Overview

During the Renaissance, mathematicians continued their centuries-old fascination with π. As part of this, they calculated π to ever-greater precision while developing new formulae to add digits more quickly. Part of this fascination with π was the equally old quest to "square the circle," and part was simply human curiosity. In spite of their lack of success in quadrature (the term for squaring the circle), these efforts did yield greater insights into the nature of π, some aspects of geometry, and other areas of mathematics.

Background

The ancient Egyptians and Babylonians may have been the first to notice that the ratio of a circle's circumference to its diameter was not an even number. By about 2000 B.C., in fact, the Egyptians had determined this ratio was about 31/8, while the Babylonians put it at about 4 × (8/9)². These come out...