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| Keywords: Closed-five-link-chain-knots.svg Various decorative depictions of the L10a174 link of mathematical knot theory i e a closed 5-link chain including interlinked circles and pentagons and interlaced yin-yang type shapes Self-made graphic converted from a version of the following vector PostScript source code <pre> gsave 152 432 translate 55 dup scale 12 5 setlinewidth/plr 25 sub 2 47213472 12 5 mul mul dup 3 2 roll 72 mul 90 add dup 3 1 roll cos mul 3 1 roll sin mul def/P 4 4 plr 3 4 plr 2 4 plr 1 4 plr 0 4 plr moveto 4 lineto repeat closepath stroke def gsave 0 5 5 plr translate P grestore gsave 4 5 5 plr translate P grestore gsave 3 5 5 plr translate P grestore gsave 2 5 5 plr translate P grestore gsave 1 5 5 plr translate P grestore grestore gsave 152 132 translate 55 dup scale 12 5 setlinewidth gsave 2 5 plr translate P grestore gsave 3 5 plr translate P grestore gsave 4 5 plr translate P grestore gsave 0 5 plr translate P grestore gsave 1 5 plr translate P grestore grestore gsave 452 432 translate 825 dup scale/plr dup 3 2 roll 72 mul 90 add dup 3 1 roll cos mul 3 1 roll sin mul def 10 setlinewidth 0 1 4 100 plr 75 0 360 arc closepath stroke for grestore gsave/archim PostScript program to display an Archimedean spiral by approximating it with Bezier curves Parameters centerx horizontal coordinate of center of spiral centery vertical coordinate of center of spiral rotf degrees to rotate sepwid width separating successive turnings of spiral incrm insert a curve point every these degrees /sweeps swp2 def number of 360 degree turnings to show double - 0 to display single spiral else double /pi 3 1415926535898 def/radians 57 295779513082 def /sepwid sepwid pi div 2 div def gsave centerx centery translate rotf rotate /aspiral /first 1 def lower incrm sweeps 360 mul 8 dup repeat phase add cos/costh exch def phase add sin/sinth exch def costh mul radians div/thcosth exch def sinth mul radians div/thsinth exch def thcosth sepwid mul/x exch def thsinth sepwid mul/y exch def 0 eq phase 90 eq phase 270 eq or and /slope 999999999 def /slope sinth thcosth add costh thsinth sub div def ifelse sinth 0 gt sinth 0 eq costh -1 eq and or /flag -1 def /flag 1 def ifelse /A exch def phase 0 eq phase 180 eq or A 49 29348 lt A 180 gt A 196 273450852 lt and A 360 gt A 368 8301 lt and A 540 gt A 545 9907 lt and A 720 gt A 724 5217 lt and A 900 gt A 903 6281968 lt and or or or or or /flag flag neg def if if phase 120 eq phase 300 eq or A 10 lt A 80 gt A 100 lt and or /flag flag neg def if if incrm sub 3 dup repeat phase add cos sepwid mul mul radians div /prevx exch def phase add sin sepwid mul mul radians div /prevy exch def incrm add 3 dup repeat phase add cos sepwid mul mul radians div /nextx exch def phase add sin sepwid mul mul radians div /nexty exch def /prevdist x prevx sub dup mul y prevy sub dup mul add sqrt pi div def /nextdist x nextx sub dup mul y nexty sub dup mul add sqrt pi div def /normaliz slope slope mul 1 add sqrt def 0 eq 0 0 moveto/prevbezx phase cos nextdist mul def/prevbezy phase sin nextdist mul def/first 0 def first 1 eq x y moveto/first 0 def prevbezx prevbezy x 1 flag mul normaliz div prevdist mul sub y slope flag mul normaliz div prevdist mul sub x y curveto ifelse /prevbezx x 1 flag mul normaliz div nextdist mul add def /prevbezy y slope flag mul normaliz div nextdist mul add def ifelse for stroke def /phase 0 def aspiral grestore def 460 150 translate 2875 dup scale 56 setlinewidth 0 224 224 270 90 arcn stroke 1 224 plr 224 342 162 arcn stroke 2 224 plr 224 54 234 arcn stroke 3 224 plr 224 126 306 arcn stroke 4 224 plr 224 198 18 arcn stroke 0 setgray 32 setlinewidth 1 224 plr 236 186 8118 341 arc 3 224 plr 212 125 306 arcn stroke 2 224 plr 236 258 8118 53 arc 4 224 plr 212 197 18 arcn stroke 3 224 plr 236 330 8118 125 arc 0 224 212 269 90 arcn stroke 4 224 plr 236 42 8118 197 arc 1 224 plr 212 341 162 arcn stroke 0 224 236 114 8118 269 arc 2 224 plr 212 53 234 arcn stroke gsave 1 -1 scale/centerx 0 def/centery 0 def/incrm 18 def /sepwid 120 def/rotf -318 def/lower 1308 def/swp2 4 0334 def archim /sepwid 120 def/rotf -390 def archim /sepwid 120 def/rotf -462 def archim /sepwid 120 def/rotf -534 def archim /sepwid 120 def/rotf -606 def archim grestore 16 setlinewidth 1 0 0 setrgbcolor 1 224 plr 236 186 8118 341 arc 3 224 plr 212 125 306 arcn stroke 8 0 8 setrgbcolor 2 224 plr 236 258 8118 53 arc 4 224 plr 212 197 18 arcn stroke 0 5 1 setrgbcolor 3 224 plr 236 330 8118 125 arc 0 224 212 269 90 arcn stroke 0 9 0 setrgbcolor 4 224 plr 236 42 8118 197 arc 1 224 plr 212 341 162 arcn stroke 1 1 0 setrgbcolor 0 224 236 114 8118 269 arc 2 224 plr 212 53 234 arcn stroke 1 0 0 setrgbcolor 1 224 plr 236 341 331 arcn stroke 1 -1 scale 0 5 1 setrgbcolor /sepwid 120 def/rotf -318 def/lower 1308 def/swp2 4 0334 def archim 0 9 0 setrgbcolor/sepwid 120 def/rotf -390 def archim 1 1 0 setrgbcolor/sepwid 120 def/rotf -462 def archim 1 0 0 setrgbcolor/sepwid 120 def/rotf -534 def archim 8 0 8 setrgbcolor/sepwid 120 def/rotf -606 def archim 0 5 1 setrgbcolor /sepwid 120 def/rotf -318 def/lower 1344 def/swp2 3 8334 def archim 0 9 0 setrgbcolor/sepwid 120 def/rotf -390 def archim 1 1 0 setrgbcolor/sepwid 120 def/rotf -462 def archim 1 0 0 setrgbcolor/sepwid 120 def/rotf -534 def archim 8 0 8 setrgbcolor/sepwid 120 def/rotf -606 def archim grestore grestore showpage EOF</pre> 2009 AnonMoos Regular pentagons Linked circles Decorative knots Images with PostScript source code 5-fold rotational symmetry 10 crossing number knots and links | ||||
