What is the best formula to calculate pi?

Answer

Dear Clara,

There are many ways to calculate Pi.

On the webpage APPROACHES TO THE NUMBER PI THROUGH THE HISTORY OF MATHEMATICS you will find a nice overview of some possibilities that have been historically devised by mathematicians.

The approximation through regular polygons with increasing number of sides is perhaps the most comprehensible approach, but it certainly won’t give you the “best” formula for calculating Pi, because it takes too long to find a sufficient number of digits of Pi. This is called convergence rate in mathematics.

At the time I found it fascinating to note that you can quickly calculate a good approximation for Pi numerically using the definite integral of the function 4/(1+x²) between 0 and 1. Which then returns 4×ArcTan[1]=Pi

As soon as you have learned something about numerical integration – which is probably not the case given your age – you can test it yourself.

Philippe J. Roussel
imec