MOCAA Seminar Series for 2005-2006
Experimental Mathematics in the Normality of Pi
David Bailey, Computational Research Department, Lawrence Berkley National Laboratory
Abstract: Modern computer technology now makes it possible to compute high-precision numeric values of mathematical expressions and then to identify these values analytically. This talk summarizes a number of recent results in this area, including: (1) the 1996 discovery of a new formula for pi (with Peter Borwein and Simon Plouffe), (2) the discovery of a large number of other BBP-like identities, and (3) the recent discovery of analytic evaluations for some integrals that arise in mathematical physics. Interestingly, there is a connection between this theory and the age-old question of whether (and why) the binary digits of constants such as pi and log(2) are "normal" (i.e. statistically random in a certain sense). This realization has now led to a simple proof (using ergodic theory techniques) of normality for a large (uncountably infinite) class of real numbers.