File:Belt trick 1.gif
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Summary
| Description |
English: An illustration of the belt trick, showing a homotopy between a one-parameter rotation through an angle of 4π in three dimensions and the identity rotation. |
| Date | |
| Source | Created in Mathematica 9.0 (source below) |
| Author | Slawekb |
| Other versions |
 |
- Source
F1[s_, t_] = {{E^(2 \[Pi] I t), Tan[][Pi] s/2]}, {-Tan[][Pi] s/2],
E^(-2 \[Pi] I t)}};
F2[s_, t_] = (F1[s, t]/Sqrt[][][s, t]]);
F[s_, t_] = FullSimplify[][][s, 0].F2[s, t];
i = {{I, 0}, {0, -I}};
j = {{0, -1}, {1, 0}};
k = i.j;
Components[A_] := (1/2) {Tr[][i],
Tr[][j], Tr[][k]};
R[s_][t_] =
Transpose[][][][][s, t].i.ConjugateTranspose[][s, t]]]],
FullSimplify[][][][s, t].j.ConjugateTranspose[][s, t]]]],
FullSimplify[][][][s, t].k.ConjugateTranspose[][s, t]]]]}];
PlotRotation[R_] :=
ParametricPlot3D[][t][[1]] t + R[t][[2]] s, {t, 0, 1}, {s, 0, 1/7.5},
Boxed -> False, Axes -> False, PlotPoints -> 20, PlotRange -> All];
a = Table[][][s], {s, 0, 1, 0.02}];
Export["a.gif", a];
Licensing
Slawekb at English Wikipedia, the copyright holder of this work, hereby publishes it under the following licenses:
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Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License. |
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
Attribution: Slawekb at English Wikipedia
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Original upload log
The original description page was here. All following user names refer to en.wikipedia.
- 2014-09-07 18:24 Slawekb 514×402× (651115 bytes) Reverted to version as of 17:13, 7 September 2014
- 2014-09-07 17:14 Slawekb 550×441× (670939 bytes) Reverted to version as of 17:07, 7 September 2014
- 2014-09-07 17:13 Slawekb 514×402× (651115 bytes) Trying again...
- 2014-09-07 17:07 Slawekb 550×441× (670939 bytes) Trying again...
- 2014-09-07 13:50 Slawekb 577×476× (646122 bytes) trying again...
- 2014-09-07 12:14 Slawekb 599×494× (651769 bytes) Improved resolution, made image loop, and cropped.
- 2014-09-06 19:22 Slawekb 360×349× (165290 bytes) Thickened the ribbon
- 2014-09-06 14:57 Slawekb 360×349× (144404 bytes) Fixed bounding boxes. Improved mesh.
- 2014-09-06 14:15 Slawekb 360×199× (151047 bytes) Uploading a self-made file using [[Wikipedia:File_Upload_Wizard|File Upload Wizard]]
File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 20:35, 5 August 2017 | | 514 × 402 (636 KB) | wikimediacommons>OgreBot | (BOT): Reverting to most recent version before archival |
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