Suppose you drop your pen onto a wooden floor. If the pen is the same length as the boards are wide, what is the probability that the pen will lie across a join? This problem may seem somewhat obscure but the answer is sure to surprise. Another interesting question, why is it called Buffon’s needle?
- ACMSP226 – Calculate relative frequencies from given or collected data to estimate probabilities of events.
About the Lesson
Unlike many probability questions at this level, the theoretical result is not obvious. Students start by estimating the probability to Buffon’s Needle problem. This estimation creates a level of ‘buy-in’ to the actual result. An animation on the calculator is used to generate a relatively small number of trials. A program is then used to simulate 1000’s of results, combining class aggregates produces 10,000’s of results. The aggregated result is approximately equal to 2 / pi. The lesson provides an opportunity to discuss trigonometry, sampling distributions, calculus and some lovely mathematics history.
George-Louis Leclerc was a French naturalist, mathematician and cosmologist. He was born into wealth. His Father Benjamin Leclerc purchased an estate containing a nearby village called Buffon. After his father sold the estate, George repurchased it and called himself Comte De Buffon [Translated “The Count of Buffon”] Leclerc’s work included introducing differential and integral calculus to probability theory of which Buffon’s Needle problem is a lovely example.