John Machin

Infobox Scientist
name = John Machin
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caption = John Machin
birth_date = 1680
birth_place = England
death_date = 9 June 1751
death_place = London, England
residence = flag|England
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nationality = flag|England|name=English
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field = Mathematician and astronomer
work_institutions = Gresham College
alma_mater =
doctoral_advisor =
doctoral_students = Brook Taylor
known_for = Machin-like formula
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influences =
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John Machin, ("bapt." 1686?—June 9, 1751), [Anita McConnell, ‘Machin, John (bap. 1686?, d. 1751)’, Oxford Dictionary of National Biography, Oxford University Press, 2004. Accessed 26 June 2007. DOI: [http://dx.doi.org/10.1093/ref:odnb/17533 10.1093/ref:odnb/17533] ] a professor of astronomy at Gresham College, London, is best known for developing a quickly converging series for Pi in 1706 and using it to compute Pi to 100 decimal places.

Machin's formula is:

: $frac\{pi\}\{4\}\; =\; 4\; arctanfrac\{1\}\{5\}\; -\; arctanfrac\{1\}\{239\}$

The benefit of the new formula, a variation on the Gregory/Leibniz series (Pi/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 Pi 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 Pi-hunters for centuries (well into the computer era).

Several other Machin-like formulas are known.

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

ee also

* Gresham Professor of Astronomy

References

External links

*
* [http://mathworld.wolfram.com/MachinsFormula.html "Machin's Formula" at MathWorld]