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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 $a$ and $b$ apart, with $\ell>a,b$.

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

See also Buffon's Needle Problem

© 1996-9 Eric W. Weisstein