Buffon’s Leaf Problem
Ruka Iguchi, Hideaki Kida, Keisuke Matsuda, Miki Ono, Miu Shibata, Haruka Takano · Mathematics Magazine · 2023
SummaryAccording to Buffon’s needle problem, you can approximate the value of π by throwing needles onto arrays of parallel lines and counting the number of needles crossing the lines. However, it is time-consuming to do the experiment in reality (in 1901, Lazzarini threw 3408 needles to approximate the value of π). In this paper, we tried to approximate the value of π from easily-accesible images of fallen leaves. We extended Buffon’s needle problem in two ways: instead of a simple needle we considered a complex shape, and instead of a uniform size we considered various sizes. After we confirmed the extension by a computer simulation, we approximated the value of π from the images we took experimentally and we while walking. From the experimentally-taken images (50 leaves/image × 20 images), the value of π was approximated as 3.1569. The approximated value of π using the images we took while walking was 3.5961 (the accuracy was not good because it was calculated from one image).