Classical Approximations of Pi

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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.

Contributed by: Rob Morris (March 2011)
Open content licensed under CC BY-NC-SA



Here are the various methods used in this Demonstration:

Vieta's formula:

Wallis's product:

Gregory series:

Euler's series:

Euler's series variant:

Machin's arc tangent formula:

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