Archimedes knew that he had not found the value of π but only an approximation within those limits. Since the actual area of the circle lies between the areas of the inscribed and circumscribed polygons, the areas of the polygons gave upper and lower bounds for the area of the circle. ![]() Archimedes approximated the area of a circle by using the Pythagorean Theorem to find the areas of two regular polygons: the polygon inscribed within the circle and the polygon within which the circle was circumscribed. The first calculation of π was done by Archimedes of Syracuse (287–212 BC), one of the greatest mathematicians of the ancient world. The Egyptians calculated the area of a circle by a formula that gave the approximate value of 3.1605 for π. The Rhind Papyrus (ca.1650 BC) gives us insight into the mathematics of ancient Egypt. 1900–1680 BC) indicates a value of 3.125 for π, which is a closer approximation. The ancient Babylonians calculated the area of a circle by taking 3 times the square of its radius, which gave a value of pi = 3.
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