Some people seem born clumsy – I definitely count myself among them. I often accidentally drop or knock something over. However, if a box full of matches falls on the floor, it can be interesting from a mathematical point of view. Especially if the mishap happens over laminate or wood floorboards. Because of the position of the small wooden sticks you can – who would have thought it? – once again calculate the number pi.
This was first recognized by the French naturalist Georges-Louis Leclerc (1707-1788), whose noble name was Comte de Buffon. He found that the size of pi can be calculated by counting all the matches and dividing by the number of matches that landed on a gap between two floorboards. As usual with such calculations, the more matches, the more accurate the result is, as a rule.
Inspired by a pastime of nobles
Leclerc probably didn’t come across this unexpected connection because he was clumsy and threw down matches. He was probably more inspired by a game that was popular among the nobility at the time: you tossed a coin onto a tile pattern and bet on whether it would land on a joint or not. However, Leclerc gave the wrong formula for square patterns – unlike in the case of matches, which is now known as the Buffon needle problem.
Again, it seems incredible that such a simple method, which at first sight has nothing to do with the geometry of the circle, could result in the irrational number pi. To understand why this is so, let’s assume for simplicity that the floorboards are exactly twice the width of the matchsticks. Of course, the calculation also works for other length ratios, but in the end you have to multiply the result by a corresponding factor that depends on the length ratio to get Pi.