Pythagoreanism to have survived as part of, or deeply influenced, the Bacchic cults and Orphism. Pythagoras was already in ancient times well known for the mathematical achievement of the Pythagorean theorem. Although the Babylonians had used this formula for centuries, Pythagoras had discovered that "in a right-angled triangle the square of the hypotenuse is equal to the squares of the other two sides". In ancient times Pythagoras was also noted for his discovery that music had mathematical foundations. Antique sources that credit Pythagoras as the philosopher who first discovered music intervals also credit him as the inventor of the monochord, a
Pythagorean theorem used as a triangle "C" on its hypotenuse, and two similar right triangles ("A" and "B" ) constructed on the other two sides, formed by dividing the central triangle by its altitude. The sum of the areas of the two smaller triangles therefore is that of the third, thus "A" + "B" = "C" and reversing the above logic leads to the Pythagorean theorem a + b = c. ("See also Einstein's proof by dissection without rearrangement") The Pythagorean theorem is a special case of the more general theorem relating the lengths of sides in any triangle, the law of