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.

This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at https://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet.

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.

What Is Shear Transform?

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

71222929