\(\pi\) is a mathematical constant defined as the ratio of the circumference of a circle to its diameter. There are many other definitions including the ratio of the area of a circle to the square of its radius. It is a constant that also appears in many formulae used in mathematics, physics and engineering.
\(\pi\) is an irrational number. It cannot be expressed as a ratio of two whole numbers $a/b$. Throughout history ingenious ways have been devised to calculate this constant with increasing accuracy. In this article I’ll describe three methods to determine a decimal representation of \(\pi\) (3.14159…):
- The Monte Carlo method where we use a statistical approach to estimate the area of a circle
- The Leibniz formula for \(\pi\) consisting of the evaluation of a simple series
- Machin’s formula for \(\pi\). A more advanced method using a trigonometric relationship