John Machin
Encyclopedia
John Machin, 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:
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
.
Astronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...
at Gresham College
Gresham College
Gresham College is an institution of higher learning located at Barnard's Inn Hall off Holborn in central London, England. It was founded in 1597 under the will of Sir Thomas Gresham and today it hosts over 140 free public lectures every year within the City of London.-History:Sir Thomas Gresham,...
, London, is best known for developing a quickly converging series for Pi
Pi
' is a mathematical constant that is the ratio of any circle's circumference to its diameter. is approximately equal to 3.14. Many formulae in mathematics, science, and engineering involve , which makes it one of the most important mathematical constants...
in 1706 and using it to compute Pi to 100 decimal places.
Machin's formula 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
Taylor series
In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point....
expansion for the inverse tangent. (Brook Taylor
Brook Taylor
Brook Taylor FRS was an English mathematician who is best known for Taylor's theorem and the Taylor series.- Life and work :...
was Machin's contemporary in Cambridge University
University of Cambridge
The University of Cambridge is a public research university located in Cambridge, United Kingdom. It is the second-oldest university in both the United Kingdom and the English-speaking world , and the seventh-oldest globally...
.) 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
Royal Society
The Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...
from 1718 to 1747. He was also a member of the commission which decided the Calculus priority dispute between Leibniz
Gottfried Leibniz
Gottfried Wilhelm Leibniz was a German philosopher and mathematician. He wrote in different languages, primarily in Latin , French and German ....
and Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...
in 1712.
In 1728, he was listed as one of the subscribers to the Cyclopaedia
Cyclopaedia, or Universal Dictionary of Arts and Sciences
Cyclopaedia: or, An Universal Dictionary of Arts and Sciences was an encyclopedia published by Ephraim Chambers in London in 1728, and reprinted in numerous editions in the eighteenth century...
of Ephraim Chambers
Ephraim Chambers
Ephraim Chambers was an English writer and encyclopaedist, who is primarily known for producing the Cyclopaedia, or a Universal Dictionary of Arts and Sciences.-Early life:...
.