Classical Approximations of Pi
Since the discovery of in antiquity, people have been fascinated with calculating its numerical value. Various infinite sums or products have been developed over the years. The success of such a method is determined by how fast it approaches its goal. This Demonstration compares several classical approximations for and their rates of convergence.
Here are the various methods used in this Demonstration:
Euler's series variant:
Machin's arc tangent formula: