Buffon's Needle

One of the oldest problems in the field of geometrical probability, Buffon's Needle is an intriguing problem relating the theory of probability to the number pi. The problem involves randomly dropping a needle on a grid of parallel lines and determining the probability of the needle crossing one of the lines.

If the needle is of length L and the lines are a distance D apart, then we get the remarkable result that the probablity of crossing a line is P = 2*L/D*pi.

This suggests a method for estimating pi by dropping a needle repeatedly and counting how many times it intersects a line. If R is the number of times the needle intersected a line and N is the total number of trials, then we can estimate the probablity that the needle intersects a line by P = R/N.

Thus we can estimate pi by pi = 2L*N/R*D.

If you should have any comments or questions, please send email to angelx@alum.mit.edu.

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