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

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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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Date/TimeThumbnailDimensionsUserComment
current13:36, 9 February 2012Thumbnail for version as of 13:36, 9 February 2012200 × 200 (64 KB)TdadamemdFour 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 2010Thumbnail for version as of 00:05, 8 November 2010200 × 200 (32 KB)JohnBlackburne{{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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