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
Annulus (mathematics) within the annulus, which is the chord tangent to the inner circle, in the accompanying diagram. That can be shown using the Pythagorean theorem since this line is tangent to the smaller circle and perpendicular to its radius at that point, so and are sides of a right-angled triangle with hypotenuse , and the area of the annulus is given by The area can also be obtained via calculus by dividing the annulus up into an infinite number of annuli of infinitesimal width and area and then integrating from to : The area of an annulus sector of angle ,