The Measurement of π

One of the important mathematical themes that runs throughout Dunham's book is the measurement of the ratio π. He documents a passage in the Bible that indicates that it has long been known that a circle's diameter is roughly one-third its circumference. He charts the ever-increasing accuracy of the estimation of the number, using it as a kind of measuring stick to gauge how advanced the state of mathematics is at a given point in history. It is also used as a measurement of the ability of an individual scholar.

Archimedes is the first mathematician Dunham describes who reaches an estimate of π to two decimal places of accuracy, although Archimedes did not use a decimal system. Dunham praises Archimedes for having come so close using only the computational tools that were available to him. For centuries afterward, Archimedes' method of measuring the perimeter of multi-sided polygons that...