Eighteenth-Century Advances in Understanding π | Research & Encyclopedia Articles

Eighteenth-Century Advances in Understanding π

Overview

Mankind has been fascinated with π for millennia and attempts to calculate it exactly have taken place for nearly as long as mathematics has existed. In the eighteenth century, rapid advances in mathematics led to a deeper understanding of numbers in general and of π in specific. This enhanced understanding captured the public's attention, discouraged those trying to solve the ancient problem of "squaring the circle," and helped to advance mathematics enormously.

Background

Earlier than 2000 B.C. Babylonian and Egyptian mathematicians realized that the relationship between a circle's diameter and its circumference (which is what π is) was unchanging, regardless of the circle's size. They also quickly realized that this number fell somewhere between the values of 3 1/7 and 3 1/8, values that were to crop up repeatedly for the next three millennia.

One of the first formal mathematical attempts to calculate a value for π was conducted by Archimedes (287-212 B.C.) in the third century B.C. in his attempt to square the circle (described later in this essay). Archimedes realized that he could draw a polygon on the outside of a circle with the center of each side just touching the outer edge of the circle as it was drawn.

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