Proof of Pythagoras' Theorem
An applet that demonstrates a proof of the Pythagorean theorem was kindly sent to me by David King. The proof is similar to #12 in that it relies on a shearing transformation, yet I think it's sufficiently different to warrant its own place in the list of proofs. The text below is David's.
This simulation shows a simple graphical proof. It occurred to me while I was trying to get to sleep, and for a mad moment I thought it might be original. That was of course too much to hope for; it is just a variation on a well known theme. It's still quite therapeutic to watch though...
Click on the simulation to start or stop it.
How it proves Pythagoras:
The red square on the hypoteneuse is just covered by the green and blue squares built on the other two sides, once they have been rotated and sheared into position.
Copyright © 1996-2008 Alexander Bogomolny
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