William Brouncker, 2nd Viscount Brouncker (1620–5 April 1684) was an English mathematician. Events September 6 - English emigrants on the Mayflower depart from Plymouth, England for the future New England and arrive at the end of the year. ... April 5 is the 95th day of the year in the Gregorian calendar (96th in leap years). ... Events France under Louis XIV makes Truce of Ratisbon separately with the Empire and Spain. ... The English are an ethnic group originating in the lowlands of Great Britain and are descendent primarily from the Anglo-Saxons, the Celts with minor influences from the Scandanavians and other groups. ... A mathematician is a person whose area of study and research is mathematics. ...

Brouncker obtained a PhD at the university of Oxford in 1647. He was one of the founders and the first President of the Royal Society. In 1662, he became Chancellor to Queen Catherine, then chief of the Saint Catherine hospital. His mathematical work concerned in particular the calculations of the lengths of the parabola and cycloid, and the quadrature of the hyperbola, which requires approximation of the natural logarithm function by infinite series. He was the first in England to be take interested in generalised continued fractions and, following work of John Wallis, he provided development in the generalised continued fraction of pi. Doctor of Philosophy (Ph. ... The University of Oxford, located in the city of Oxford, England, is the oldest university in the English-speaking world. ... // Events March 14 - Thirty Years War: Bavaria, Cologne, France and Sweden sign the Truce of Ulm. ... The Royal Society of London for the Improvement of Natural Knowledge, known simply as the Royal Society, is claimed to be the oldest learned society still in existence. ... Events March 18 – Short-timed experiment of the first public buses holding 8 passengers begins in Paris May 3/May 2 - Catherine of Braganza marries Charles II of England – as part of the dowry, Portugal cedes Bombay and Tangier to England May 9 - Samuel Pepys witnessed a Punch and Judy... Catherine of Braganza. ... A parabola A parabola (from the Greek: παραβολή) is a conic section generated by the intersection of a cone and a plane tangent to the cone or parallel to some plane tangent to the cone. ... Cycloid (red) generated by a rolling circle A cycloid is the curve defined by a fixed point on a wheel as it rolls, or, more precisely, the locus of a point on the rim of a circle rolling along a straight line. ... In numerical analysis, numerical integration constitutes a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe numerical algorithms for solving differential equations. ... A graph of a hyperbola, where h = k = 0 and a = b = 2. ... The natural logarithm is the logarithm to the base e, where e is approximately equal to 2. ... In mathematics, a series is a sum of a sequence of terms. ... Royal motto: Dieu et mon droit (French: God and my right) Englands location within the UK Official language English de facto Capital London de facto Largest city London Area  - Total Ranked 1st UK 130,395 km² Population  - Total (2001)  - Density Ranked 1st UK 49,138,831 377/km² Ethnicity... In mathematics, a continued fraction is an expression such as where a0 is some integer and all the other numbers an are positive integers. ... John Wallis John Wallis (November 22, 1616 - October 28, 1703) was an English mathematician who is given partial credit for the development of modern calculus. ... The minuscule, or lower-case, pi The mathematical constant Ï€ represents the ratio of a circles circumference to its diameter and is commonly used in mathematics, physics, and engineering. ...

Brouncker's formula

This formula provides a development in generalized continued fraction of π:

External link

• Biography at the MacTutor archive