File:Figure8knot-rose-limacon-curve.svg

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Original file ‎(SVG file, nominally 696 × 600 pixels, file size: 27 KB)

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The figure-eight knot of mathematical knot theory depicted in symmetric form. The curves were generated from the polar coordinates equation r=b+sin(aθ), which is a slight generalization of the Limaçon and Rose/rhodonea curves, using parameters a=(2/3) and b=2.

The same curve (with a different rotation about the origin) is generated by the following non-polar parametric equations:

For an equivalent simple square depiction, see File:Figure8knot-math-square-alternate.svg .
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Self-made graphic, generated from the following vector PostScript source-code: 

%!
300 396 translate 45 rotate 72.5 dup scale 1 setgray .175
setlinewidth/z{{w lineto}for stroke}def/ecc{2}def/w{/th
exch def th 2 mul 3 div/x exch def x sin ecc add th cos
mul x sin ecc add th sin mul}def/y{dup w moveto 1 add 1}
def 0 y 1080{w lineto}for closepath gsave 0 setgray .455
setlinewidth stroke grestore stroke 0 setgray .455
setlinewidth 24 y 64 z 296 y 336 z 564 y 604 z 836 y 876
z .175 setlinewidth 1 setgray 23 y 65 z 295 y 337 z 563 y
605 z 835 y 877 z showpage
%EOF
Author AnonMoos
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Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
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current02:36, 27 February 2010Thumbnail for version as of 02:36, 27 February 2010696 × 600 (27 KB)AnonMoos (talk | contribs)Thefigure-eight knot of mathematical knot theory depicted in symmetric form. The curves were generated from the polar coordinates equation r=b+sin(aθ), which is a slight generalization of the Limaçon and Rose/rhod

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