Computing π to "infinite" binary precision in C#

Answer 1

Wikipedia details a lot of ways to get numerical approximations of pi here. They also give some sample pseudo-code

Edit : If you're interested in this kind of mathematical problems without having any related real-world problem to solve (which is definitely a good attitude to have, IMHO), you could visit the Euler Project page

Answer 2

There exists such possibility to process big rational numbers in DLR-based dynamic languages (e.g. IronPython). Or you can use any portable C/C++ implementation of big real numbers through P/Invoke.

Answer 3

By far my favorite Haskell spigot for pi comes from Jeremy Gibbons:

pi = g(1,0,1,1,3,3) where
    g(q,r,t,k,n,l) = 
        if 4*q+r-t<n*t
        then n : g(10*q,10*(r-n*t),t,k,div(10*(3*q+r))t-10*n,l)
        else g(q*k,(2*q+r)*l,t*l,k+1,div(q*(7*k+2)+r*l)(t*l),l+2)

The mathematical background that justifies that implementation can be found in:

A Spigot Algorithm for the Digits of Pi