Pi Day: One Irrational Number

[David Lockmiller]

New York Times
By Steven Strogatz
March 14, 2019

Pi, as we all learned in school (and are reminded every March 14, on Pi Day), is defined as the ratio of a circle’s circumference to its diameter. Denoted by the Greek letter π, this curious little number is approximately 3.14, although computers have calculated it out past 22 trillion digits and counting: 3.141592653589793238462643383279502…, a sequence never repeating, never betraying any pattern, going on forever, infinity on a platter.

It was the Greek geometer Archimedes, some 2,300 years ago, who first showed how to rigorously estimate the value of pi. Among mathematicians of his time, the concept of infinity was taboo; Aristotle had tried to banish it for being too paradoxical and logically treacherous. In Archimedes’s hands, however, infinity became a mathematical workhorse.

imagine measuring the distance around a circular track near your house. To obtain an estimate, you could walk one lap and then consult a pedometer app on your phone to see how far you traveled. A pedometer computes the distance straightforwardly: It estimates the length of your stride based on your height (which you typed into the app), and it counts how many steps you’ve taken. Then it multiplies stride length times the number of steps to calculate how far you walked.

Archimedes used a similar method to estimate the circumference of a circle, and so to estimate pi. . . . In taming infinity, Archimedes paved the way for the invention of calculus 2,000 years later.