File:Klein continued fraction.svg

Original file (SVG file, nominally 207 × 248 pixels, file size: 25 KB)

Summary

Description
English: The Klein continued fraction for the golden ratio
Date
Source Own work
Author RandoomJD
SVG development
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The SVG code is valid.
 
This vector image was created with MetaPost.
Source code
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PostScript code

u=1cm; w=6; h=8;
 m=0.3;

 z1=(1,0)*u;
 z2=(1,1)*u;
 z3=(2,3)*u;
 z4=(5,8)*u;
 z5=(13,21)*u;
 z6=z4+(z5-z4)*m/(21-8);
 pickup pencircle scaled 1pt;
 fill z1--z2--z3--z4--z6--(w+m,h+m)*u--(w+m,0)*u--cycle withcolor 0.9white+blue;
 draw z1--z2--z3--z4--z6 withcolor blue+0.5white;

 z11=(0,1)*u;
 z12=(1,2)*u;
 z13=(3,5)*u;
 z14=(8,13)*u;
 z15=z13+(z14-z13)/8*(3+m);
 fill z11--z12--z13--z15--(0,h+m)*u--cycle withcolor 0.9white+red;
 draw z11--z12--z13--z15 withcolor red+0.5white;

 drawarrow (-m,0)*u--(w+m+0.1,0)*u;
 drawarrow (0,-m)*u--(0,h+m+0.1)*u;

 pickup pencircle scaled 3pt;
 for i=0 upto w: for j=0 upto h:
   drawdot (i*u,j*u);
 endfor endfor

 label.ulft(btex $O$ etex scaled 1, (0,0));
 label.urt(btex $(1,0)$ etex scaled 1, z1);

 pickup pencircle scaled 1pt;
 draw (0,0)--(13,21)*u*(h+m)/21;

 drawarrow (0,0)--(1,21/13)*u;
 drawarrow (0,0)--(1,0)*u;
 drawarrow (0,0)--(0,1)*u;

 label.ulft(btex $(1,\varphi)$ etex scaled 1, (1,21/13)*u);
 label.lft(btex $(0,1)$ etex scaled 1, (0,1)*u);

Licensing

I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
You are free:
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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.

Captions

The Klein continued fraction for the golden ratio

Items portrayed in this file

depicts

24 June 2024

image/svg+xml

File history

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Date/TimeThumbnailDimensionsUserComment
current16:31, 24 June 2024Thumbnail for version as of 16:31, 24 June 2024207 × 248 (25 KB)RandoomJDUploaded own work with UploadWizard

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