History of mathematical notation back to any school or period before that of the Ionian Greeks, but the subsequent history may be divided into periods, the distinctions between which are tolerably well marked. Greek mathematics, which originated with the study of geometry, tended from its commencement to be deductive and scientific. Since the fourth century AD, Pythagoras has commonly been given credit for discovering the Pythagorean theorem, a theorem in geometry that states that in a right-angled triangle the area of the square on the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares of
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+),