Grad Student Colloquium

Friday, March 4, 2022 4:00 pm - 4:00 pm EST (GMT -05:00)

Nicole Kitt, Pure Math Department, University of Waterloo

"Buffon's Needle Problem"

 In 1777, Georges Louis Leclerc de Buffon posed the following problem: If one were to drop a needle on ruled paper with equally spaced lines, what is the probability that the needle lands in a position where it crosses at least one of the lines? This answer will of course depend on many things, such as the length of the needle, the distance between two successive lines, etc. In the case that the length of the needle is at most the distance between two successive lines on the paper, Buffon found an elegant answer to this problem which happens to involve $\pi$. This is neat because it means that one can perform an experiment, dropping a bunch of needles onto ruled paper, to get an approximate value for $\pi$. In this talk, we will discuss Buffon's problem in more detail, provide some interesting history, and sketch a proof for the specific case mentioned above.  

Location: Online