File:J-inv-poincare.jpeg
J-inv-poincare.jpeg (600 × 600 pixels, file size: 37 KB, MIME type: image/jpeg)
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Captions
DescriptionJ-inv-poincare.jpeg | Klein's J-invariant, modulus on Poincaré disk (600x600 pixels) | ||||||||
Date | 22 May 2005, 01:30 (original upload date) | ||||||||
Source | Transferred from en.wikipedia to Commons by Keyi. | ||||||||
Author | en:user:Linas | ||||||||
Permission (Reusing this file) |
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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.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
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Original upload log
[edit]The original description page is/was here. All following user names refer to en.wikipedia.
Klein's J-invariant, modulus on Poincaré disk (600x600 pixels)
Detailed description
[edit]This image shows the modulus |j| of the J-invariant as a function on the Poincare disk. The Poincaré disk is a mapping of the upper half-plane to the unit disk by means of the Mobius transformation
where τ is the half-period ratio, that is, the coordinate on the upper half-plane. The left-right symmetry of this image corresponds to the symmetry of the J-invariant, as small values for the imaginary part of τ are mapped to z=−1 on the left hand side, while large values for the imaginary part of τ are mapped to z=+1 on the right side. The fundamental domain is a triangle spanning the two vertically oriented dots in the center, with the cusp at z=+1 on the right. The transformation
corresponds to walking the fundamental domain from dot to dot on the boundary of the largest red area on the right; the cusp z=+1 remains unchanged.
For a detailed description of other aspects of this picture, including the coloration, please refer to Image:J-inv-modulus.jpeg.
- See also Image:J-inv-real.jpeg for the real part.
- See also Image:J-inv-phase.jpeg for the phase.
It, and other related images, can be seen at http://www.linas.org/art-gallery/numberetic/numberetic.html
Source of Image
[edit]Created by Linas Vepstas User:Linas <linas@linas.org> on 21 May 2005 using custom software written entirely by Linas Vepstas.
Copyright status
[edit]Released under the Gnu Free Documentation License (GFDL) by Linas Vepstas.
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This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. Subject to disclaimers. | |
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This licensing tag was added to this file as part of the GFDL licensing update.http://creativecommons.org/licenses/by-sa/3.0/CC BY-SA 3.0Creative Commons Attribution-Share Alike 3.0truetrue |
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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. Subject to disclaimers.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 11:17, 12 December 2008 | ![]() | 600 × 600 (37 KB) | Keyi (talk | contribs) | {{Information |Description=Klein's J-invariant, modulus on Poincaré disk (600x600 pixels) |Source= Transferred from [http://en.wikipedia.org en.wikipedia]; transferred to Commons by User:Keyi. |Date=01:30, 22 May 2005 (original upload date) |Author=[ |
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