Han: where did you find that Pythagoras proof? I've seen a lot of proofs in my time (and have read systematically through books that contain more than 50 of them), but don't recall anything like that one.
Here's what I consider one of the simplest proofs:
4 triangles + 4 triangles + square on hypotenuse sum of squares on other two sides
I mentioned another one on geometry forum recently: Plainly the truth-value of the theorem would be unaltered if we place d any similar figures (eg., semicircles) on the edges, instead of squares. But look:
C /| \ / | \ / | \ A---D-----------B
The triangles ADC, CDB, and ACB ARE similar figures, and plainly ADC + CDB = ACB.