| John Machin | |
|---|---|
 John Machin |
|
| Born | 1680 England |
| Died | 9 June 1751 London, England |
| Residence |  England |
| Nationality | English |
| Field | Mathematician and astronomer |
| Institutions | Gresham College |
| Notable students | Brook Taylor |
| Known for | Machin-like formula |
John Machin, (bapt. 1686?—June 9, 1751),[1] a professor of astronomy at Gresham College, London, is best known for developing a quickly converging series for π in 1706 and using it to compute π to 100 decimal places. Machin's formula 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 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). Several other Machin-like formulas are known. John Machin served as secretary of the Royal Society from 1718 to 1747. He was also member of the commission which decided the Calculus priority dispute between Leibniz and Newton in 1712.
See also
References
- ^ Anita McConnell, ‘Machin, John (bap. 1686?, d. 1751)’, Oxford Dictionary of National Biography, Oxford University Press, 2004. Accessed 26 June 2007. DOI:10.1093/ref:odnb/17533
External links
- O'Connor, John J; Edmund F. Robertson "John Machin". MacTutor History of Mathematics archive.
- Machin's Formula at MathWorld
