Mathematics by experiment: Plausible reasoning in the 21st Century (2008)

Abstract

its friends," and "Normality: A stubborn question," from Mathematics by Experiment: Plausible Reasoning in the 21st Century, A. K. Peters, Natick, MA, 2nd edition, 2008. Reproduced with permission of AK Peters. Synopsis: Experiment. The first chapter presents an overview of computations the ages, followed by a summary of computer-age developments, includ-analysis of the BBP formula and algorithm for computing binary digits beginning at an arbitrary starting position. The second selection from our book takes a look at a question that has puzzled mathematicians from time immemorial (and which has spurred many computations of π): whether and why the digits of π and other well-known mathematical constants are "normal," meaning that every m-long string of base-b digits appears, in the limit, with frequency 1/b m. Included here are some details of some recent results in this area, such as a proof of normality of the Stoneham numbers, namely constants of the form α b,c = ∞ k=0 1 c k b c k , where b ≥ 2 and c ≥ 2 are relatively prime. Mathematics by We present here excerpts from two chapters of the second edition of our book of π through ing a detailed of π