Mathematics · Study 058
Buffon's Needles
Drop needles on a lined floor, count how many cross a line, and pi falls out of the ratio. A live Monte Carlo estimate that sharpens as you watch.
What you're looking at
The lines are spaced exactly one needle length apart. Each needle lands at a random position and angle. Those that cross a line are drawn in orange. For this spacing the chance of crossing is 2 divided by pi, so twice the number dropped divided by the number crossing gives an estimate of pi.
The idea behind it
The Comte de Buffon posed the problem in the 1700s and it became the first famous example of geometric probability. It is a slow way to compute pi: the error shrinks only with the square root of the number of needles, so each extra correct digit costs about a hundred times more drops.
Try this
Watch the estimate wander toward 3.14159. Restart for a fresh floor.
