How dropping needles on a floor reveals the number π: Buffon's needle

Toss a match onto a plank floor and ask: does it touch a crack? Do it thousands of times and the fraction that do will quietly spell out π, though no circle is anywhere in sight.

Georges-Louis Leclerc, Comte de Buffon, posed the puzzle in 1733. Drop needles below, tune their length, and watch chance itself home in on the most famous number in maths.