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I know that there was a guy that could get 100 decimal digits of $\pi$ before computers were able to get thousands.

How did the guy do that?

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  • $\begingroup$ At least two ways: Machin's formulae or the arithmetic-geometric mean. See this. $\endgroup$ – J. M. is a poor mathematician Dec 1 '10 at 12:45
  • $\begingroup$ Sorry.. duplicated :( $\endgroup$ – Diego Dec 1 '10 at 12:47
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According to Wikipedia, John Machin combined the formula $$\frac{\pi}{4}=4\cot^{-1}5-\cot^{-1}239$$ with the Taylor series expansion for the inverse tangent in order to compute $\pi$ to 100 decimal places.

A previous record was due to Abraham Sharp who used an arcsine series to find 72 decimal digits.

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This page on the chronology of pi contains many useful notes on how the pre-computer era calculations of $\pi$ were performed.

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See also Pi: A Source Book.

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Check this, you can find n-th PI digit without computing previous ones :) It was a big surprise when this formula was discovered.

http://en.wikipedia.org/wiki/Bailey%E2%80%93Borwein%E2%80%93Plouffe_formula

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