Did you ever wonder how people find the decimal expansion of it to a large number of places? One method depends on the following identity?
( = 16 tan-1 (1/5) - 4 tan-1 (1/239)
Find the first 6 digits of ( using this identity and the series for tan-1 x. (You will need terms through x9 / 9 for tan-1(1/5), but only the first term for tan-1(1/239).) In 1706, John Machin used this method to calculate the first 100 digits of (, while in 1973, Jean Guilloud and Martine Bouyer found the first 1 million digits using the related identity
( = 48tan-1(1/18) + 32tan-1 (1/57) - 20tan-1 (1/239)
In 1983, it was calculated to over 16 million digits by a somewhat different method. Of course, computers were used in these recent calculations?