Pi approximation using the Monte Carlo method
A Monte Carlo method relies on repeated random sampling to simulate some process or compute a value. See Wikipedia: http://en.wikipedia.org/wiki/Monte_Carlo_method
Pi can be computed using Monte Carlo simulation through a series of experiments. Here is a single experiment:
- Choose a pair of random floating point numbers between 0 and 1
- Call the numbers x and y, think of (x,y) as a point on the plane in the unit square
- Test whether the point falls within the unit circle by measuring the distance from the point to the origin:
Now suppose you do m experiments and in n of those experiments, the random point chosen falls within the upper right quarter of the unit circle. Since the area of a circle is known to be pi * r^2 and the area of a square is r^2 (and here we are dealing with a radius/square side of length 1), the following equations hold:
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