Lord William Brouncker (born 1620 in Castlelyons , County Cork, Ireland and died on 5 April 1684 in Westminster, London, UK) was an English mathematician.

The Viscount William Brouncker obtained a doctorate of philosophy at the university of Oxford in 1647. He is one of the founders and the first president of Royal Society. In 1662, he became chancellor to Queen Catherine, then chief of the Saint Catherine hospital . His mathematical work concerns 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.

Brouncker's formula

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