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
Group of rational points on the unit circle Group of rational points on the unit circle In mathematics, the rational points on the unit circle are those points ("x", "y") such that both "x" and "y" are rational numbers ("fractions") and satisfy "x" + "y" = 1. The set of such points turns out to be closely related to primitive Pythagorean triples. Consider a primitive right triangle, that is, with integral side lengths "a", "b", "c", with "c" the hypotenuse, such that the sides have no common factor larger than 1. Then on the unit circle there exists the rational point ("a"/"c", "b"/"c"), which, in the complex plane,