# Monte Carlo Method

**Monte Carlo Method** are algorithms that rely on repeated random sampling. It was named by Stanislaw Ulam while he was working on nuclear weapons projects at the Los Alamos National Laboratory, after the Monte Carlo Casino, where his grandfather often gambled.

Monte Carlo methods are frequently used in mathematical or physics problems. They are typically utilized in optimization problems, numerical integration, and drawing from a distribution of probabilities. In physics, Monte Carlo methods are useful for simulating fluid dynamics and cellular structures. In economics, Monte Carlo methods can be used to simulate uncertainty and risk in business ventures.

A simple example of using a Monte Carlo method would be to draw a unit square and a unit circle inside it, and then scatter coins on the square in a uniformly random manner. By calculating the ratio of coins that fall inside the circle to those that fall outside of it (assuming all coins fell within the unit square), one could approximate the area of the circle. The more coins thrown, the closer the approximation would come to the actual area, which for the unit circle is pi.