Datei:12crossings-rose-rhodonea-limacon-symmetrical-knot.svg
Originaldatei (SVG-Datei, Basisgröße: 620 × 600 Pixel, Dateigröße: 50 KB)
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Beschreibung
| Beschreibung |
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"). |
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| Quelle |
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
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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
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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 |
| Urheber | AnonMoos |
| Andere Versionen |
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 . |
Lizenz
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Ich, der Urheberrechtsinhaber dieses Werkes, veröffentliche es als gemeinfrei. Dies gilt weltweit. In manchen Staaten könnte dies rechtlich nicht möglich sein. Sofern dies der Fall ist: Ich gewähre jedem das bedingungslose Recht, dieses Werk für jedweden Zweck zu nutzen, es sei denn, Bedingungen sind gesetzlich erforderlich. |
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| Version vom | Vorschaubild | Maße | Benutzer | Kommentar | |
|---|---|---|---|---|---|
| aktuell | 05:44, 20. Feb. 2010 | | 620 × 600 (50 KB) | AnonMoos | 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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