` M. Gallant 10/17/97 3/14/2022`

The trancendental number

The Greek letter

and combining this identity with the series definition for ATN:

one can easily calculate

The image below shows the standard system-output from a
standalone Java application for
calculating **π** to 500 significant digits (10 seconds
on a 486dx2/66 and 1 second on a Pentium GXPro200;
Using a Dell XPS 15 9510 Intel Core i7-11800H processor with 16GB ram, 5000 digits
of **π** are calculated in about 1 sec).
The user is prompted for the digits of precision to be used in the computation.

References:

- Pi (wiki)
- Pi Day (wiki)
- Pi to 62.8 Trillion Digits
- Squaring The Circle (wiki)
- The Man Who Invented Pi
- D. Shanks and J. Wrench, Mathematics of Computation, 16, 1962 p.76.
- P. Beckmann, "A History of Pi", St. Martin's Press 1971.
- J. Borwein and P. Borwein, "Pi and the AGM", Wiley 1987.
- J. Borwein and P. Borwein, "Ramanuan and Pi", Sci. Am. Feb. 1988 p.112.

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