monte-carlo-method.nb

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Monte Carlo Methods are a technique for numerical integration. In the 2D \
case, given a region of interest, the technique consists of drawing a \
bounding box around the region and then randomly generating points uniformly \
at random within this box. The proportion of points inside the region of \
interest should approximate the proportion of the bounding box\
\[CloseCurlyQuote]s area taken up by the region, and since the box has a \
known area, we can multiply the proportion by that area to obtain an \
approximation of the region\[CloseCurlyQuote]s area. As the number of sample \
points increases, by the Law of Large Numbers, the approximation should \
approach the true area, although any given realization may vary.\
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