Published on 10/16/2016

#### Activity Overview

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?

#### Objectives

**ACMSP226**– Calculate relative frequencies from given or collected data to estimate probabilities of events.

#### Vocabulary

- Probability
- Trial
- Estimate
- Reciprocal

#### 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.