In mathematics, the **Pythagorean theorem** (in American English) or **Pythagoras' theorem** (in British English) is a relation in Euclidean geometry among the three sides of a right triangle (*right-angled triangle* in British English). It states:

In any right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the two sides that meet at a right angle).

The Pythagorean theorem is named after the Greek mathematician Pythagoras, who by tradition is credited with its discovery and proof,^{ }although it is often argued that knowledge of the theory predates him. (There is much evidence that Babylonian mathematicians understood the principle, if not the mathematical significance.)