File:J-inv-poincare.jpeg
J-inv-poincare.jpeg (600 × 600 pixels, file size: 37 KB, MIME type: image/jpeg)
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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 |
Contents
Original upload log
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
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
Created by Linas Vepstas User:Linas <linas@linas.org> on 21 May 2005 using custom software written entirely by Linas Vepstas.
Copyright status
Released under the Gnu Free Documentation License (GFDL) by Linas Vepstas.
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 |
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 |
Relevant Links
Items portrayed in this file
depicts
22 May 2005
File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 12:17, 12 December 2008 | 600 × 600 (37 KB) | wikimediacommons>Keyi | {{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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