Ramanujan’s Formula for Pi
First found by Ramanujan. It’s my favourite formula for pi. I have no idea how it works.
A Ramanujan-type formula due to the Chudnovsky brothers used to break a world record for computing the most digits of pi:
For implementations, it may help to use \(640320^3 = 8\cdot 100100025\cdot 327843840\)