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Original file (200 × 200 pixels, file size: 64 KB, MIME type: image/gif, looped, 31 frames, 6.8 s)

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三平方の定理が成り立つことを、正方形と4つの直角三角形を用いて視覚的に示した図。

Summary

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DescriptionPythag anim.gif
English: Animation of a proof of Pythagoras' theorem, showing how by rearranging triangles the areas a2 + b2 and c2 can be shown to be the same. The area of the outer square never changes, and the total area of the four right triangles is the same at both the beginning and the end, therefore the black area at the beginning, a2 + b2, must equal the black area at the end, c2. The angle of the triangles is arbitrary, therefore this works as a general proof. To be more explicit...


The situation at the start is:

Area_of_the_Outer_Square - (4 x Area_of_a_Triangle) = a2 + b2

...and the situation at the end is:

Area_of_the_Outer_Square - (4 x Area_of_a_Triangle) = c2

The values on both left-hand sides of these two equations are exactly the same (only positions have changed) therefore the values on the right-hand sides must also be exactly the same: a2 + b2 = c2.
Source Own work
Author JohnBlackburne


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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.
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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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Date/TimeThumbnailDimensionsUserComment
current13:36, 9 February 2012👁 Thumbnail for version as of 13:36, 9 February 2012
200 × 200 (64 KB)Tdadamemd (talk | contribs)Four minor tweaks: 1) Reverse loop added to appear continuous instead of staggered, 2) Whole image rotated so that the letters are read in the same sequence that the theorem is typically stated, 3) Dashed line added to explicitly identify the 'a' and 'b'
00:05, 8 November 2010👁 Thumbnail for version as of 00:05, 8 November 2010
200 × 200 (32 KB)JohnBlackburne (talk | contribs){{Information |Description={{en|1=Animation of a proof of Pythagoras's theorem, showing how by rearranging triangles the areas c<sup>2</sup> and a<sup>2</sup> + b<sup>2</sup> can be shown to be the same}} |Source={{own}} |Author=[[User:JohnBlackburne|John

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