Buffon’s Leaf Problem

Abstract

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).MSC: 60-01 Notes1 Note that the online version of this article has color diagramsAdditional informationNotes on contributorsRuka IguchiRUKA IGUCHI is a 3rd-year high school student at Hiroshima University High School. She is a runner and has often participated in a marathon.Hideaki KidaHIDEAKI KIDA is a mathematics teacher at Hiroshima University High School. After receiving a Master of Education degree from Hiroshima University, he has been a high school teacher for 22 years.Keisuke MatsudaKEISUKE MATSUDA is a graduate student at Osaka University, studying beetle horn formation using mathematical modeling. He seeks the rules underlying the natural phenomena around us and the shapes of living things.Miki OnoMIKI ONO is a 3rd-year high school student at Hiroshima University High School and a singer who has an attractive voice.Miu ShibataMIU SHIBATA is a 3rd-year high school student at Hiroshima University High School and a violinist who is good at computer programming.Haruka TakanoHARUKA TAKANO is a 3rd-year high school student at Hiroshima University High School and a contrabassist who loves grilled meat and ice cream as much as mathematics.