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Buffon's Needle - 9/30

Another way of estimating $\pi$: Buffon's needle
The probability of a needle of length L overlapping a crack, if the cracks are distant by D was shown in class to be:

\begin{displaymath}\frac{2L}{\pi D}\end{displaymath}

Now if we do simulation experiments to find $\pi$ by this method, we should drop needles a large number of times and count the number of hits overlapping a crack, this proportion estimates the above probability.

Try it out on any of these sites: Buffon1 Buffon2 Buffon3 Buffon4 Buffon5

A favorite: http://www.mste.uiuc.edu/ictm/ictm96.html

Some of these sites take the length of the needle to be equal to the distance between the cracks, this gives a simplified expression for $\pi$

\begin{displaymath}\hat{\pi}=2\frac{\char93 Trials}{\char93 hits}\end{displaymath}



Susan Holmes
1998-12-07