John Machin

John Machin
John Machin
Born	1680 England
Died	9 June 1751 (aged 70–71) London, England
Residence	England
Nationality	English
Fields	Mathematician and astronomer
Institutions	Gresham College
Doctoral students	Brook Taylor
Known for	Machin-like formula

John Machin, (bapt. 1686?—June 9, 1751), 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:

$\frac{\pi}{4} = 4 \cot^{-1}5 - \cot^{-1}239$

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.

In 1728, he was listed as one of the subscribers to the Cyclopaedia of Ephraim Chambers.

See also

• Gresham Professor of Astronomy
• Pi Day

References

Part of a series of articles on
the mathematical constant π
Uses
Area of disk Circumference Use in other formulae
Properties
Irrationality Transcendence Less than 22/7
Value
Approximations Memorization
People
Archimedes Liu Hui Zu Chongzhi Madhava of Sangamagrama William Jones John Machin John Wrench Ludolph van Ceulen Aryabhata
History
Chronology Book
In culture
Legislation Holiday
Related topics
Squaring the circle Basel problem Tau (τ) Other topics related to π

External links

• Works written by or about John Machin at Wikisource
• O'Connor, John J.; Robertson, Edmund F., "John Machin", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Machin.html .