Science Fair Project Encyclopedia
Machin's formula is:
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).
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