Formal Book

27 Buffon’s needle problem

Theorem 27.1 Buffon’s needle problem

If a short needle, of length \(\ell \), is dropped on paper that is ruled with equally spaced lines of distance \(d \geq \ell \), then the probability that the needle comes to lie in a position where it crosses one of the lines is exactly

\[ p = \frac{2 \ell }{\pi d}. \]
Proof

TODO