Proofs of The Pythagorean Theorem

The Pythagorean Theorem.
(a) In a right triangle with legs a and b and hypoteneuse c,

a²+b² = c² (b) If a triangle has sides a, b, and c, and a²+b² = c² then the triangle is a right triangle with hypoteneuse c.

Here are several proofs of the Pythagorean Theorem. The first four require a Java-enabled Web browser. If you don't have one, you will see non-interactive pictures in some cases, and blanks in others.

A cut-and-paste proof.
Leonardo da Vinci's proof.
Euclid's proof
A proof based on Euclid's, using shear transformations. (More fun to watch than Euclid's.)
A whole page of proofs (25 of them); most of them are non-interactive.

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