Simple numerical methods for calculating the digits of $\pi$ Are there any simple methods for calculating the digits of $\pi$? Computers are able to calculate billions of digits, so there must be an algorithm for computing them. Is there a simple algorithm that can be computed by hand in order to compute the first few digits?

Check out the wiki page on approximations to pi, http://en.wikipedia.org/wiki/Numerical_approximations_of_%CF%80#20th_century
I really love Ramanujan's method, which I recall converges extremely rapidly.
