|Died||9 June 1751 (aged 70–71)
|Fields||Mathematician and astronomer|
|Notable students||Brook Taylor|
|Known for||Machin-like formula|
John Machin (bapt. c. 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.
On 16 May 1713 he succeeded Alexander Torriano as professor of astronomy in Gresham College, and held the post until his death, which occurred in London on 9 June 1751. Machin enjoyed a high mathematical reputation. His ingenious quadrature of the circle was investigated by Hutton, and in 1706 he computed the value of π by Halley's method to one hundred decimals places. A mass of his manuscripts is preserved by the Royal Astronomical Society; and writing to William Jones in 1727, he asserted his claim to the parliamentary reward of £10,000 for amending the lunar tables.
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 formulae are known.
|Part of a series of articles on the|
|mathematical constant π|
- 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
- Clerke 1893.
- List of Subscribers to the Cyclopaedia at library.wisc.edu
- Machin's Formula at MathWorld
- This article incorporates text from a publication now in the public domain: Clerke, Agnes Mary (1893). "Machin, John (d.1751)". In Lee, Sidney. Dictionary of National Biography 35. London: Smith, Elder & Co.
- O'Connor, John J.; Robertson, Edmund F., "John Machin", MacTutor History of Mathematics archive, University of St Andrews.