The GregoryLeibniz series is another method for approximating pi from "summary" of A History of [pi] (pi) by Petr Beckmann
Another method for approximating pi is the Gregory-Leibniz series. This series involves summing an infinite number of terms, with each term becoming smaller and smaller as the series progresses. The formula for the Gregory-Leibniz series is 4/1 - 4/3 + 4/5 - 4/7 + 4/9 -... and so on. By adding up more and more terms, one can get closer and closer to the value of pi. The Gregory-Leibniz series is a straightforward way to estimate pi, but it converges very slowly. This means that it takes a large number of terms to get an accurate approximation of pi. For example, to get just two decimal places of precision using the Gregory-Leibniz series...
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