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Pi, the Infinite Doorway to Calculus

Happy Pi Day! In celebration of this gloriously nerdy event, mathematician Steven Strogatz wrote about how pi was humanity’s first glimpse of the power of calculus and an early effort to come to grips with the idea of infinity.

As a ratio, pi has been around since Babylonian times, but 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.

He used it to discover the area of a circle, the volume of a sphere and many other properties of curved shapes that had stumped the finest mathematicians before him. In each case, he approximated a curved shape by using a large number of tiny straight lines or flat polygons. The resulting approximations were gemlike, faceted objects that yielded fantastic insights into the original shapes, especially when he imagined using infinitely many, infinitesimally small facets in the process.

Here’s a video that runs through Archimedes’ method for calculating pi:

Strogatz’s piece is an excerpt from his forthcoming book, Infinite Powers: How Calculus Reveals the Secrets of the Universe.