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# Buffon's Needle: a simple Monte Carlo Method for the Estimation of the Value of Pi

Buffons Needle refers to a simple Monte Carlo method for the estimation of the value of pi 314159265 The idea is very simple Suppose you have a tabletopwith a number of parallel lines drawn on it which are equally spaced say the spacing is 1 inch for example Suppose you also have a pin or needle which is also aninch long If you drop the needle on the table you will find that one of two things happens 1 The needle crosses or touches one of the lines or 2 the needlecrosses no lines The idea now is to keep dropping this needle over and over on the table and to record the statistics Namely we want to keep track of both thetotal number of times that the needle is randomly dropped on the table call this N and the number of times that it crosses a line call this C If you keep droppingthe needle eventually you will find that the number 2NC approaches the value of pi Why does this work It is not hard to show with a little bit of calculus that the probability on any given drop of the needle that it should cross a line is given by 2piAfter many trials the value of CN the number of crossing needles divided by the total number of needles will approach the value of the probability Bibliographyhttpwwwangelfirecomwahurbenbuffhtml

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