In 1777 Buffon realised you can measure π by dropping needles on floorboards. Watch the probability of a needle crossing a line converge on 2/π — π again, this time from pure geometry and chance.
A needle of length L dropped on lines spaced L apart crosses a line with probability 2/π ≈ 0.637. So count the crossings: π ≈ 2 × needles ÷ crossings. The connection comes from averaging over every possible angle — the needle's projected height is L·sinθ, and the average of sin over all angles drags π out of the shadows.