File:Brunnian-4loops.svg

From Wikimedia Commons, the free media repository

Jump to: navigation, search

Brunnian-4loops.svg(SVG file, nominally 588 × 600 pixels, file size: 3 KB)

[edit] Summary

4-loop Brunnian link — no two loops are directly linked, but all four are collectively linked, and cutting any loop frees all the other loops.

Redrawn version of illustration in Hermann Brunn's 1892 article "Über Verkettung", by way of Dale Rolfsen's 1976 book Knots and Links (p. 67).

SVG version of Image:Brunnian.png . Converted from the following PostScript code:

%!
.1 dup scale
105 setlinewidth/c{rcurveto}def/m{moveto}def/l{rlineto}def/x
{gsave 135 setlinewidth 0 setgray stroke grestore stroke}def
0 .6 0 setrgbcolor
4000 3960 m
0 276.14 -447.72 500 -1000 500 c
-552.28 0 -1000 -223.86 -1000 -500 c
0 -276.14 447.72 -500 1000 -500 c
552.28 0 1000 223.86 1000 500 c closepath x
0 0 1 setrgbcolor
2787.38 5338.86 m
121.9 121.9 287.23 190.38 459.62 190.38 c
130 0 l
172.39 0 337.72 -68.48 459.62 -190.38 c
919.24 -919.24 l
121.9 -121.9 190.38 -287.23 190.38 -459.62 c
0 -172.39 -68.48 -337.72 -190.38 -459.62 c
-919.24 -919.24 l
-121.9 -121.9 -287.23 -190.38 -459.62 -190.38 c
-130 0 l
-172.39 0 -337.72 68.48 -459.62 190.38 c
-1206.5 1206.5 l
-45.71 45.71 -71.39 107.71 -71.39 172.36 c
0 64.65 25.68 126.65 71.39 172.36 c closepath x
1 0 0 setrgbcolor
2163.38 5338.86 m
121.9 121.9 287.23 190.38 459.62 190.38 c
130 0 l
172.39 0 337.72 -68.48 459.62 -190.38 c
1206.5 -1206.5 l
45.71 -45.71 71.39 -107.71 71.39 -172.36 c
0 -64.65 -25.68 -126.65 -71.39 -172.36 c
-1206.5 -1206.5 l
-121.9 -121.9 -287.23 -190.38 -459.62 -190.38 c
-130 0 l
-172.39 0 -337.72 68.48 -459.62 190.38 c
-919.24 919.24 l
-121.9 121.9 -190.38 287.23 -190.38 459.62 c
0 172.39 68.48 337.72 190.38 459.62 c closepath x
1 1 0 setrgbcolor
3690 5260 m
0 381.08 -308.92 690 -690 690 c
-381.08 0 -690 -308.92 -690 -690 c
0 -2600 l
0 -381.08 308.92 -690 690 -690 c
381.08 0 690 308.92 690 690 c closepath x
135 setlinewidth 0 setgray
2000.15 3951.27 m
9.52 -272.7 454.37 -491.27 999.85 -491.27 c
545.48 0 990.33 218.57 999.85 491.27 c stroke
105 setlinewidth 0 .6 0 setrgbcolor
2000 3960 m
0 -276.14 447.72 -500 1000 -500 c
552.28 0 1000 223.86 1000 500 c stroke
135 setlinewidth 0 setgray
3388.34 5529.14 m
164.52 -2.87 321.82 -68.03 440.18 -182.33 c stroke
3828.53 2573.19 m
-118.36 -114.3 -275.67 -179.46 -440.18 -182.33 c stroke
1881.14 4432.62 m 624 624 l stroke
1881.14 3487.38 m 624 -624 l stroke
105 setlinewidth 0 0 1 setrgbcolor
3377 5529.24 m
172.39 0 337.72 -68.48 459.62 -190.38 c stroke
3836.62 2581.14 m
-121.9 -121.9 -287.23 -190.38 -459.62 -190.38 c stroke
1868.14 4419.62 m 650 650 l stroke
1868.14 3500.38 m 650 -650 l stroke
showpage
%EOF

[edit] Licensing

Public domain I, the copyright holder of this work, hereby release it into the public domain. This applies worldwide.

In case this is not legally possible:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.


Afrikaans | Alemannisch | Aragonés | العربية | Asturianu | Azərbaycan | Беларуская (тарашкевіца) | Български | Català | Cebuano | Soranî / کوردی | Česky | Cymraeg | Dansk | Deutsch | Ελληνικά | English | Esperanto | Español | Eesti | Euskara | Estremeñu | فارسی | Suomi | Français | Galego | עברית | हिन्दी | Hrvatski | Magyar | Հայերեն | Bahasa Indonesia | Ido | Íslenska | Italiano | 日本語 | ქართული | ភាសាខ្មែរ | 한국어 | Ripoarisch | Kurdî / كوردی | Latina | Lietuvių | Latviešu | 文言 | Македонски | Bahasa Melayu | Plattdüütsch | Nederlands | ‪Norsk (nynorsk)‬ | ‪Norsk (bokmål)‬ | Polski | Português | Română | Русский | Slovenčina | Slovenščina | Shqip | Српски / Srpski | Svenska | ไทย | Tagalog | Türkçe | Українська | Vèneto | Tiếng Việt | Walon | 吴语 | 中文 | ‪中文(简体)‬ | ‪中文(繁體)‬ | 粵語 | +/−

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current19:53, 5 September 2006Thumbnail for version as of 19:53, 5 September 2006588×600 (3 KB)AnonMoos (talk | contribs) (fixing typo in file comment -- vector data remains unchanged )
03:06, 5 September 2006Thumbnail for version as of 03:06, 5 September 2006588×600 (3 KB)AnonMoos (talk | contribs) (4-loop Brunnian link — no two loops are directly linked, but all four are collectively linked, and cutting any loop frees all the other loops. SVG version of Image:Brunnian.png . Converted from the following PostScript code: <pre>%! .1 dup scale)

The following 2 pages link to this file:

Global file usage

The following other wikis use this file: