File:Belt trick 2.gif
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Summary
| Description | Illustration of the belt trick, showing a homotopy between two one-parameter subgroups of the rotation group, one through an angle of 2π and one through an angle of −2π. |
| Date | |
| Source | Created in Mathematica 9.0 (source code below) |
| Author | Slawekb |
- Source
F1[s_, t_] = {{E^(2 \[Pi] I t), Tan[][Pi] s/2]}, {-Tan[][Pi] s/2],
E^(-2 \[Pi] I t)}}.{{E^(-\[Pi] I t), 0}, {0, E^(\[Pi] I t)}}
F2[s_, t_] = (F1[s, t]/Sqrt[][][s, t]])
F[s_, t_] = FullSimplify[][][s, 0].F2[s, t]
Clear[i, j, k]
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 -> {{-1, 1}, {-1, 1}, {-1, 1}}, Mesh -> {0, 3},
ImageSize -> 768]
b = Join[][][][s], {s, 0.01, 0.99, 0.02}],
Table[][][s], {s, 0.99, 0.01, -0.02}]];
Export["b.gif", b]
Licensing
I, the copyright holder of this work, hereby publish 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. |
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- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
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- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
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Original upload log
The original description page was here. All following user names refer to en.wikipedia.
| Date/Time | Dimensions | User | Comment |
|---|---|---|---|
| 14:19, September 7, 2014 | 533 × 391 (366 KB)) | Slawekb |
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 14:56, 15 June 2016 | | 533 × 391 (366 KB) | wikimediacommons>Bruno Max Melo | ==Summary== {{Information |Description = Illustration of the belt trick, showing a homotopy between two one-parameter subgroups of the rotation group, one through an angle of 2π and one through an angle of −2π. |Source = Created in Mathemat... |
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