Buffon's Needle Problem

Buffon's Needle Problem is a famous problem in mathematics. The problem is: What is the probability that a randomly dropped needle will cross one of the horizontal lines. An illustration of the problem is shown below.

We can estimate the value of pi during this proces. A paper and a program in R has been written. You can read more in details in this paper. The approximation is slow. If we drop a needle every second to compute the first 9 digits of pi, it would take about 32 billion years. That's more than the age of the Universe which is 13.7 billion years.

Simulation with 300 drops.
Another simulation with 36000 drops.