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
Origins and architecture of the Taj Mahal organisational ones. The smaller grids were also used to establish elevational proportion throughout the complex. Koch and Barraud explain such apparently peculiar numbers as making more sense when seen as part of Mughal geometric understanding. Octagons and triangles, which feature extensively in the Taj, have particular properties in terms of the relationships of their sides. A right-angled triangle with two sides of 12 will have a hypotenuse of approximately 17 (16.97+); similarly if it has two sides of 17 its hypotenuse will be approximately 24 (24.04+). An octagon with a width of 17 will have sides of approximately 7 (7.04+),