File:12crossings-rose-rhodonea-limacon-symmetrical-knot.svg
Original file (SVG file, nominally 620 × 600 pixels, file size: 50 KB)
Captions
Captions
Summary[edit]
| Description |
Decorative knot with twelve crossings, depicted with three-fold visual symmetry. 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=(3/5) and b=(3/2). If the three outermost curve segments which directly connect the three outer crossings are deleted, and the lines which intersect at these three outer crossings are joined together there, then you get the 9-crossing knot seen in image File:Knot-9crossings-symmetrical.svg. If everything outside of the three next-to-outermost crossings is deleted, and the lines which intersect at these three crossings are joined together there, then you get the Borromean rings configuration. If everything outside of the three next-to-inner crossings is deleted, and the lines which intersect at these three crossings are joined together there, then you get a Triquetra (topologically equivalent to a Trefoil knot). If everything outside of the three innermost crossings is deleted, and the lines which intersect at these three crossings are joined together there, then you get a form of triangle (topologically equivalent to a simple circle or closed loop, i.e. "unknot"). |
| Date | |
| Source |
Self-made graphic, converted from the following vector PostScript source code: %!
300 396 translate 75 dup scale .125 setlinewidth 1
setgray/z{{w lineto}for stroke}def/ecc{1.5}def/w{/th
exch def th 3 mul 5 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 1800{w lineto}for closepath gsave 0
setgray .325 setlinewidth stroke grestore stroke 0
setgray .325 setlinewidth 16 y 44 z 188 y 232 z 316 y
344 z 488 y 528 z 616 y 644 z 788 y 832 z 916 y 944 z
1088 y 1128 z 1216 y 1244 z 1388 y 1432 z 1516 y 1544
z 1688 y 1728 z 0.125 setlinewidth 1 setgray 15 y 45
z 187 y 233 z 315 y 345 z 487 y 529 z 615 y 645 z 787
y 833 z 915 y 945 z 1087 y 1129 z 1215 y 1245 z 1387
y 1433 z 1515 y 1545 z 1687 y 1729 z showpage
%EOF |
| Author | AnonMoos |
| Other versions |
For other curves generated from the polar coordinates equation r=b+sin(aθ), see File:Mathematical-polar-equation-flowers.svg , File:Quinquetra-interlaced-alternate.svg , and File:Interlaced-Triangles Brunnian-link alternate.svg . For a different decorative knot, see File:12crossing-decorative-knot-triskele.svg . |
Licensing[edit]
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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/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 03:44, 20 February 2010 | | 620 × 600 (50 KB) | AnonMoos (talk | contribs) | Decorative knot with twelve crossings, depicted with three-fold visual symmetry. 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=(3/ |
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