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{{Infobox scientist
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|name              = John Machin
|image            = john machin.jpg|100px
|image_size        = 100px
|caption          = John Machin
|birth_date        = c. 1686
|birth_place      = [[England]]
|death_date        = 9 June {{death year and age|1751|1680}}
|death_place      = [[London]], England
|residence        =
|citizenship      =
|nationality      = [[England|English]]
|ethnicity        =
|field            = [[Mathematician]] and [[astronomer]]
|work_institutions = [[Gresham College]]
|alma_mater        =
|doctoral_advisor  =
|notable_students  = [[Brook Taylor]]
|known_for        = [[Machin-like formula]]
|author_abbrev_bot =
|author_abbrev_zoo =
|influences        =
|influenced        =
|prizes            =
|religion          =
|footnotes        =
|signature        =
}}


'''John Machin''' (bapt. c. 1686 &ndash; June 9, 1751),<ref>Anita McConnell, ‘Machin, John (bap. 1686?, died 1751)’, Oxford Dictionary of National Biography, Oxford University Press, 2004. Accessed 26 June 2007. {{doi|10.1093/ref:odnb/17533}}</ref> 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.
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== History ==
John Machin served as secretary of the [[Royal Society]] from 1718 to 1747. He was also a member of the commission which decided the [[Leibniz and Newton calculus controversy|Calculus priority dispute]] between [[Gottfried Leibniz|Leibniz]] and [[Isaac Newton|Newton]] in 1712.
 
In 1728, he was listed as one of the subscribers to the ''[[Cyclopaedia, or Universal Dictionary of Arts and Sciences|Cyclopaedia]]'' of [[Ephraim Chambers]].<ref>[http://digicoll.library.wisc.edu/cgi-bin/HistSciTech/HistSciTech-idx?type=turn&entity=HistSciTech000900240045&isize=M List of Subscribers to the Cyclopaedia] at library.wisc.edu</ref>
 
== Formula ==
 
Machin's formula<ref>[http://mathworld.wolfram.com/MachinsFormula.html ''Machin's Formula'' at MathWorld]</ref> (for which the [[Machin-like_formula#Derivation|derivation]] is straightforward) is:
 
: <math>\frac{\pi}{4} = 4 \arctan \frac{1}{5} - \arctan \frac{1}{239}</math>
 
The benefit of the new formula, a variation on the [[Leibniz formula for π|Gregory/Leibniz series]] (Pi/4&nbsp;=&nbsp;arctan&nbsp;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 [[University of Cambridge|Cambridge University]].) Machin's formula remained the primary tool of Pi-hunters for centuries (well into the computer era).
 
Several other [[Machin-like formula]]e are known.
 
==See also==
* [[Gresham Professor of Astronomy]]
* [[Pi Day]]
==References==
{{Pi box}}
<references />
 
== External links ==
{{wikisource author-inline|John Machin}}
* {{MacTutor Biography|id=Machin}}
 
{{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
| NAME              = Machin, John
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION = British mathematician
| DATE OF BIRTH    = c. 1686
| PLACE OF BIRTH    = [[England]]
| DATE OF DEATH    = 1752
| PLACE OF DEATH    = [[London]], [[England]]
}}
{{DEFAULTSORT:Machin, John}}
[[Category:1752 deaths]]
[[Category:18th-century English mathematicians]]
[[Category:Fellows of the Royal Society]]
[[Category:1680 births]]

Latest revision as of 07:18, 8 September 2014

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