Estimation of the value of $π$ using Monte Carlo method and related study of errors. (English)

Math. Sch. (Leicester) 42, No. 5, 21-23 (2013).

From the text: The number it holds a special interest in the history as well as in the current use of mathematics and science. This constant, is a number whose value is close to 3.14. It is defined mathematically as “the ratio of the circumference of a circle to the diameter of a circle". $π$ has numerous applications in mathematics as well as in science and technology. However, it is an irrational number, i.e. it cannot be expressed in the form $\frac{p}{q}$, where $p$ and $q$ are co-prime integers and $q\ne 0$. Because it is irrational, no exact value of $n$ can been found. Only estimates of $n$ have been put up. There are several methods to get an approximate value of $π$. One of them, discussed in this article, is by making use of the Monte Carlo method. This article describes a simulation method using the probability that a point chosen at random inside a square lies inside the inscribed circle.