Pythagorean Triples

A website dedicated entirely to Pythagoras based problems, always using integer triples. Handy!

sPythagoras

I had a minor brain wave when reading this wonderful book by my favourite author. In it he mentions a good idea for teaching Pythagoras proofs. Take a square photograph, and chop it up in the exact proportions of a dissection proof, then get students to rearrange it to ‘prove’ the Pythagorean theorem. A simple idea, and one I’m sure has been used countless times before and since. I immediately took to the idea and went about planning it out. I’ve always had a bugbear that students are usually shown only one proof of the Pythagorean Theorem, when in fact, there are hundreds. So I wanted to dissect several images in several different ways. Granted, this negates all proofs apart from proof by dissection, but it’s a start. Pythagoras lends itself nicely to sPythagoras… so… behold, the James Bond Pythagorean Proofs, featuring six James Bond actors, and six different dissection proofs:

Classic Sean:

Boring George:

Cheesey Roger:

Cold Timothy:

Sleazy Pierce:

Blue Eyed Daniel:

And the dissections:

…oh and all in a PowerPoint: spythagoras_final

The Pythagorean Proof(s)

A lot of people don’t realise that there are literally hundreds of proofs of the Pythagorean Theorem. You are not prescribed to show any one particular way. Take your pick! And there are way more than the ones listed on that site!

Incidentally, that site inspired this display in my office: