File:Closed-five-link-chain-knots.svg

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Original file(SVG file, nominally 720 × 720 pixels, file size: 17 KB)

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Summary[edit]

Description 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...
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Source

Self-made graphic, converted from a version of the following vector PostScript source code:

%!
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
Author AnonMoos

Licensing[edit]

Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

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Date/TimeThumbnailDimensionsUserComment
current16:49, 12 August 2009Thumbnail for version as of 16:49, 12 August 2009720 × 720 (17 KB)AnonMoos (talk | contribs)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 followi

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