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
Nonhypotenuse number Nonhypotenuse number In mathematics, a nonhypotenuse number is a natural number whose square "cannot" be written as the sum of two nonzero squares. The name stems from the fact that an edge of length equal to a nonhypotenuse number "cannot" form the hypotenuse of a right angle triangle with integer sides. The numbers 1, 2, 3 and 4 are all nonhypotenuse numbers. The number 5, however, is "not" a nonhypotenuse number as 5 equals 3 + 4. The first fifty nonhypotenuse numbers are: Although nonhypotenuse numbers are common among small integers, they become more-and-more sparse for larger numbers. Yet, there