But Ramanujan’s series — bizarre and arbitrary as they might appear — had an important feature: they took far fewer terms to compute π to a given accuracy. In 1977, Bill Gosper — himself a rather Ramanujan-like figure, whom I’ve had the pleasure of knowing for more than 35 years — took the last of Ramanujan’s series from the list above, and used it to compute a record number of digits of π. There soon followed other computations, all based directly on Ramanujan’s idea — as is the method we use for computing π in Mathematica and the Wolfram Language.
Who Was Ramanujan?
Stephen Wolfram
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Mathematical efficiency at work. And when it leads to accuracy — so much the better!