Monte Carlo Integration - This Really Works

It is of course not necessary to use Monte Carlo techniques to find the area of our figure. As all the borders are described by an analytic function it is simple enough to find its area by standard integration using a piece of paper, a pocket calculator or something like Maple. When using Maple, we found,

area=0.4678097245

covering approximately 47% of the total area.
To compare this result to the one we get from our parallel Monte Carlo program, we ran the parallel program several times increasing the number of points we checked from only five hundred thousand per quadrant to twenty-five million points per quadrant and plotted the results.

As it is typical for Monte Carlo methods the results oscillates around the real value but you can also see that the amplitude of this oscillation decreases.

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