# John Machin

John Machin, (16801752), a professor of astronomy in London, is best known for developing a quickly converging series for π in 1706 and using it to compute π to 100 decimal places.

Machin's formula is:

[itex]\frac{\pi}{4} = 4 \arctan\frac{1}{5} - \arctan\frac{1}{239}[itex]

The benefit of the new formula, a variation on the Gregory/Leibniz series (π/4 = arctan 1), was that it had a significantly increased rate of convergence, which made it a much more practical method of calculation.

To compute π to 100 decimal places, he combined his formula with the Taylor series expansion for the inverse tangent. (Brook Taylor was Machin's contemporary in Cambridge University.) Machin's formula remained the primary tool of π-hunters for centuries (well into the computer era).

John Machin served as secretary of the Royal Society from 1718 to 1747. He was also member of the commission which decided the Calculus priority dispute between Leibniz and Newton in 1712.

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