Education Technology

Buffon’s Needle Extension

Published on 10/20/2016

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? Simulating the event provides an approximate solution. Taking lots of samples produces a sampling distribution and solving analytically produces a lovely result through calculus.

Objectives

  • Simulate events to produce an approximate solution
  • Collect multiple samples to produce a sampling distribution (optional)
  • Use analytic means to provide a solution using integral calculus

Vocabulary

  • Integral
  • Proportion
  • Probability
  • Variation (variance)
  • Integration (integral)

About the Lesson

Students start by estimating the probability to Buffon’s Needle problem using a digital simulation. 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 activity then includes a dynamic representation of the needle and boards integrated with a corresponding graph to help students arrive and understand the analytic solution.
Schools using a TI-Navigator system can also use this activity to help students understand sampling distributions. As a bonus feature, schools without a Navigator system can use the extra program on page 4.1 to generate multiple samples and the corresponding sampling distributions. This is a brilliant way of showing students how the standard deviation changes with increased sample size.