For this pi day (14th March 2021), I’m going to approximate pi by simulating Buffon’s needle. This is a problem proposed by Georges-Louis Leclerc, Comte de Buffon which involves the probability of a dropped needle overlapping one of a series of parallel lines.

The solution to this turns out to involve pi. Specifically, if the lines are a needle’s length apart, the probability of a needle intersecting one of them is 2/pi. Since the probability can be approximated as c/n, where n needles are dropped and c of them intersect a line. Rearranging this gives 2n/c as an estimate of pi.



Total dropped: 0
Number intersecting: 0
Pi: 0