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!
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.