Customer Reviews

Elementary Geometry from an Advanced Standpoint (3rd Edition)

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This is probably the only math book I've actually read in its entirety. Moise delivers what could be very dry material with a lightness and sense of humor that kept me poking on through the book. The connections to other areas of math, especially (and not surprisingly) non-Euclidean geometries, is a big plus. I also liked the occasional historical interludes. There are a few spots where you may not see good pointers to the figures provided, but in general it is very clear what the author is referring to. The problem sets and Moise's own explanations afford excellent practice for the "proof-challenged," as well. I keep this book on my shelf as "ready reference." I wish Moise had written more math books!

Beginning by the elementary axioms the author builds all the great geometry theorems and formulas. Like a great romance, after begin to read you don't want stop until end.

Moise's book has a long history. In the 1960's, the same author wrote a simpler version of this book (with Downs) for use in high schools, a revolutionary deed since very precise mathematics is not usual in high school. One may be question if high school is the place to teach geometry in this way, but for the book written for undergrads this is unquestionable. I really do not know of any other book of its kind (there are advanced books of elementary geometry, but usually from the synthetic viewpoint which make them difficult to read at this point). In the same way that real analysis books (e.g., Apostol) gives for the student absolute rigour and precise proofs in the realm of real numbers and functions, Moise's book do the same for elementary Euclidean geometry. And it does so with easy-to-follow arguments and a good historical discussion. Although focused on the easier analytical viewpoint, that starts with real numbers as given entities, it explains how to obtain the same results by the more beautiful and historical synthetic viewpoint. The book has irresistible taste, as other reviewers already pointed out. But it is much more than that. It is possible to be a graduated mathematician and still not be able to prove with rigour results from elementary geometry. This book gives you this power. Once read, you can complement it with other results from elementary books, that can be reworked with the formalism you get from Moise's book. And you are much better prepared to understand more advanced books on the same subject, as the amazing Projective Geometry from Veblen and Young (probably one of the best books in Geometry ever written). So Elementary Geometry from an Advanced Viewpoint is really a book that gives immense power and helps you to understand the great human endeavour called Geometry. Very important work.

As an exercise in considering how I might write my own Geometry book one day, a friend and colleague directed me at Moise's title. I simply treated the book as both a trained mathematician and as an editor. Without a doubt, this book has been thoroughly built from the bottom up without flaw (save for, if I recall, 2 typos and 1 problem that in my opinion only deserved delay to a future section). Consider the hundreds of pages therein, this feat is monumental. While I would absolutely hate to learn geometry for a first time this way, an collegiate level student seeking to fully develop a sense of geometries (yes, plural) would be best served to take a few months as I did to challenge what you think you know by working (not skimming) your way through Moise's material. It has earned its place amongst my favorite resource books for its thoroughness, its accuracy, and its thoughtfulness.

This book has a few errors and is not very descriptive. However, it is a course requirement. So, I guess it has to be okay.