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How Euler Did It.

How Euler Did It Edward Sandifer Published by The Mathematical Association of America 2007 Hard cover, 304 pp, $US51.95.

Euler and Modern Science Edward Sandifer Published by The Mathematical Association of America (2007) Hard cover, 425 pp. US$59.95.

We have here Volumes 2 and 4 of the MAA Tercentenary Euler Celebration. Reviews of two other volumes in this series appeared earlier this year in AMT 63 (1).

The same expressions of magnificence expressed there, and admiration for the quality of these books continue to hold for these two volumes. They are beautifully written and put together.

Euler and Modern Science is the larger of these two books. It is mainly a collection of addresses presented in Moscow and St Petersburg in 1983, 200 years after Euler's death. The papers are translated from the original Russian, but you would never know. The papers deal with Euler's life and work, his mathematical notebooks, and his contributions to various areas of mathematics, music and science, but in a descriptive style with relatively little actual mathematics. There is even a discussion of his family tree! Each chapter is referenced in great detail.

In spite of my admiration for this book, I would have to say that in my view it will appeal only to a limited audience: libraries, Euler's descendants, mathematical historians, and those who have a special fascination for this great man and his contributions to mathematics. The text is generally easy to read and follow, but you need some special motivation to read about Euler in such detail.

How Euler Did It is quite different. This is a collection of 40 columns about Euler which appeared on MAAOnline between 2003 and 2007. The book is divided into four main sections: Geometry, Number Theory, Combinatorics, and some 20 chapters on Analysis. Here we have some quite fascinating descriptions of Euler's work. Each topic is dealt with in a chatty style, giving the background, a discussion of Euler's approach, and a good sampling of Euler's actual mathematics. Each chapter concludes with a collection of references.

As an example of the type of inspiration given here, let ABC be a given triangle with edges a, b, c. We know that if [angle]B = [angle]C, then the triangle is isosceles, and b = c. Now what if [angle]B = 2[angle]C? What, if anything, can be said about the sides b and c?

This is an interesting book for secondary and tertiary teachers to read, and should be a good source of teaching enrichment ideas. It illustrates the ways in which Euler approached his mathematics, and that must be a good model to follow!

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Title Annotation:Reflections on Resources; Euler and Modern Science
Author:Scott, Paul
Publication:Australian Mathematics Teacher
Article Type:Book review
Date:Dec 22, 2007
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