Depending on how many toothpicks you tossed, your approximation of pi may or may not be impressively close. But if you had the patience to toss toothpicks all day—or all week—and then averaged your results, you’d get an increasingly accurate estimate.
This surprising method of calculating pi, known as Buffon’s Needle, was first discovered in the late 18th century by French naturalist Georges-Louis Leclerc, Comte de Buffon. Count Buffon was inspired by a then-popular game of chance that involved tossing a coin onto a tiled floor and betting on whether it would land entirely within one of the tiles.
The method can work on any lined surface (hardwood floors are handy) as long as the separation between the lines is greater than the length of the object thrown. A general expression of the approximation is below (click to enlarge):
In this Snack, we made the distance between the lines two times the length of a toothpick so we could just divide the total number of toothpicks tossed by the number that touched a line.
The proof of why this works involves a bit of meaty math, and makes a delightful diversion for those so inclined (see the Math Root below). In general, this experiment in geometric probability is an example of a Monte Carlo method, in which a random sampling of a system yields an approximate solution.