»√2

David Flannery's book √2 is a beautiful explanation of the properties of this irrational number, presented as a dialogue between a master mathematician and an eager student. The dialogue is in the tradition of Socrates, of Galileo; it is an explication of a sublime concept, presented clearly and logically, with succinct interludes of history and anecdote. I learned more about the symmetry of standard paper sizes in Chapter 2 of this book than I ever thought I might encounter!

This book uses an alternative spelling of minuscule: miniscule. Perhaps the result of years of pervasive mis-spelling, many dictionaries now present this spelling as a variant of the original. As a fan of alternatives, I appreciate this; however, the vowel shortening alarms me. Aside: I notice "break" commonly used to indicate the mechanical device used to stop cars, elevators, trains, et c.; will this, too, become an accepted spelling?)

Both the author's approach and prose make for a much more enjoyable read than either of the volumes I read (or tried reading) on 0; or π; or e. I really enjoyed this dialogue, and the genuinely useful illustrations and algebra. The final chapter, "Odds and Ends", presents some of the more engaging problems of number theory, including a demonstration of taxicab problem. The discussion and proofs of Pell's Sequence uses simple, clear algebra to show the increasingly-accurate approximations of the square root of two; the awesome power of the Heron Sequence becomes apparent as the dialogue reveals how to rapidly advance through the approximations in Pell's Sequence. The inherent beauty of the numbers is dazzling (although I would stop short of describing some of the algebra as "witchcraft", as does the Teacher in this dialogue).