"Lord Brouncker's continued fraction for pi" is a well-known result. In this article, we show that Brouncker found not only this one continued fraction, but an entire infinite sequence of related continued fractions for pi. These were recorded in the "Arithmetica Infinitorum" by John Wallis, but appear to have been ignored and forgotten by modern…

An intuitive derivation of Stirling's formula is presented, together with a modification that greatly improves its accuracy. The derivation is based on the closed form evaluation of the gamma function at an integer plus one-half. The modification is easily implemented on a hand-held calculator and often triples the number of significant digits…