Pythagorean theorem

The Pythagorean theorem states that, for a right triangles with side lengths a,ba, b and hypotenuse cc:

a2+b2=c2.a^2 + b^2 = c^2.

There are many proofs, but my favourite for its geometric simplicity is the following proof by rearrangement.

A proof by rearrangement of the Pythagorean theorem

Depending on where you put four copies of the right triangle in a square with side length a+ba+b, the remainder can either form a square of area c2c^2 or two squares with respective areas a2a^2 and b2b^2.