The Square Root of 2: A Dialogue Concerning a Number and a Sequence 2006th Edition by David Flannery (PDF)

Description

An elegantly dramatized and illustrated dialog on the square root of two and the whole concept of irrational numbers.

User’s Reviews

Editorial Reviews: Review 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)

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐There have been plenty of mathematics books written about specific numbers, like pi, zero, e, the golden ratio, etc. All of these books typically go into a detailed the history of the number, give examples of where the number shows up, and how work with the number has affected the world. I bought this book because I was expecting it to show the square root of 2 along those same lines. Unfortunately, that wasn’t the case at all.This book is written in the form of a continuous dialogue between a teacher and student. Throughout the book, they play around with different equations and uncommon series related to the square root of two. They also not only tackle a few proofs of the number’s irrationality, but discuss the nature of proof itself. The only real world examples they show are the diagonal of a square (and as usual this leads into some discussion of the ancient Greeks and the discovery of irrational numbers in general), and how the square root of 2 relates to the business standard A4 paper and why it was created (a great example that I wasn’t aware of).Again, this wasn’t what I was expecting at all. But I’ll give it 4 stars because it is a nice introduction to mathematical thinking, and how mathematicians go about examining and solving problems, and the reasoning behind the approaches.

⭐…This book, among probably all mathematics books I have, has a unique format – a professor/teacher dialogue with a motivated, learning pupil, as their repartee delves deeper into ever more exact approximations of the 2nd (?!?!) most famous irrational number from antiquity (pi probably being the most well-known?!). The sequences include continued fractions as well as ordinary fractions to depict the square root of 2, along with some strategically-placed drawings and diagrams. Some readers might find the format a bitdisconcerting at first, shifting from the teacher’s/professors’ points of view/experience/wisdom to the student’s, then back again,back and forth, much like a very sustained, stimulating, in-depth one-on-one conversation. The book’s green cover and yellow binding help it stand out on the shelf, along with its austere “/2” symbol on binding. Highly recommended for a thorough exploration of that irrational number, which has been upstaged at times by pi, e, phi, and others.

⭐This book is somewhat curiously organized, in the form of a dialog between a Master, who is a mathematician well acquainted with the material, and a student, who is apparently someone who has had elementary algebra but is a little uncomfortable with it. By the device of dialog, a lot of mathematics is brought out, all concerned in some way with the square root of 2.I found it pleasant to read, and recommend this book to anyone who is not so totally afraid of math that an equation scares them. You might learn some interesting math!

⭐This book takes the form of a conversation between a wise and patient teacher and a curious former mathematics student. It begins by motivating the need for a number that is the square root of two and quickly works its way to the embarrassing (at least to the ancients) fact that one cannot find a rational number that is exactly the square root of two. There are many adventures connected with a sequence of rational numbers that approaches, but never quite reaches, the square root of two. The student is making many of the discoveries himself rather than being given the answers by the teacher. I would jump at any further mathematics books by this author.

⭐This is an excellent book for anyone interested in mathematical reasoning using the value of square root of 2 as a test case. The format is akin to a tutor-student (Socratic?) dialogue which makes the text quite interesting. Anyone with basic math skills can grasp it’s contents. The text does require concentration to get the most out of it.There are quite a few editing errors in this book which is a shame because it does take away from it’s quality and disrupts one’s train of thought. These errors were quite annoying after a while. Some of the errors are howlers (like the one on pi). All in all a good read.

⭐Conversational treatment of interesting ideas. Effective. Pleasure to read.Ok. Amazon tells me “11 more words required.”You’ll probably be glad you read this book.

⭐Since the book arrived I have been unable to put it down – and a maths book too! For the first time, as a student of maths, have I been able to really understand how a mathematician thinks – almost in 3D. The dialogue between master and student is superb and very clearly illustrates the reasoning that maths geeks must aspire to. The text is not perfect, with one or two errors, but this did not detract from the overall force of the text.

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