Book Reviews

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

How the publisher describes it:

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

Review by John T Harrison

In brief:

It is now and will continue to be one of my most read books.

“Written in an engaging style as a conversation”

As the title suggests this book has as its central theme an in depth study of the square root of 2, and is written in an engaging style as a conversation between a teacher and student.

The approach is simple, and takes the reader on a journey which is simple to follow, but mathematically rigorous, and encompasses many concepts along the way, such as irrationality, reductio ad absurdum, continued fractions, convergence, conversion of recurring decimals to fractions, Pell equations, Hero sequence and many others.

Many sections could be used on their own as subjects for lessons.

The two chapters entitled ‘Witchcraft’ and ‘Odds and Ends’ are fairly wide ranging and are particularly fascinating, using techniques for investigation which aspiring number enquirers like myself can use.

It is a book about a lot more than the title suggests, and introduces ways of investigating number sequences and other mathematical matters in a manner that is in no way daunting to those whose knowledge of algebra is limited, but who nevertheless have a desire to further their understanding of numbers.

It is now and will continue to be one of my most read books.

John T Harrison • Retired engineer, creator of NumDrum