October 12th, 2010

A "houses" proof of the Pythagorean theorem

For the geometry cognitive science cognitive-science-via-geometry course I'm taking this semester, the assignment for tomorrow is to write a "non-algebraic" and "intuitive" proof of the Pythagorean theorem. As far as I can tell, that means something like: no equations or plus signs, but we're allowed to use the words "equals" and "sum"; no ratios if we can help it; lots of pictures and colors and similar triangles and appeals to various geometric results; bonus points for recursive behavior; and extra bonus points if it's the kind of proof you could explain to someone at a dinner party in a couple of minutes.1

Figuring out how to do this kind of thing has been difficult and uncomfortable. First of all, I don't care for the implication that intuitiveness can be measured objectively; I think that intuitive equals familiar. Second, I've spent the last year being trained to express proofs in ways that computers can understand, which is to say, not very much like this. Third, dammit, I like algebra.

But hey, I'll give it my best shot. What do you think of my proof -- is it convincing? (I didn't come up with the "houses" idea myself -- I'm just expanding on something that was done in class.)

  1. "A dinner party without whiteboards, I mean," I clarified to Chris chrisamaphone. "Sounds like a pretty dull dinner party," she said.