beginfig(1) % example of triangle and its neighbors numeric s; (1685-72)*s=2in; z1=(0,1000) scaled s; z2=(-500,500) scaled s; z3=(500,500) scaled s; z12=(-222,797) scaled s; z23=(85,519) scaled s; z31=(245,735) scaled s; z123=(0,72) scaled s; z231=(491,1364) scaled s; z312=(-483,1685) scaled s; z1231=(220,1176) scaled s; z2312=(-518,1144) scaled s; z3123=(229,302) scaled s; z1223=(-204,246) scaled s; z2331=(448,888) scaled s; z3112=(-242,1309) scaled s; draw (z1..z12..z2); draw (z2..z23..z3); draw (z3..z31..z1); draw (z1..z1231..z231) dashed evenly scaled 1/2; draw (z231..z2331..z3) dashed evenly scaled 1/2; draw (z2..z2312..z312) dashed evenly scaled 1/2; draw (z312..z3112..z1) dashed evenly scaled 1/2; draw (z3..z3123..z123) dashed evenly scaled 1/2; draw (z123..z1223..z2) dashed evenly scaled 1/2; labeloffset:=5pt; pickup pencircle scaled 2pt; drawdot z1; label.top(btex \$A\$ etex,z1+(0,3pt)); drawdot z2; label.lft(btex \$B\$ etex,z2); drawdot z3; label.rt(btex \$C\$ etex, z3); drawdot z123; label.bot(btex \$A'\$ etex,z123); drawdot z231; label.rt(btex \$B'\$ etex, z231); drawdot z312; label.lft(btex \$C'\$ etex, z312); label.lft(btex \$\scriptstyle90\$ etex,z1); label.bot(btex \$\scriptstyle90\$ etex,z1); label.rt (btex \$\scriptstyle90\$ etex,z1); label.urt(btex \$\scriptstyle45\$ etex,z2+(-2pt,8pt)); label.urt(btex \$\scriptstyle45\$ etex,z2+(6pt,0)); label.lrt(btex \$\scriptstyle45\$ etex,z2+(6pt,2pt)); label.llft(btex \$\scriptstyle36\$ etex,z3-(6pt,-2pt)); label.ulft(btex \$\scriptstyle36\$ etex,z3-(6pt,0)); label.ulft(btex \$\scriptstyle36\$ etex,z3+(0,8pt)); label.lrt(btex \$ \scriptstyle36\$ etex,z312-(4pt,10pt)); label.llft(btex \$\scriptstyle45\$ etex,z231-(1pt,6pt)); label.top(btex \$\scriptstyle90\$ etex,z123+(0,1pt)); endfig; numeric u; u=8in; def arc(expr c,r) = draw (((r,0){up}..(r*cosd30,r*sind30)..(r*cosd60,r*sind60)..(0,r).. (-r*cosd60,r*sind60)..(-r*cosd30,r*sind30)..(-r,0){down}) shifted (c,0)) scaled u; enddef; beginfig(2) arc(0.58823,0.831883) arc(0,0.58823) arc(1.21068,1.05817) arc(3.49892,3.05817) arc(0.74824,0.462438) arc(-1.70002,2.40419) arc(0.418912,0.366142) arc(1.11179,0.485868) arc(0.639073,0.2498) arc(2.16245,1.33647) arc(0.799585,0.266942) arc(0.605339,0.142901) arc(0.957563,0.197575) arc(0.816908,0.156016) arc(0.487024,0.162593) arc(1.09075,0.225056) arc(0.706482,0.10548) arc(0.594094,0.0832668) arc(1.40753,0.469903) arc(0.82285,0.0915697) arc(0.643675,0.0752921) arc(0.929204,0.0893442) arc(1.00562,0.106166) arc(0.768774,0.0793109) arc(0.590252,0.0488208) arc(0.876681,0.0731701) arc(0.8249,0.0538228) arc(0.689932,0.0474515) arc(0.655143,0.0427465) arc(0.545018,0.0637519) arc(0.983511,0.058445) arc(0.719445,0.0480374) arc(0.755026,0.0445594) arc(0.62485,0.0322315) arc(0.588929,0.0286856) arc(0.923283,0.0412517) arc(0.892091,0.0402199) arc(1.02037,0.0606352) arc(0.786674,0.034475) arc(0.825609,0.0316518) arc(0.658927,0.0248453) arc(0.605844,0.024558) arc(0.948204,0.0391288) arc(0.863355,0.0325534) arc(0.976508,0.0336327) arc(1.08623,0.104443) arc(0.750552,0.0258104) arc(0.806972,0.0267001) arc(0.686499,0.0218855) arc(0.704292,0.0242571) arc(0.644093,0.0227014) arc(0.588472,0.0168672) arc(0.896962,0.0231339) arc(0.844217,0.0259664) arc(0.722175,0.0222127) arc(0.766017,0.0238822) arc(0.825854,0.0186168) arc(0.673586,0.0188272) arc(0.660215,0.0145548) arc(0.62117,0.0147179) arc(0.610237,0.0137563) arc(0.572068,0.0231889) arc(0.922015,0.0191306) arc(0.937181,0.0203829) arc(0.883001,0.0218815) arc(1.0003,0.0243613) arc(0.974155,0.0196363) arc(0.735301,0.0193167) arc(0.749036,0.0151025) arc(0.790237,0.0157899) arc(0.80201,0.0148982) arc(0.700001,0.0136025) arc(0.630186,0.0144474) arc(0.640754,0.0129193) arc(0.60046,0.0107153) arc(0.588313,0.00992045) arc(0.910675,0.016943) arc(0.952021,0.0179483) arc(0.898598,0.0135044) arc(0.860627,0.01498) arc(0.849378,0.0143794) arc(1.02527,0.0353123) arc(0.985822,0.0175921) arc(0.708423,0.0136502) arc(0.780597,0.01538) arc(0.769379,0.0136292) arc(0.812609,0.0117035) arc(0.825939,0.0109506) arc(0.685764,0.0101471) arc(0.677982,0.0101889) arc(0.649905,0.00967912) arc(0.660658,0.00854942) arc(0.611661,0.00796038) arc(0.594153,0.00833495) arc(0.933931,0.0115332) arc(0.962591,0.0151726) arc(0.869719,0.0143881) arc(0.880166,0.0125453) arc(0.839126,0.0114735) arc(0.973349,0.0115209) arc(0.722761,0.0103045) arc(0.73069,0.0104148) arc(0.759729,0.0101315) arc(0.748515,0.0088676) arc(0.80041,0.00861034) arc(0.819496,0.00915364) arc(0.691847,0.00940357) arc(0.670666,0.00847587) arc(0.698608,0.00787418) arc(0.639648,0.00751491) arc(0.655615,0.00734528) arc(0.620392,0.00680943) arc(0.625861,0.00740793) arc(0.606887,0.00739008) arc(0.588259,0.00583523) arc(0.921742,0.00888029) arc(0.914869,0.00907504) arc(0.941008,0.0113609) arc(0.889043,0.00919748) arc(0.899159,0.00792283) arc(0.851025,0.00829037) arc(0.832379,0.00906583) arc(0.996658,0.010992) arc(0.988582,0.0099662) arc(0.716593,0.00950086) arc(0.738178,0.00871725) arc(0.70977,0.00791082) arc(0.770496,0.00793519) arc(0.753749,0.00765128) arc(0.790993,0.00731007) clip currentpicture to ((0,0)--(1,0){up}..(cosd30,sind30).. (cosd60,sind60)..(0,1){left}--cycle) scaled u; draw((1,0){up}..(cosd30,sind30)..(cosd60,sind60)..(0,1){left}) scaled u; draw (0,0)--(0,u); setbounds currentpicture to ((0,0)--(u,0)--(u,u)--(0,u)--cycle); endfig; beginfig(3) arc(-0,0.346014) arc(-0.58823,0.831883) arc(-0,0.58823) arc(1.21068,1.05817) arc(0.418912,0.366142) arc(0.74824,0.462438) arc(0.203536,0.287843) arc(3.49892,3.05817) arc(0.384694,0.168117) arc(0.639073,0.2498) arc(0.258902,0.16001) arc(0.487024,0.162593) arc(0.605339,0.142901) arc(0.377416,0.0778727) arc(0.4396,0.0839561) arc(0.799585,0.266942) arc(0.331331,0.0683638) arc(0.500937,0.0747912) arc(0.594094,0.0832668) arc(0.276668,0.0923658) arc(0.42578,0.0473823) arc(0.545018,0.0637519) arc(0.375852,0.0361387) arc(0.347959,0.036735) arc(0.454928,0.0469329) arc(0.590252,0.0488208) arc(0.397455,0.0331727) arc(0.421255,0.0274859) arc(0.503903,0.0346569) arc(0.530409,0.0346079) arc(0.643675,0.0752921) arc(0.353062,0.0209806) arc(0.4831,0.0322566) arc(0.459883,0.0271409) arc(0.555233,0.0286405) arc(0.588929,0.0286856) arc(0.375515,0.0167778) arc(0.388659,0.0175227) arc(0.340309,0.0202228) arc(0.440691,0.0193127) arc(0.419719,0.016091) arc(0.525866,0.0198282) arc(0.572068,0.0231889) arc(0.365538,0.0150844) arc(0.401349,0.0151332) arc(0.354759,0.0122186) arc(0.321518,0.0309144) arc(0.461559,0.0158723) arc(0.429251,0.0142025) arc(0.504541,0.0160847) arc(0.491877,0.0169412) arc(0.53788,0.0189579) arc(0.588472,0.0168672) arc(0.386019,0.00995596) arc(0.410252,0.0126185) arc(0.479582,0.014751) arc(0.452145,0.0140966) arc(0.419191,0.0094496) arc(0.514092,0.0143692) arc(0.524348,0.0115595) arc(0.557349,0.0132058) arc(0.567305,0.0127885) arc(0.605844,0.024558) arc(0.375442,0.00778995) arc(0.369382,0.00803377) arc(0.392103,0.00971662) arc(0.346117,0.00842936) arc(0.355339,0.00716265) arc(0.4709,0.0123708) arc(0.462134,0.00931783) arc(0.438036,0.0087525) arc(0.431583,0.0080171) arc(0.494492,0.00960903) arc(0.549356,0.0125943) arc(0.540231,0.0108925) arc(0.576432,0.0102865) arc(0.588313,0.00992045) arc(0.380085,0.00707143) arc(0.363582,0.00685456) arc(0.385147,0.00578812) arc(0.402171,0.00700014) arc(0.407491,0.00689857) arc(0.337886,0.0116374) arc(0.351103,0.00626547) arc(0.488611,0.00941479) arc(0.443441,0.00873705) arc(0.449873,0.00796929) arc(0.425895,0.00613387) arc(0.419008,0.00555537) arc(0.504678,0.00746763) arc(0.510475,0.00767158) arc(0.532526,0.00793097) arc(0.523829,0.00677875) arc(0.565792,0.00736342) arc(0.582481,0.00817121) arc(0.370549,0.00457594) arc(0.359551,0.00566734) arc(0.397955,0.00658351) arc(0.393204,0.00560446) arc(0.412428,0.00563921) arc(0.355538,0.00420829) arc(0.478837,0.00682684) arc(0.473641,0.00675096) arc(0.455526,0.00607473) arc(0.462333,0.00547722) arc(0.432347,0.00465093) arc(0.422281,0.00471682) arc(0.500224,0.00679903) arc(0.516009,0.00652132) arc(0.495354,0.00558325) arc(0.541019,0.00635617) arc(0.527837,0.0059137) arc(0.557802,0.00612243) arc(0.552939,0.00654479) arc(0.570231,0.00694372) arc(0.588259,0.00583523) arc(0.375426,0.00361695) arc(0.378249,0.00375204) arc(0.36776,0.00443999) arc(0.38924,0.00402684) arc(0.38485,0.00339106) arc(0.406624,0.00396118) arc(0.415743,0.00452805) arc(0.347217,0.00382942) arc(0.350046,0.00352892) arc(0.482945,0.00640307) arc(0.468806,0.0055362) arc(0.487563,0.00543419) arc(0.449128,0.00462548) arc(0.459105,0.00466036) arc(0.43748,0.00404303) clip currentpicture to ((0,0)--(1,0){up}..(cosd30,sind30).. (cosd60,sind60)..(0,1){left}--cycle) scaled u; draw((1,0){up}..(cosd30,sind30)..(cosd60,sind60)..(0,1){left}) scaled u; draw (0,0)--(0,u); setbounds currentpicture to ((0,0)--(u,0)--(u,u)--(0,u)--cycle); endfig; beginfig(4) arc(0,0.346014) arc(0,0.119726) arc(0,0.0414269) arc(0,0.0143343) arc(-0,0.346014) arc(-0,0.119726) arc(-0,0.0414269) arc(-0,0.0143343) arc(0.58823,0.831883) arc(0.203536,0.287843) arc(0.0704264,0.0995979) arc(0.0243685,0.0344623) arc(0.00843186,0.0119245) arc(-0.58823,0.831883) arc(-0.203536,0.287843) arc(-0.0704264,0.0995979) arc(-0.0243685,0.0344623) arc(-0.00843186,0.0119245) arc(0,0.58823) arc(0,0.203536) arc(0,0.0704264) arc(0,0.0243685) arc(0,0.00843186) arc(-0,0.58823) arc(-0,0.203536) arc(-0,0.0704264) arc(-0,0.0243685) arc(-0,0.00843186) arc(1.21068,1.05817) arc(0.418912,0.366142) arc(0.144949,0.126691) arc(0.0501546,0.0438367) arc(0.0173542,0.0151681) arc(1.21068,1.05817) arc(0.418912,0.366142) arc(0.144949,0.126691) arc(0.0501546,0.0438367) 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