File:Riemann Sphere.gif
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Captions
Captions
Matting of the coimplex plane on the Riemann sphere
Summary edit
| Description |
English: A complex number c can be mapped on the surface of a sphere, where the south pole corresponds to c=0+i0, the equator to |c|=1, and the north pole to complex numbers with infinite modulus (their phase doesn't matter). |
| Date | |
| Source | https://twitter.com/j_bertolotti/status/1143077137861230592 |
| Author | Jacopo Bertolotti |
| Permission (Reusing this file) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
Mathematica 11.0 code edit
riemannsphere[c_] := {(2 Re[c])/(1 + Re[c]^2 + Im[c]^2), (2 Im[c])/(1 + Re[c]^2 + Im[c]^2), (Re[c]^2 + Im[c]^2 - 1)/(1 + Re[c]^2 + Im[c]^2)};
p1 = Table[
c =3 Sin[2 j] + I 2 Sin[1 j];
Graphics3D[{Text[Style["Re", Bold, Large], {3.4, 0, 0}], Text[Style["Im", Bold, Large], {0, 3.6, 0}], Thick, Arrow[{{-3.1, 0, 0}, {3, 0, 0}}], Arrow[{{0, -3.1, 0}, {0, 3, 0}}], Line[{{0, 0, 1}, {Re[c], Im[c], 0}}], Line[{{0, 0, 1}, riemannsphere[c]}], PointSize[0.03], Blue, Point[riemannsphere[c] ], Black, Point[{Re[c], Im[c], 0}], Opacity[0.5], White, Sphere[], Polygon[{{3, 3, 0}, {3, -3, 0}, {-3, -3, 0}, {-3, 3, 0}}]}, Boxed -> False, Lighting -> "Neutral", ViewPoint -> {3, 3, 3}, PlotLabel -> Style[StringForm["c\!\(\*SubscriptBox[\(=\), \(``\)]\)", Round[c, 0.01], j], Medium, FontFamily -> "DejaVu Serif"], LabelStyle -> {Black, Bold} ]
, {j, 0, 2 \[Pi], 0.05}];
ListAnimate[p1, 15]
Licensing edit
I, the copyright holder of this work, hereby publish it under the following license:
 
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This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. |
| The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 08:04, 26 June 2019 | | 360 × 286 (710 KB) | Berto (talk | contribs) | User created page with UploadWizard |
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