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You can think of the number of points inside the circle as directly related to the area of that circle.

In this article you are going to use one in particular, which makes the algebra a little less cumbersome. # Relation between areas and number of pointsĪs stated in the introduction, the idea is to relate areas and number of points. Here is a short list of topics you need to know for a better understanding of this article, along with a link with more information. Solving for will bring an equation where the only variables will be the number of points randomly generated.īefore continuing with this reading, you need to have some basic knowledge of Mathematics and Python. The idea is to relate the area of the square and the area of the circle with the number of points inside and outside the circle.Īfter some simple algebra you can obtain an equation from such a relation, and will be one of the parameters involving that equation. Calculating Pi using a Monte Carlo simulation.*Īnd where is the value of $\pi$ coming from? You know the area of the circle is $\pi\cdot R^2$.

The basic idea is to randomly generate a set of points on a square, and count how many of them lies inside the circle which is inscribed in the square, and how many of them lies outside of it. Have you ever wondered how the value of $\pi$ can be obtained? There are several methods to do this, and in this article you are going to learn one way of estimating the value of using a Monte Carlo Simulation in Python.