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© 1999-2010 by Francis Edward Su

From the Fun Fact files, here is a Fun Fact at the Easy level:

# Buffon Needle Problem

 Figure 1

A plane is ruled with parallel lines 1 cm apart. A needle of length 1 cm is dropped randomly on the plane. What is the probability that the needle will be lying across one of the lines?

This gives an interesting way to calculate Pi! If you throw down a large number of needles, the fraction of needles which lie across a line will get closer to 2/Pi the more needles that you throw. So, you can just throw down needles and count them to get an estimate for Pi!

Presentation Suggestions:
Draw a picture and a few "random" needles. As a challenge, ask students to prove this formula using calculus, and assuming that needle centers and needle angles are uniformly distributed.

The Math Behind the Fact:
This method of calculating Pi is very slow. There are faster formulas, see pi formula. However, the idea of using a probabilistic means to get answers like this is very powerful, and is the basis of something called the Monte Carlo method in probability theory.

Su, Francis E., et al. "Buffon Needle Problem." Math Fun Facts. <http://www.math.hmc.edu/funfacts>.

Keywords:    pi formula, probability
Subjects:    probability
Level:    Easy
Fun Fact suggested by:   Francis Su
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