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.
In taming infinity, Archimedes paved the way for the invention of calculus 2,000 years later. And calculus, in turn, helped make the world modern. Archimedes’s mathematical strategy is used in computer-generated movies, approximating Shrek’s smooth belly and trumpet-like ears with millions of tiny polygons. The smooth glide of an Ella Fitzgerald song is digitally represented in streaming audio by an enormous number of bits.
In every field of human endeavor, from reconstructive facial surgery to the simulation of air flowing past a jet’s wing, billions of tiny, discrete elements stand in for an inherently smooth and analog reality. It all began with the computation of pi. Pi represents a mathematical limit: an aspiration toward the perfect curve, steady progress toward the unreachable star. It exists, clear as night, with no end in sight.
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