Wallis's product, Brouncker's continued fraction, and Leibniz's series

Abstract

A historical sketch is given of Wallis's infinite product for 4/π, and of the attempts which have been made, over more than three centuries, to find the method by which Brouncker obtained his equivalent continued fraction. A derivation of Brouncker's formula is given. Early results obtained by Indian mathematicians for the series for π/4, later named for Leibniz, are reviewed and extended. A conjecture is made concerning Brouncker's method of obtaining close bounds for π.