π: A 2000-Year Search Changes Direction

One of the charms of mathematics is that it is possible to make elementary discoveries about objects that have been studied for millenia. A most striking example occurred recently when David Bailey of NASA/Ames and Peter Borwein and Simon Plouffe of the Centre for Experimental and Computational Mathematics at Simon Fraser University (henceforth, BBP) discovered a remarkable, and remarkably simple new formula for π. In this paper we will discuss the BBP formula and show how Mathematica can be used to generate many other formulas of the same sort. Moreover, the Mathematica-based methods are symbolic, and so a proof of the formula is a natural consequence of the discovery.