Buffon's Needle Experiment (UMAP)

A unit applying calculus to Buffon's needle experiment. With completion of this module students will: 1) understand the meaning of the statement The probability of an event is x.; 2) know and be able to replicate the Buffon needle experiment for approximating pi; 3) approximate the probability underlying the Buffon needle experiment by an appropriate Riemann sum; 4) express the limit of this Riemann sum as a definite integral, and evaluate this integral.

Table of Contents:

1. INTRODUCTION
1.1 The Experiment
1.2 A Sample Run

2. PROBABILITY
2.1 Equally Likely Events
2.2 In the Long Run
2.3 Compound Events

3. THE THEORETICAL RESULT OF THE EXPERIMENT
3.1 Statement of the Result
3.2 Application of the Result

4. PROOF OF THE RESULT
4.1 Locating the Needle Numerically
4.2 Equally Likely Positions
4.3 A Finite Approximation
4.4 Counting Successes in the Finite Case
4.5 Approximating the Count
4.6 Taking the Limit

5. VARYING THE NEEDLE LENGTH

6. GETTING THE COMPUTER TO HELP