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)
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arc(0.62485,0.0322315)
arc(0.588929,0.0286856)
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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)
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arc(0.630186,0.0144474)
arc(0.640754,0.0129193)
arc(0.60046,0.0107153)
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arc(0.952021,0.0179483)
arc(0.898598,0.0135044)
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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)
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arc(0.331331,0.0683638)
arc(0.500937,0.0747912)
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arc(0.42578,0.0473823)
arc(0.545018,0.0637519)
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arc(0.422281,0.00471682)
arc(0.500224,0.00679903)
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arc(0.495354,0.00558325)
arc(0.541019,0.00635617)
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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)
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arc(0.347217,0.00382942)
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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)
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arc(-0.00843186,0.0119245)
arc(0,0.58823)
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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)
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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;
bye.