971238323,P325) p(14.774696028680173,15.914386599256003,P326) p(15.279337129354612,15.051057369176256,P327) p(14.783992634613103,14.182360741158574,P328) p(12.944331550504062,14.388995875488508,P329) p(12.920728053713038,15.388717274148776,P330) p(13.798313930055247,14.909297802657813,P331) p(13.821917426846271,13.90957640399754,P332) p(12.831228437363244,12.172183147962173,P333) p(12.326587336688815,13.035512378041929,P334) p(11.831242841947304,12.16681575002426,P335) p(11.326601741272881,13.030144980104005,P336) p(11.821946236014394,13.898841608121685,P337) p(13.661607320123434,13.692206473791732,P338) p(13.685210816914445,12.692485075131462,P339) p(12.807624940572236,13.171904546622436,P340) p(12.78402144378123,14.1716259452827,P341) p(14.539193196465636,13.212787002300754,P342) p(18.633862738767387,13.335342009960318,P343) p(17.563178858341757,15.02461286692693,P344) p(16.728447070388576,14.473956129766211,P345) p(16.668930241218938,15.472183432060431,P346) p(15.834198453265758,14.921526694899715,P347) p(15.893715282435396,13.923299392605497,P348) p(17.63471603065808,13.29404000426642,P349) p(18.098520798554574,14.179977438443624,P350) p(17.099374090445266,14.138675432749727,P351) p(16.635569322548776,13.252737998572524,P352) p(15.683919100462427,12.945554250950703,P353) p(18.038683921005426,11.425954104141418,P354) p(17.36068940938695,12.161021068584262,P355) p(18.336273329886406,12.380648057050863,P356) p(17.658278818267927,13.115715021493711,P357) p(16.68269489776847,12.896088033027112,P358) p(16.34226648753658,11.076428866965582,P359) p(17.291374449156997,10.761477954617877,P360) p(17.08957595938495,11.74090501648911,P361) p(16.140467997764517,12.055855928836815,P362) p(16.7334612071643,-2.1276240096143617,P363) p(18.334216697941482,1.378325765410425,P364) p(18.0207229282438,-0.5969518495998631,P365) p(17.036107010254845,-0.422219213716426,P366) p(17.377092067704048,-1.3622879296071124,P367) p(16.392476149715094,-1.187555293723678,P368) p(16.05149109226589,-0.247486577832988,P369) p(17.40052295845424,1.020253145901031,P370) p(18.177469813092642,0.3906869579052836,P371) p(17.243776073605396,0.03261433839588346,P372) p(16.466829218966993,0.6621805263916283,P373) p(15.784859104068591,2.5423179581730255,P374) p(16.76947502205753,2.367585322289575,P375) p(16.428489964608342,3.307654038180267,P376) p(17.413105882597282,3.1329214022968177,P377) p(17.75409094004648,2.192852686406127,P378) p(16.405059073858126,0.9251129626721246,P379) p(15.628112219219725,1.5546791506678819,P380) p(16.561805958706977,1.9127517701772714,P381) p(17.338752813345366,1.2831855821815115,P382) p(15.471365334370871,0.5670403431627369,P383) p(12.90748722528073,-2.592408966556457,P384) p(14.885020590870937,-2.891343387420772,P385) p(15.016430553672876,-1.9000152774206596,P386) p(15.809240899017617,-2.509483698517567,P387) p(15.94065086181956,-1.5181555885174571,P388) p(15.14784051647482,-0.9086871674205472,P389) p(13.53131296794532,-1.8108455060563093,P390) p(13.896253908075833,-2.7418761769886135,P391) p(14.520079650740424,-1.960312716488465,P392) p(14.155138710609918,-1.0292820455561582,P393) p(14.54705138551064,-0.10927962422666049,P394) p(11.855832151176003,-0.8912265527307728,P395) p(12.855379513124381,-0.8611421510904398,P396) p(12.381659688228371,-1.7418177596436095,P397) p(13.381207050176743,-1.711733358003288,P398) p(13.854926875072747,-0.8310577494501157,P399) p(12.704021145680935,0.6189308660837591,P400) p(11.843981752292835,0.10870322882707306,P401) p(12.715871544564134,-0.3809989154740352,P402) p(13.575910937952248,0.12922872178267308,P403) nolabel() s(P1,P2) s(P1,P3) s(P3,P4) s(P2,P4) s(P3,P5) s(P4,P5) s(P1,P6) s(P6,P7) s(P3,P7) s(P7,P8) s(P5,P8) s(P8,P9) s(P5,P9) s(P8,P10) s(P9,P10) s(P10,P11) s(P9,P11) s(P96,P11) s(P6,P12) s(P7,P12) s(P15,P13) s(P16,P13) s(P10,P13) s(P12,P14) s(P12,P15) s(P14,P15) s(P14,P16) s(P15,P16) s(P16,P17) s(P13,P17) s(P26,P17) s(P27,P17) s(P6,P18) s(P14,P18) s(P1,P19) s(P18,P19) s(P19,P20) s(P18,P20) s(P23,P21) s(P24,P21) s(P20,P22) s(P20,P23) s(P22,P23) s(P22,P24) s(P23,P24) s(P21,P25) s(P21,P26) s(P25,P26) s(P25,P27) s(P26,P27) s(P25,P28) s(P27,P28) s(P203,P28) s(P204,P28) s(P19,P29) s(P22,P29) s(P1,P30) s(P29,P30) s(P30,P31) s(P29,P31) s(P34,P32) s(P35,P32) s(P24,P32) s(P31,P33) s(P31,P34) s(P33,P34) s(P33,P35) s(P34,P35) s(P32,P36) s(P35,P36) s(P45,P36) s(P46,P36) s(P30,P37) s(P33,P37) s(P1,P38) s(P37,P38) s(P38,P39) s(P37,P39) s(P42,P40) s(P43,P40) s(P39,P41) s(P39,P42) s(P41,P42) s(P41,P43) s(P42,P43) s(P40,P44) s(P40,P45) s(P44,P45) s(P44,P46) s(P45,P46) s(P44,P47) s(P46,P47) s(P38,P48) s(P41,P48) s(P1,P49) s(P48,P49) s(P49,P50) s(P48,P50) s(P53,P51) s(P54,P51) s(P43,P51) s(P50,P52) s(P50,P53) s(P52,P53) s(P52,P54) s(P53,P54) s(P51,P55) s(P54,P55) s(P64,P55) s(P65,P55) s(P49,P56) s(P52,P56) s(P1,P57) s(P56,P57) s(P57,P58) s(P56,P58) s(P61,P59) s(P62,P59) s(P58,P60) s(P58,P61) s(P60,P61) s(P60,P62) s(P61,P62) s(P59,P63) s(P59,P64) s(P63,P64) s(P63,P65) s(P64,P65) s(P63,P66) s(P65,P66) s(P294,P66) s(P295,P66) s(P57,P67) s(P60,P67) s(P1,P68) s(P67,P68) s(P68,P69) s(P67,P69) s(P72,P70) s(P73,P70) s(P62,P70) s(P69,P71) s(P69,P72) s(P71,P72) s(P71,P73) s(P72,P73) s(P70,P74) s(P73,P74) s(P83,P74) s(P84,P74) s(P68,P75) s(P71,P75) s(P1,P76) s(P75,P76) s(P76,P77) s(P75,P77) s(P80,P78) s(P81,P78) s(P77,P79) s(P77,P80) s(P79,P80) s(P79,P81) s(P80,P81) s(P91,P81) s(P78,P82) s(P78,P83) s(P82,P83) s(P82,P84) s(P83,P84) s(P82,P85) s(P84,P85) s(P76,P86) s(P79,P86) s(P1,P87) s(P86,P87) s(P87,P88) s(P86,P88) s(P2,P89) s(P87,P89) s(P89,P90) s(P88,P90) s(P92,P91) s(P93,P91) s(P88,P92) s(P90,P92) s(P90,P93) s(P92,P93) s(P91,P94) s(P93,P94) s(P253,P94) s(P254,P94) s(P2,P95) s(P89,P95) s(P4,P96) s(P95,P96) s(P96,P97) s(P95,P97) s(P11,P98) s(P97,P98) s(P98,P99) s(P97,P99) s(P198,P99) s(P100,P99) s(P98,P100) s(P197,P100) s(P198,P100) s(P101,P102) s(P101,P103) s(P102,P104) s(P103,P104) s(P103,P105) s(P104,P105) s(P101,P106) s(P103,P107) s(P106,P107) s(P105,P108) s(P107,P108) s(P105,P109) s(P108,P109) s(P108,P110) s(P109,P110) s(P109,P111) s(P110,P111) s(P196,P111) s(P106,P112) s(P107,P112) s(P110,P113) s(P115,P113) s(P116,P113) s(P112,P114) s(P112,P115) s(P114,P115) s(P114,P116) s(P115,P116) s(P113,P117) s(P116,P117) s(P126,P117) s(P127,P117) s(P106,P118) s(P114,P118) s(P101,P119) s(P118,P119) s(P118,P120) s(P119,P120) s(P123,P121) s(P124,P121) s(P120,P122) s(P120,P123) s(P122,P123) s(P122,P124) s(P123,P124) s(P121,P125) s(P121,P126) s(P125,P126) s(P125,P127) s(P126,P127) s(P125,P128) s(P127,P128) s(P119,P129) s(P122,P129) s(P101,P130) s(P129,P130) s(P129,P131) s(P130,P131) s(P124,P132) s(P134,P132) s(P135,P132) s(P131,P133) s(P131,P134) s(P133,P134) s(P133,P135) s(P134,P135) s(P132,P136) s(P135,P136) s(P145,P136) s(P146,P136) s(P130,P137) s(P133,P137) s(P101,P138) s(P137,P138) s(P137,P139) s(P138,P139) s(P142,P140) s(P143,P140) s(P139,P141) s(P139,P142) s(P141,P142) s(P141,P143) s(P142,P143) s(P140,P144) s(P140,P145) s(P144,P145) s(P144,P146) s(P145,P146) s(P144,P147) s(P146,P147) s(P376,P147) s(P377,P147) s(P138,P148) s(P141,P148) s(P101,P149) s(P148,P149) s(P148,P150) s(P149,P150) s(P143,P151) s(P153,P151) s(P154,P151) s(P150,P152) s(P150,P153) s(P152,P153) s(P152,P154) s(P153,P154) s(P151,P155) s(P154,P155) s(P164,P155) s(P165,P155) s(P149,P156) s(P152,P156) s(P101,P157) s(P156,P157) s(P156,P158) s(P157,P158) s(P161,P159) s(P162,P159) s(P158,P160) s(P158,P161) s(P160,P161) s(P160,P162) s(P161,P162) s(P159,P163) s(P159,P164) s(P163,P164) s(P163,P165) s(P164,P165) s(P163,P166) s(P165,P166) s(P157,P167) s(P160,P167) s(P101,P168) s(P167,P168) s(P167,P169) s(P168,P169) s(P162,P170) s(P172,P170) s(P173,P170) s(P169,P171) s(P169,P172) s(P171,P172) s(P171,P173) s(P172,P173) s(P170,P174) s(P173,P174) s(P183,P174) s(P184,P174) s(P168,P175) s(P171,P175) s(P101,P176) s(P175,P176) s(P175,P177) s(P176,P177) s(P180,P178) s(P181,P178) s(P177,P179) s(P177,P180) s(P179,P180) s(P179,P181) s(P180,P181) s(P191,P181) s(P178,P182) s(P178,P183) s(P182,P183) s(P182,P184) s(P183,P184) s(P182,P185) s(P184,P185) s(P335,P185) s(P336,P185) s(P176,P186) s(P179,P186) s(P101,P187) s(P186,P187) s(P186,P188) s(P187,P188) s(P102,P189) s(P187,P189) s(P188,P190) s(P189,P190) s(P192,P191) s(P193,P191) s(P188,P192) s(P190,P192) s(P190,P193) s(P192,P193) s(P191,P194) s(P193,P194) s(P232,P194) s(P233,P194) s(P102,P195) s(P189,P195) s(P104,P196) s(P195,P196) s(P195,P197) s(P196,P197) s(P111,P198) s(P197,P198) s(P223,P199) s(P224,P199) s(P213,P200) s(P214,P200) s(P207,P201) s(P208,P201) s(P201,P202) s(P201,P203) s(P202,P203) s(P202,P204) s(P203,P204) s(P202,P205) s(P204,P205) s(P209,P205) s(P200,P206) s(P200,P207) s(P206,P207) s(P206,P208) s(P207,P208) s(P206,P209) s(P208,P209) s(P209,P210) s(P205,P210) s(P215,P210) s(P219,P210) s(P217,P211) s(P218,P211) s(P211,P212) s(P211,P213) s(P212,P213) s(P212,P214) s(P213,P214) s(P212,P215) s(P214,P215) s(P219,P215) s(P199,P216) s(P199,P217) s(P216,P217) s(P216,P218) s(P217,P218) s(P216,P219) s(P218,P219) s(P234,P220) s(P238,P220) s(P227,P221) s(P228,P221) s(P221,P222) s(P221,P223) s(P222,P223) s(P222,P224) s(P223,P224) s(P222,P225) s(P224,P225) s(P229,P225) s(P239,P225) s(P220,P226) s(P220,P227) s(P226,P227) s(P226,P228) s(P227,P228) s(P226,P229) s(P228,P229) s(P239,P229) s(P236,P230) s(P237,P230) s(P230,P231) s(P230,P232) s(P231,P232) s(P231,P233) s(P232,P233) s(P231,P234) s(P233,P234) s(P238,P234) s(P239,P235) s(P239,P236) s(P235,P236) s(P235,P237) s(P236,P237) s(P235,P238) s(P237,P238) s(P244,P240) s(P245,P240) s(P264,P240) s(P265,P240) s(P255,P241) s(P259,P241) s(P248,P242) s(P249,P242) s(P242,P243) s(P242,P244) s(P243,P244) s(P243,P245) s(P244,P245) s(P243,P246) s(P245,P246) s(P250,P246) s(P260,P246) s(P241,P247) s(P241,P248) s(P247,P248) s(P247,P249) s(P248,P249) s(P247,P250) s(P249,P250) s(P260,P250) s(P257,P251) s(P258,P251) s(P251,P252) s(P251,P253) s(P252,P253) s(P252,P254) s(P253,P254) s(P252,P255) s(P254,P255) s(P259,P255) s(P260,P256) s(P256,P257) s(P260,P257) s(P256,P258) s(P257,P258) s(P256,P259) s(P258,P259) s(P274,P261) s(P275,P261) s(P268,P262) s(P269,P262) s(P262,P263) s(P262,P264) s(P263,P264) s(P263,P265) s(P264,P265) s(P263,P266) s(P265,P266) s(P270,P266) s(P261,P267) s(P261,P268) s(P267,P268) s(P267,P269) s(P268,P269) s(P267,P270) s(P269,P270) s(P266,P271) s(P270,P271) s(P276,P271) s(P280,P271) s(P278,P272) s(P279,P272) s(P272,P273) s(P272,P274) s(P273,P274) s(P273,P275) s(P274,P275) s(P273,P276) s(P275,P276) s(P280,P276) s(P85,P277) s(P85,P278) s(P277,P278) s(P277,P279) s(P278,P279) s(P277,P280) s(P279,P280) s(P285,P281) s(P286,P281) s(P305,P281) s(P306,P281) s(P296,P282) s(P300,P282) s(P289,P283) s(P290,P283) s(P283,P284) s(P283,P285) s(P284,P285) s(P284,P286) s(P285,P286) s(P284,P287) s(P286,P287) s(P291,P287) s(P301,P287) s(P282,P288) s(P282,P289) s(P288,P289) s(P288,P290) s(P289,P290) s(P288,P291) s(P290,P291) s(P301,P291) s(P298,P292) s(P299,P292) s(P292,P293) s(P292,P294) s(P293,P294) s(P293,P295) s(P294,P295) s(P293,P296) s(P295,P296) s(P300,P296) s(P301,P297) s(P297,P298) s(P301,P298) s(P297,P299) s(P298,P299) s(P297,P300) s(P299,P300) s(P315,P302) s(P316,P302) s(P309,P303) s(P310,P303) s(P303,P304) s(P303,P305) s(P304,P305) s(P304,P306) s(P305,P306) s(P304,P307) s(P306,P307) s(P311,P307) s(P302,P308) s(P302,P309) s(P308,P309) s(P308,P310) s(P309,P310) s(P308,P311) s(P310,P311) s(P307,P312) s(P311,P312) s(P317,P312) s(P321,P312) s(P319,P313) s(P320,P313) s(P313,P314) s(P313,P315) s(P314,P315) s(P314,P316) s(P315,P316) s(P314,P317) s(P316,P317) s(P321,P317) s(P47,P318) s(P47,P319) s(P318,P319) s(P318,P320) s(P319,P320) s(P318,P321) s(P320,P321) s(P326,P322) s(P327,P322) s(P346,P322) s(P347,P322) s(P337,P323) s(P341,P323) s(P330,P324) s(P331,P324) s(P324,P325) s(P324,P326) s(P325,P326) s(P325,P327) s(P326,P327) s(P325,P328) s(P327,P328) s(P332,P328) s(P342,P328) s(P323,P329) s(P323,P330) s(P329,P330) s(P329,P331) s(P330,P331) s(P329,P332) s(P331,P332) s(P342,P332) s(P339,P333) s(P340,P333) s(P333,P334) s(P333,P335) s(P334,P335) s(P334,P336) s(P335,P336) s(P334,P337) s(P336,P337) s(P341,P337) s(P342,P338) s(P338,P339) s(P342,P339) s(P338,P340) s(P339,P340) s(P338,P341) s(P340,P341) s(P356,P343) s(P357,P343) s(P350,P344) s(P351,P344) s(P344,P345) s(P344,P346) s(P345,P346) s(P345,P347) s(P346,P347) s(P345,P348) s(P347,P348) s(P352,P348) s(P343,P349) s(P343,P350) s(P349,P350) s(P349,P351) s(P350,P351) s(P349,P352) s(P351,P352) s(P348,P353) s(P352,P353) s(P358,P353) s(P362,P353) s(P360,P354) s(P361,P354) s(P354,P355) s(P354,P356) s(P355,P356) s(P355,P357) s(P356,P357) s(P355,P358) s(P357,P358) s(P362,P358) s(P166,P359) s(P166,P360) s(P359,P360) s(P359,P361) s(P360,P361) s(P359,P362) s(P361,P362) s(P367,P363) s(P368,P363) s(P387,P363) s(P388,P363) s(P378,P364) s(P382,P364) s(P371,P365) s(P372,P365) s(P365,P366) s(P365,P367) s(P366,P367) s(P366,P368) s(P367,P368) s(P366,P369) s(P368,P369) s(P373,P369) s(P383,P369) s(P364,P370) s(P364,P371) s(P370,P371) s(P370,P372) s(P371,P372) s(P370,P373) s(P372,P373) s(P383,P373) s(P380,P374) s(P381,P374) s(P374,P375) s(P374,P376) s(P375,P376) s(P375,P377) s(P376,P377) s(P375,P378) s(P377,P378) s(P382,P378) s(P383,P379) s(P379,P380) s(P383,P380) s(P379,P381) s(P380,P381) s(P379,P382) s(P381,P382) s(P397,P384) s(P398,P384) s(P391,P385) s(P392,P385) s(P385,P386) s(P385,P387) s(P386,P387) s(P386,P388) s(P387,P388) s(P386,P389) s(P388,P389) s(P393,P389) s(P384,P390) s(P384,P391) s(P390,P391) s(P390,P392) s(P391,P392) s(P390,P393) s(P392,P393) s(P389,P394) s(P393,P394) s(P399,P394) s(P403,P394) s(P401,P395) s(P402,P395) s(P395,P396) s(P395,P397) s(P396,P397) s(P396,P398) s(P397,P398) s(P396,P399) s(P398,P399) s(P403,P399) s(P128,P400) s(P128,P401) s(P400,P401) s(P400,P402) s(P401,P402) s(P400,P403) s(P402,P403) color(blue) pen(2) m(P3,P1,MA10) m(P1,P6,MB10) f(P1,MA10,MB10) color(maroon) pen(2) m(P2,P1,MA20) m(P1,P3,MB20) f(P1,MA20,MB20) color(gold) pen(2) pen(2) color(red) s(P81,P91) abstand(P81,P91,A0) print(abs(P81,P91):,-5.96,17.12) print(A0,-3.66,17.12) color(red) s(P11,P96) abstand(P11,P96,A1) print(abs(P11,P96):,-5.96,16.82) print(A1,-3.66,16.82) color(red) s(P18,P29) abstand(P18,P29,A2) print(abs(P18,P29):,-5.96,16.52) print(A2,-3.66,16.52) \geooff \geoprint() Diese Graphen sind alle mit neuem Streichholzgraph-519.htm gezeichnet.


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