Here is a more efficient way of computing pi; there are a bunch more!

ETA: Here’s what you do if you only have a six-digit approximation for e and want pi. Add up 1/(e – 1) + 2/(e^2 – 1) + 3/(e^3 – 1) + … for about ten terms, add 11/24, multiply by 6 and take the square root. Voila! 3.14. That’s good enough.