Monte-Carlo Pi

[ttw]

(01-11-2022 02:12 PM)KeithB Wrote:  It might have been mine, which I learned at Cal Tech in the seventies at a Programming for High Schoolers program they had.

1. Generate 2 uniform random numbers between 0 and 1.
2. calculate the square root of sum of the squares. This represents the distance from the origin.
3. If the sum is <= 1 you have a hit - the point is inside the unit circle
4 calculate the ratio of the number of hits / the number of total pairs
5 multiply by 4 to get Pi.

It is cool to graph the hits and see the circle gradually fill up.

Note: I see Andres beat me to it, but I had to name drop Cal Tech.

A big speedup is possible through skipping the square root.

Another trick is to run batches of size 113.