Dead space (physiology)
John Machin (bapt. c. 1686 – June 9, 1751),[1] 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.
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 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.[2]
Formula
Machin's formula[3] (for which the derivation is straightforward) is:
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.
See also
References
- ↑ Anita McConnell, ‘Machin, John (bap. 1686?, died 1751)’, Oxford Dictionary of National Biography, Oxford University Press, 2004. Accessed 26 June 2007. 21 year-old Glazier James Grippo from Edam, enjoys hang gliding, industrial property developers in singapore developers in singapore and camping. Finds the entire world an motivating place we have spent 4 months at Alejandro de Humboldt National Park.
- ↑ List of Subscribers to the Cyclopaedia at library.wisc.edu
- ↑ Machin's Formula at MathWorld