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?
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?
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.
This page on the chronology of pi contains many useful notes on how the pre-computer era calculations of $\pi$ were performed.
See also Pi: A Source Book.
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