Education Technology

# Activities

• ##### Subject Area

• Standard: National Curriculum 7-10: Statistics and Probability: Chance

Middle

30 Minutes

• ##### Device
• TI-Nspire™ CX
• TI-Nspire™ CX CAS
• TI-Nspire™ Apps for iPad®
• ##### Software

TI-Nspire™
TI-Nspire™ CAS

4.3

## Buffon’s Needle

#### 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.

• 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.