In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c².
The Pythagorean theorem relates the three sides of a right triangle: the legs (a, b) and the hypotenuse (c, opposite the right angle). The theorem works only for right triangles but has countless applications in construction, navigation, engineering, physics, and coordinate geometry.
The theorem was known to Babylonian mathematicians 1000 years before Pythagoras. Named after Pythagoras (570-495 BCE), whose school proved it. There are over 400 known proofs, including one by US President James Garfield.