Pythagoras is the mathematician traditionally associated with the theorem that a right triangle’s sides satisfy a² + b² = c². Here, a and b are the legs of the triangle, while c is the hypotenuse, the side opposite the right angle.
The relationship was known before Pythagoras in several mathematical cultures. Babylonian tablets show knowledge of special right-triangle triples, and Indian and Chinese texts also contain related results. The theorem is named for Pythagoras because Greek tradition connects his school with a proof or formal development, not because he necessarily discovered the underlying relationship first.
The theorem has many proofs, including geometric rearrangements and algebraic demonstrations. It is used in surveying, construction, navigation, physics, and coordinate geometry. A frequent mistake is applying it to any triangle; the equation works directly only for right triangles. The converse is also useful: if a triangle’s side lengths satisfy the equation, the triangle is right-angled.