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.
- Shearing Butterflies in Quadrilaterals
- Area of Parallelogram Formula by Shearing
- Parallelogram and Ellipses
- Proof 37 of the Pythagorean theorem - by David King
- Shearing a Polygon into a Triangle of Equal Area
- Pythagoras' Theorem By Sheer Shearing
- Shearing and Translation in Pythagorean Pants