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Pythagoras' Theorem:  Aha Proof, Version 2

This is a slight variation on the classic "Aha!" proof.  I find this version a little clearer.  The picture says most of it; we'll explain the details below.

Aha Proof, version 2

The pink inner square has side length c, and hence has area c2.  The outer square, which contains it, has side length a+b, and hence has total area (a+b)2, which, multiplied out, is equal to a2+b2 + 2ab.

From the picture, we see that the four blue triangles each have area ab/2, and the total area of the four blue triangles together is 2ab.  So, adding the blue triangles and the pink inner square, the outer square must also have area c2 + 2ab.

And so, we have a2+b2 + 2ab = c2 + 2ab.   Canceling the "cross term" we're left with a2+b2 = c2.

Page created on 2/16/2008