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lines changed Original file line number Diff line number Diff line change @@ -21,6 +21,7 @@ Change Log / Ray Tracing in One Weekend
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### The Rest of Your Life
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- Fix -- Fix typo of "arbitrary" (#1589 )
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+ - New -- Added a bit more explanation of Buffon's needle problem (#1529 )
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Estimating Pi
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--------------
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The canonical example of a Monte Carlo algorithm is estimating $\pi$, so let's do that. There are
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- many ways to estimate $\pi$, with the Buffon Needle problem being a classic case study. We’ll do a
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- variation inspired by this method. Suppose you have a circle inscribed inside a square:
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+ many ways to estimate $\pi$, with _Buffon's needle problem_ being a classic case study. In Buffon's
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+ needle problem, one is presented with a floor made of parallel strips of floor board, each of the
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+ same width. If a needle is randomly dropped onto the floor, what is the probability that the needle
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+ will lie across two boards? (You can find more information on this problem with a simple Internet
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+ search.)
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+ We’ll do a variation inspired by this method. Suppose you have a circle inscribed inside a square:
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![Figure [circ-square]: Estimating $\pi$ with a circle inside a square
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](../images/fig-3.01-circ-square.jpg)
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One Dimensional Monte Carlo Integration
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====================================================================================================
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- Our Buffon Needle example is a way of calculating $\pi$ by solving for the ratio of the area of the
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- circle and the area of the circumscribed square:
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+ Our variation of Buffon's needle problem is a way of calculating $\pi$ by solving for the ratio of
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+ the area of the circle and the area of the circumscribed square:
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$$ \frac{\operatorname{area}(\mathit{circle})}{\operatorname{area}(\mathit{square})}
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= \frac{\pi}{4}
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