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

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

Summary

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...
Date
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

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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f3144c52e1744efead13a6ed1e5a2570942300a0

17,082 byte

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720 pixel

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Date/TimeThumbnailDimensionsUserComment
current16:49, 12 August 2009Thumbnail for version as of 16:49, 12 August 2009720 × 720 (17 KB)AnonMoosVarious 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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