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William Brouncker




Brouncker obtained a Ph.D 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 take interest in generalised Continued Fraction s and, following the 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:

rac4{\pi}=1 / (1+1^2 / (2+3^2 / (2+5^2 / (2+7^2 / (2+9^2 / (2+11^2 / (2+13^2 / (2+15^2 / (2+17^2 / (2+\cdots


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