Buffon's Needle.

Subject

Topic

Imagine a grid of parallel, evenly spaced lines - something like an American football field. A "needle" (a straight line segment) is tossed onto the grid. For a given grid separation and length of the needle, what is the expected number of times that the needle will cross the lines? This is a well-known problem and it's solution is also well known. For example if the needle is exactly as long as the grid width, the expected number of crossings will be 2/Pi.

Reference(s)

1. Schroeder, L., "Buffon's needle problem: An exciting application of many mathematical concepts," Mathematics Teacher, 67 (1974), 183-186.
2. Information from Math Achives by George Reese

Project Idea(s)

1. Do a simulation of the basic experiment, possibly with some graphic display. Use the results to estimate Pi. Don't expect a very good approximation however. This is done (see archive below) - a more detailed analysis of the error between pi and it's estimate could be done however. This would require knowledge of confidence intervals.
2. Generalize toward the Buffon's Noodle problem. Imagine that the needle is a strand of spaghetti and that you've cooked it. What is the expected number of times that the noodle will cross the grid lines.

Prerequisite Mathematics

Required Programming Level

Key Words

Reviewer

Archive

• Dan Jones (Fall 97 at UML) did a good job simulating the Buffon's Needle experiment that had a graphical display. He also discussed how the empirical probablities obtained from several experiments can be combined with the theoretical results to give a crude estimate of pi. jonespr.nb