File:Belt trick 1.gif
Belt_trick_1.gif (514 × 402 pixels, file size: 636 KB, MIME type: image/gif, looped, 102 frames, 1.0 s)
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Summary
editDescriptionBelt trick 1.gif |
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
editSlawekb at English Wikipedia, the copyright holder of this work, hereby publishes it under the following licenses:
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.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
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
editThe 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 | 19:35, 5 August 2017 | 514 × 402 (636 KB) | OgreBot (talk | contribs) | (BOT): Reverting to most recent version before archival | |
19:35, 5 August 2017 | 550 × 441 (655 KB) | OgreBot (talk | contribs) | (BOT): Uploading old version of file from en.wikipedia; originally uploaded on 2014-09-07 17:07:19 by Slawekb | ||
19:35, 5 August 2017 | 577 × 476 (631 KB) | OgreBot (talk | contribs) | (BOT): Uploading old version of file from en.wikipedia; originally uploaded on 2014-09-07 13:50:13 by Slawekb | ||
19:35, 5 August 2017 | 599 × 494 (636 KB) | OgreBot (talk | contribs) | (BOT): Uploading old version of file from en.wikipedia; originally uploaded on 2014-09-07 13:46:43 by Slawekb | ||
19:35, 5 August 2017 | 599 × 494 (636 KB) | OgreBot (talk | contribs) | (BOT): Uploading old version of file from en.wikipedia; originally uploaded on 2014-09-07 13:45:34 by Slawekb | ||
19:35, 5 August 2017 | 599 × 494 (636 KB) | OgreBot (talk | contribs) | (BOT): Uploading old version of file from en.wikipedia; originally uploaded on 2014-09-07 12:14:26 by Slawekb | ||
19:35, 5 August 2017 | 360 × 349 (161 KB) | OgreBot (talk | contribs) | (BOT): Uploading old version of file from en.wikipedia; originally uploaded on 2014-09-06 19:22:26 by Slawekb | ||
19:35, 5 August 2017 | 360 × 349 (141 KB) | OgreBot (talk | contribs) | (BOT): Uploading old version of file from en.wikipedia; originally uploaded on 2014-09-06 14:57:01 by Slawekb | ||
19:35, 5 August 2017 | 360 × 199 (148 KB) | OgreBot (talk | contribs) | (BOT): Uploading old version of file from en.wikipedia; originally uploaded on 2014-09-06 14:15:26 by Slawekb | ||
14:05, 15 June 2016 | 514 × 402 (636 KB) | Bruno Max Melo (talk | contribs) | ==Summary== {{Information |Description = 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. |Source = Created in Mathematica 9.0 (source be... |
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