Pythagoras' proof

Move four right triangles around a square — and out falls a² + b² = c².

Many proofs of a² + b² = c² exist — the rearrangement proof is the simplest.

Rearrangement proof

Take four right triangles and a square of side a + b. Arrange them two ways — once leaving an a²+b² gap, once a c² gap. Same outer area, so a² + b² = c².