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In: Mathematics
For reference, Monte Carlo is famous for a casino. In mathematics, a Monte Carlo simulation is just a probabilistic method for finding a solution, especially useful when an exact or traditional approximate method would be computationally expensive.
One simple example: let’s say you want to find the area of a circle of radius 1. You can pick two random numbers between -1 and 1, and let those be x-y coordinates. Do this thousands or millions of times (or even more), and see what proportion of those fall inside the circle (i.e. satisfy `x^2+y^2<1`). Multiply that by the area of the square with sides going from -1 to 1 (area is 4), and there’s a Monte Carlo simulation for the area of the circle.
Of course, circles are easy, but this can be done with more complex shapes, with more complex types of problems (such as weather forecasting from certain models).
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