Pi Day: How One Irrational Number Made Us Modern

The famous mathematical ratio, estimated to more than 22 trillion digits (and counting), is the perfect symbol for our species’ long effort to tame infinity.

Adapted from “Infinite Powers: How Calculus Reveals the Secrets of the Universe,” which will be published on April 2 by Houghton Mifflin Harcourt.

When my children were young, they liked to stare at a pie plate hanging in our kitchen, with the digits of pi running around the rim and spiraling in toward the center, shrinking in size as the numbers swirled into the abyss.

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.

For some people, Pi Day is an occasion to marvel at circles, long revered as symbols of perfection, reincarnation and the cycles of nature. But it is the domestication of infinity that we really should be celebrating. Mathematically, pi is less a child of geometry than an early ancestor of calculus, the branch of mathematics, devised in the 17th century, that deals with anything that curves, moves or changes continuously.

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