William Brouncker, 2nd Viscount Brouncker

William Brouncker, 2nd Viscount Brouncker

William Brouncker, 2nd Viscount Brouncker FRS (* 1620 in Castle Lyons , Ireland , † April 5, 1684 in Westminster ) was an Irish mathematician and 1660 founding member of the Royal Society in London .

Live and act

He was the older son of William Brouncker, 1st Viscount Brouncker and his wife Winifred Leigh. When his father died in November 1645, he inherited his title of nobility.

He completed his education at Oxford University on June 21, 1646 as a doctor of medicine (MD). In 1660 he was a Member of Parliament (MP) for Westbury in the House of Commons . Between 1662 and 1684 he held the office of Chancellor of the Queen Consort Katharina von Braganza . He was Chancellor of the Navy between 1664 and 1679 and Lord of the Admiralty from 1680 to 1683 .

He is known for his work on continued fractions and on calculating logarithms through infinite series. He also produced some solutions to Pell's equation a x ²  + 1 = y ² .

On November 28, 1660, he was one of a dozen scholars who met at Gresham College , London. There the Society for the Promoting of Physico-Mathematical Experimental Learning to promote experimental philosophy was founded. On July 15, 1662 the society got a royal statute by receiving the "Great Seal" and became the "Royal Society of London". He was President of the Royal Society from 1662 to 1677.

In 1684 he died unmarried and childless. His younger brother Henry Brouncker inherited his title of nobility .

Brouncker's formula

In 1655 Brouncker found a continued fraction representation for the reciprocal of  : ${\displaystyle \pi /4}$

${\displaystyle 1+{\frac {1}{2}}}$	${\displaystyle =\left(1-{\frac {1}{3}}\right)^{-1}}$
${\displaystyle 1+{\frac {1}{2+{\frac {3^{2}}{2}}}}}$	${\displaystyle =\left(1-{\frac {1}{3}}+{\frac {1}{5}}\right)^{-1}}$
${\displaystyle 1+{\frac {1}{2+{\frac {3^{2}}{2+{\frac {5^{2}}{2}}}}}}}$	${\displaystyle =\left(1-{\frac {1}{3}}+{\frac {1}{5}}-{\frac {1}{7}}\right)^{-1}}$
	${\displaystyle \vdots }$
${\displaystyle 1+{\frac {1^{2}}{2+\textstyle {\frac {3^{2}}{2+\textstyle {\frac {5^{2}}{2+\textstyle {\frac {7^{2}}{2+\textstyle {\frac {9^{2}}{\;\,\ddots }}}}}}}}}}}$	${\displaystyle =\arctan(1)^{-1}={\frac {4}{\pi }}}$

Web links

• John J. O'Connor, Edmund F. Robertson :  William Brouncker, 2nd Viscount Brouncker. In: MacTutor History of Mathematics archive .
• Entry to Brouncker; William (c 1620-1684); 2nd Viscount Brouncker in the Archives of the Royal Society , London
• William Brouncker in the Galileo Project (English)
• Biography of Trinity College Dublin (English)
• William Brouncker, 2nd Viscount Brouncker of Lyons on thepeerage.com , accessed September 11, 2016.

predecessor	Office	successor
William Brouncker	Viscount Brouncker 1645-1684	Henry Brouncker