John Machin (bapt. c. 1686 – June 9, 1751) was a professor of
astronomy
Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...
at
Gresham College
Gresham College is an institution of higher learning located at Barnard's Inn Hall off Holborn in Central London, England. It does not enroll students or award degrees. It was founded in 1596 under the will of Sir Thomas Gresham, and hosts ...
, London. He 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
The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, r ...
from 1718 to 1747.
He was also a member of the commission which decided the
Calculus priority dispute between
Leibniz
Gottfried Wilhelm (von) Leibniz . ( – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat. He is one of the most prominent figures in both the history of philosophy and the history of mat ...
and
Newton in 1712.
On 16 May 1713 he succeeded
Alexander Torriano
Alexander is a male given name. The most prominent bearer of the name is Alexander the Great, the king of the Ancient Greek kingdom of Macedonia who created one of the largest empires in ancient history.
Variants listed here are Aleksandar, Al ...
as professor of astronomy in
Gresham College
Gresham College is an institution of higher learning located at Barnard's Inn Hall off Holborn in Central London, England. It does not enroll students or award degrees. It was founded in 1596 under the will of Sir Thomas Gresham, and hosts ...
, 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 Machin computed the value of π by Halley's method to one hundred decimal places.
A mass of his manuscripts is preserved by the
Royal Astronomical Society
(Whatever shines should be observed)
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; and writing to
William Jones in 1727, he asserted his claim to the parliamentary reward of £10,000 for amending the lunar tables.
In 1728, he was listed as one of the subscribers to the ''
Cyclopaedia
Cyclopedia, cyclopaedia or cyclopedien is an archaic term for encyclopedia.
The term may specifically refer to:
*''Cyclopædia, or an Universal Dictionary of Arts and Sciences'', 1728, edited by Ephraim Chambers
*''Rees's Cyclopædia'', 1802– ...
'' of
Ephraim Chambers.
Formula
Machin's formula
''Machin's Formula'' at MathWorld
/ref> (for which the derivation is straightforward) is:
:
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
In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor se ...
expansion for the inverse tangent. (Brook Taylor
Brook Taylor (18 August 1685 – 29 December 1731) was an English mathematician best known for creating Taylor's theorem and the Taylor series, which are important for their use in mathematical analysis.
Life and work
Brook Taylor w ...
was Machin's contemporary in Cambridge University
, mottoeng = Literal: From here, light and sacred draughts.
Non literal: From this place, we gain enlightenment and precious knowledge.
, established =
, other_name = The Chancellor, Masters and Schola ...
.) 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
* Gresham Professor of Astronomy
References
Attribution
*
External links
*
*
{{DEFAULTSORT:Machin, John
1752 deaths
18th-century English mathematicians
Fellows of the Royal Society
18th-century British scientists
Freemasons of the Premier Grand Lodge of England