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?
Answer: 2/Pi.
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.
How to Cite this Page:
Su, Francis E., et al. "Buffon Needle Problem."
Math Fun Facts.
<http://www.math.hmc.edu/funfacts>.
