The Square Root of 2: A Dialogue Concerning a Number and a Sequence

The square root of 2 is a fascinating number – if a little less famous than such mathematical stars as pi, the number e, the golden ratio, or the square root of –1. (Each of these has been honored by at least one recent book.) Here, in an imaginary dialogue between teacher and student, readers will learn why v2 is an important number in its own right, and how, in puzzling out its special qualities, mathematicians gained insights into the illusive nature of irrational numbers. Using no more than basic high school algebra and geometry, David Flannery manages to convey not just why v2 is fascinating and significant, but how the whole enterprise of mathematical thinking can be played out in a dialogue that is imaginative, intriguing, and engaging. Original and informative, The Square Root of 2 is a one-of-a-kind introduction to the pleasure and playful beauty of mathematical thinking.

1 Getting to the Root of the Mystery; 2 Irrationality and its Consequences; 3 The Power of a Little Algebra; 4 Witchcraft; 5 Odds and Ends

From the reviews:
"Written by an expert teacher as a conversation between a ‘master’ and a ‘pupil’ on the threshold of adulthood, this investigation of the subtleties of the number concept and sequences of rational approximations becomes an initiation into the pleasures of mathematical experimentation, exploration, and generalization. … This book is thus an ideal gift for any bright young person with computational ability and self-directed reading curiosity … ." (Andrew M. Rockett, Mathematical Reviews, Issue 2006 j)
"David Flannery’s book, The Square Root of 2, is the kind of book to recommend to a particularly bright high school senior, not to ignore a frosh in college. From page 1 through its conclusion, it is a masterful dialogue … . Flannery seeks to arouse a cool passion for mathematics in his student. … Flannery has woven an engaging dialogue from history and theory that offers the student insights into the thinking mind of the working mathematician." (Barnabas Hughes, Covergence, April, 2006)
"The book is more about some mathematics pertaining to the square root of two … . I would recommend it to good high school students … . I also think it would be a wonderful topic for a colloquium presentation for undergraduate students. … I think the book is easy to understand and interesting as long as you like math. … I would recommend it to other kids in algebra II or precalculus as well … ." (Doug Ensley and John Ensley, MAA Online, March, 2006)

Includes supplementary material: sn.pub/extras