File:WeierstrassSubstitution.svg
From Wikimedia Commons, the free media repository
Jump to navigation
Jump to search
Size of this PNG preview of this SVG file: 345 × 210 pixels. Other resolutions: 320 × 195 pixels | 640 × 390 pixels | 1,024 × 623 pixels | 1,280 × 779 pixels | 2,560 × 1,558 pixels.
Original file (SVG file, nominally 345 × 210 pixels, file size: 7 KB)
File information
Structured data
Captions
Summary
[edit]DescriptionWeierstrassSubstitution.svg |
English: Stereographic projection of the unit circle onto a line through the center illustrating the change in the length element for the Weierstrass substitution article. Created in Mathematica (see code below) and post-processed in Inkscape (fit page to selection) to correct aspect ratio. |
Date | |
Source | Own work |
Author | Sławomir Biały |
Code:
x[t_]=2t/(t^2+1);
y[t_]=(t^2-1)/(t^2+1);
t[x_,y_]=x/(1-y);
Simplify[t[x[t],y[t]]]
circ[t_]={Cos[t],Sin[t]};
\[Theta]0=\[Pi]/6;
\[Theta]1=\[Pi]/6-1/5;
{x0,y0}=circ[\[Theta]0];
{x1,y1}=circ[\[Theta]1];
Graphics[
{Hue[0.7],Thickness[0.001],
Circle[{0,0},1],
Line[{{-1.2,0},{2,0}}],
Hue[0.55],PointSize[0.01],Point[{0,1}],
Point[{x0,y0}],
Point[{x1,y1}],
Point[{t[x0,y0],0}],
Point[{t[x1,y1],0}],
Line[{{0,1},{t[x0,y0],0}}],
Line[{{0,1},{t[x1,y1],0}}],
Thickness[0.0035],Hue[0.05],
Circle[{0,0},1,{\[Theta]1,\[Theta]0}],
Line[{{t[x0,y0],0},{t[x1,y1],0}}],
Dashed,Hue[0.7],Thickness[0.001],
Line[{{0,0},circ[\[Pi]/6-1/10]}],
Circle[{0,0},1/3,{0,\[Pi]/6-1/10}],
Text[x,(1/2.5)circ[\[Pi]/6-1/4]],
Text[t,{2.1,0}],
Text[dt,{t@@circ[\[Pi]/6-1/10],-0.11}],
Text[dx,(circ[\[Pi]/6-1/10]+{0.1,0})]
}
]
Licensing
[edit]I, the copyright holder of this work, hereby publish it under the following licenses:
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- 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.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
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 |
You may select the license of your choice.
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 13:24, 4 February 2011 | 345 × 210 (7 KB) | Sławomir Biały (talk | contribs) | Resized. Tried to fix aspect ratio. | |
13:20, 4 February 2011 | 512 × 512 (3 KB) | Sławomir Biały (talk | contribs) | {{Information |Description ={{en|1=Stereographic projection of the unit circle onto a line through the center illustrating the change in the length element for the Weierstrass substitution article. Created in mathematica.}} |Source ={{own} |
You cannot overwrite this file.
File usage on Commons
There are no pages that use this file.
File usage on other wikis
The following other wikis use this file:
- Usage on en.wikipedia.org
- Usage on es.wikipedia.org
- Usage on fi.wikipedia.org
- Usage on fr.wikipedia.org
- Usage on he.wikipedia.org
- Usage on id.wikipedia.org
- Usage on it.wikipedia.org
- Usage on ko.wikipedia.org
- Usage on pt.wikipedia.org
- Usage on ru.wikipedia.org
- Usage on uk.wikipedia.org