formulasearchengine - User contributions [en]

Co-occurrence matrix

2014-08-09T18:50:43Z

216.15.58.19: /* External links */ http://cran.r-project.org/web/packages/glcm/

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2014-02-17T19:52:13Z

216.15.125.3: /* Divisors in a Riemann surface */ "class of equivalence" replaced by "equivalence class"

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Positive-definite matrix

2014-02-16T14:06:25Z

216.15.124.67: /* Examples */ For clarity, make implied vector/matrix multiplication explicit.

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Coupling (computer programming)

2014-01-05T02:33:58Z

216.15.8.219: /* Object-oriented programming */

{{Use dmy dates|date=April 2012}}
{{Infobox scientist
|name = The Viscount Brouncker
|image = William Brouncker, 2nd Viscount Brouncker by Sir Peter Lely.jpg
|image_size = 200px
|caption = Portrait of Brouncker (circa 1674) possibly after Sir [[Peter Lely]]
|birth_date = 1620
|birth_place = [[Castlelyons]], Ireland
|death_date = {{death date and age|1684|04|05|1620|01|01|df=y}}
|death_place = [[Westminster]], London, England
|residence = England
|citizenship =
|nationality =
|ethnicity =
|field = [[Mathematician]]
|work_institutions = [[Saint Catherine's Hospital]]
|alma_mater = [[University of Oxford]]
|academic_advisors = [[John Wallis]]
|doctoral_students =
|known_for = [[Brouncker's formula]]
|author_abbrev_bot =
|author_abbrev_zoo =
|influences =
|influenced =
|prizes =
|religion =
|footnotes =
|signature =
}}

'''William Brouncker, 2nd Viscount Brouncker''', [[Fellow of the Royal Society|PRS]] (1620 – 5 April 1684) was an English [[mathematician]] who introduced '''Brouncker's formula'''.

== Life ==

Brouncker was born in [[Castlelyons]], [[County Cork]], the elder son of William Brouncker, 1st [[Viscount Brouncker]] and Winifred, daughter of Sir William Leigh of Newnham. His father was created a [[Viscount]] in the [[Peerage of Ireland]] in 1645 for services to the Crown. Although the first Viscount had fought in the Anglo-Scots war of 1639, malicious gossip said that he paid the then enormous sum of £1200 for the title and was almost ruined as a result; but in any case he died only a few months afterwards.

William obtained a [[Doctor of Medicine|DM]] at the [[University of Oxford]] in 1647. He was one of the founders and the first [[President of the Royal Society|President]] of the [[Royal Society]]. In 1662, he became [[Chancellor]] to [[Catherine of Braganza|Queen Catherine]], then head of the [[Saint Catherine's Hospital]].

He was appointed one of the Commissioners of the Navy in 1664 and his career can be traced in the ''[[Diary of Samuel Pepys]]''; despite frequent disagreements Pepys on the whole respected Brouncker more than most of his other colleagues.

Brouncker never married but lived for many years with the actress Abigail Williams (much to Pepys' disgust) and left most of his property to her. His title passed to his brother [[Henry Brouncker, 3rd Viscount Brouncker|Henry]], one of the most detested men of the era.

== Works ==

His mathematical work concerned in particular the calculations of the lengths of the [[parabola]] and [[cycloid]], and the [[quadrature (mathematics)|quadrature]] of the [[hyperbola]], which requires approximation of the [[natural logarithm]] function by [[infinite series]]. He was the first European to solve what is now known as [[Pell's equation]]. He was the first in England to take interest in [[generalized continued fraction]]s and, following the work of [[John Wallis]], he provided development in the generalized continued fraction of [[pi]].

=== Brouncker's formula ===

This formula provides a development of π/4 in a generalized continued fraction:
:<math>
\frac \pi 4 = \cfrac{1}{1+\cfrac{1^2}{2+\cfrac{3^2}{2+\cfrac{5^2}{2+\cfrac{7^2}{2+\cfrac{9^2}{2+\ddots}}}}}}
</math>
The convergents are related to the [[Leibniz formula for pi]]: for instance
:<math>
\frac{1}{1+\frac{1^2}{2}} = \frac{2}{3} = 1 - \frac{1}{3}
</math>
and
:<math>
\frac{1}{1+\frac{1^2}{2+\frac{3^2}{2}}} = \frac{13}{15} = 1 - \frac{1}{3} + \frac{1}{5}.
</math>
Because of its slow convergence Brouncker's formula is not useful for practical computations of π.

== External links ==

* {{MacTutor|id=Brouncker}}
* {{Cite DNB|wstitle=Brouncker, William}}

{{s-start}}
{{s-reg|ie}}
{{succession box | before=[[William Brouncker, 1st Viscount Brouncker|William Brouncker]] | title=[[Viscount Brouncker]] | after=[[Henry Brouncker, 3rd Viscount Brouncker|Henry Brouncker]] | years=1645–1684}}
{{s-end}}
{{Royal Society presidents 1600s}}

{{Authority control|VIAF=77098447}}

{{Persondata 
| NAME = Brouncker, William Brouncker, 2nd Viscount
| ALTERNATIVE NAMES =
| SHORT DESCRIPTION = English mathematician
| DATE OF BIRTH = 1 January 1620
| PLACE OF BIRTH = [[Castlelyons]], Ireland
| DATE OF DEATH = 5 April 1684
| PLACE OF DEATH = [[Westminster]], London, England
}}
{{DEFAULTSORT:Brouncker, William Brouncker, 2nd Viscount}}
[[Category:1620 births]]
[[Category:1684 deaths]]
[[Category:17th-century English mathematicians]]
[[Category:Founder Fellows of the Royal Society]]
[[Category:Lords of the Admiralty]]
[[Category:Presidents of the Royal Society]]
[[Category:Viscounts in the Peerage of Ireland]]