Buffon-Laplace Needle Problem

$\begin{figure}\begin{center}\BoxedEPSF{BuffonLaplaceNeedle.epsf scaled 700}\end{center}\end{figure}$

Find the probability $P(\ell,a,b)$ that a needle of length $\ell$ will land on a line, given a floor with a grid of equally spaced Parallel Lines distances and apart, with $\ell>a,b$ .

$\begin{displaymath} P(\ell,a,b)={2\ell(a+b)-\ell^2\over\pi a b}. \end{displaymath}$

See also Buffon's Needle Problem