[…] The method of exhaustion provides a formula for the area of a circle. However, if you want to approximate π numerically, it is better to use Archimedes's method of inscribed and circumscribed regular polygons. Archimedes formally proved that π is in the range (3 + 10/71, 3+10/70) by using a 96-sided regular n-gon. Notice that the right-hand side of the interval is the familiar quantity 22/7, which is an excellent approximation to π by a low-denominator fraction. …