Celebrating Pi Day with Ramanujan

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Tomorrow, 3/14/15, is an especially exciting Pi Day: the date (in American notation) comes two digits closer to representing π’s numerical value than any other year this century will.

It’s common knowledge that this numerical value begins with 3.1415, but mathematicians have been trying for millennia to approximate it ever more precisely.

Of the many π-related formulas that the Indian mathematician and mystic Srinivasa Ramanujan produced, one infinite series—a sum of infinitely many fractions, miraculously adding up to a finite number—is particularly useful:

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Ramanujan’s infinite series gives the digits of π with extreme accuracy, even when just the first few fractions are added together. The very first term alone gives 3.14159273.

Compare this to the first 9 digits of π: 3.14159265.

The Old Testament suggests π equals exactly 3 (one digit accuracy), and the ancient Babylonians used the value 3 1/8 = 3.125. The Egyptians used the value 256/81, which is about 3.16, for π (both the Egyptians and Babylonians were accurate to two digits, i.e., 3.1). The Greek mathematician Archimedes was the first to find that π is about 3.14 (three digits accuracy), using a technique called the Method of Exhaustion, which was a precursor to calculus.

In the late 1980s, the brothers David and Gregory Chudnovsky tweaked Ramanujan’s formula to find the best algorithm ever for calculating the digits of π. They used their formula to calculate π to 2 billion decimal places, using a crazy supercomputer they built in their New York apartment, and broke the world record at the time. The current record, held by Alexander J. Yee and Shigeru Kondo, calculates π to over 12 trillion decimal places, but it still uses the Chudnovsky algorithm.

— Robert Schneider with Ben Phelan. Read more about Ramanujan’s extraordinary life and work in “Encounter with the Infinite.”