Suppose we have a lined piece of paper, with lines being d mm from each other. Suppose we also have a needle of length t mm. Given that the needle is shorter than the line spacing, what is the probability that a needle lands on a line when dropped randomly?
The answer may come as a surprise, but the probability is actually 2t/(dπ)
Now where does this come from? And how exactly can we use this method of throwing needles onto a piece of paper to estimate π?
First, we start off with showing how this probability is obtained. If this is not something the reader is interested in, they may skip ahead to the method of estimating π.