Pythagoras is most famous for his concept of geometry. It is believed that he was first to establish that the sum of the angles of a triangle is equal to two right angles and that for a right-angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides.
Although the last mentioned theorem was already discovered by the Babylonians, Pythagoras was first to prove it. It is also believed that he devised the tetractys, the triangular figure of four rows which add up to ten, which according him, was the perfect number.