Calculating π

Inspiration

William Shanks (1812–1882) spent over 20 years of his life calculating π to 707 decimal places — a feat of extraordinary patience and arithmetic. He still holds the record for the most digits of π one person has calculated by hand.

Later, Shank's π was revealed to only be correct to the 527th digit.

This website is made in honor of Shanks's discipline, using his same method. It contains the arithmetic required to calculate the first 100 digits of π.

The Formula

Shanks used Machin's formula, discovered by John Machin in 1706:

π  =  16 · arctan 1 5  −  4 · arctan 1 239
These arctans can be expanded into
π  =  ( 16 · 1 5  −  4 · 1 239 )  −  ( 16 · 1 3 · 5³  −  4 · 1 3 · 239³ )  +  ( 16 · 1 5 · 5⁵  −  4 · 1 5 · 239⁵ )  −  ⋯

Reading the Graph

The home page is a graph of every calculation, with arrows to show the order they need to be completed. Each task is color-coded according to the key below:

1/5 Series Terms
1/239 Series Terms
Combined Terms
Approximation of π - The previous approximation, adding or subtracting the new set of terms.
Division Reference Tables - Tables used during long-division with multi-digit denominators.

How to Participate

Every calculation on this site has been reduced to its simplest possible form:
   A single-digit operation, or
   A long division accompanied by a precomputed reference table.

If you can add, subtract, multiply, and divide, you can contribute. Click any available problem, find an unsolved equation, and answer it. Submit with tab or enter. Also, every answer is a whole number, so round down your division.

Creator

This project was built by Brick Ellis.

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