The Square Root of 2 (PDF)

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)