The Complete Idiot's Guide to Geometry (The Complete Idiot's Guide)

Good supplement to any traditional geometry text. Helpful insights and delightful humor throughout the book. Would be a great asset to any high school math teacher's personal library.

Despite the occasional cutesy dialog, this book is a solid introduction to the fundamentals of high school geometry. It begins with a definition of what geometry is and then presents a necessary review of some of the basic rules of algebra, in particular the properties of equalities and inequalities when objects are combined. The next step is to describe the fundamental objects used in geometry. Starting with the point, line, line segment, ray and plane, the basic objects used in geometry are explained and classified.
Once the fundamental descriptions of the objects is complete, the next step is to describe the nature of the mathematical proof. This is done using truth tables and explanations of the words that correspond to the symbols used to build propositions.
The next sections introduce additional geometric figures such as the triangle, quadrilateral, rhombus and circle. Proofs are used when needed and the standard objects such as the unit circle and the 30-60-90 triangle are explained. Three-dimensional objects, constructions, neutral and non-Euclidean geometry and transformations are the topics of the last chapters. A set of 64 solved multiple choice problems is also included. All of this material is presented at a level that the beginner can comprehend.
I applaud the inclusion of the sections on neutral and non-Euclidean geometry, it is often assumed that this is beyond the understanding of beginners, but that is not the case. Spherical geometry is in some ways easier to understand than plane geometry because a globe is all you need and the structure is finite. I also commend the author for including the set of problems. Mathematics is learned by doing and this gives the reader an opportunity to immediately test their level of understanding.

I recently needed a book to review my high school geometry (not having seen that sort of math for over 15 years, and not having any other text on hand) and went to the local bookstore to look at the selection. One of the available choices was this book. I had always been wary of the "Idiot's Guide's" books, mainly because I expected that they were superficial hacks slapped together to get a quick buck from genuine idiots who didn't know any better. Well, I was wrong...

The material in this book was well laid out and thorough. Although she didn't cover everything you might find in a typical high school geometry course, Dr. Szecsei certainly aimed for the highlights, and left me quite satisfied with the results. I would expect that a typical buyer (high school or early college student?) would like this book as an explainable version of his or her assigned course textbook.

The reading pace was zippy and didn't get bogged down in gory details, but still laid the foundation to tackle more difficult geometric proofs. There were also some tantalizing highlights towards the end of the book for those interested in non-Euclidean geometry, which might inspire the occasional student in looking beyond the standard high school curriculum.

The format was geared towards examples and proofs, with a few problems at the end of each chapter for the adventurous student to work out on his or her own. Complete solutions to all the problems were provided at the end of the book. Also provided was a summary of all postulates and theorems. This is a handy feature that I wish a few more math textbook authors picked up.

The only flaw in the book that I found was some of the diagrams were completely incorrect. Although this could have lowered the rating from a "5" to a "4", having found just a few errors like this out of the hundreds of diagrams in the book does not really detract from its value, but I felt bound to mention it only for the struggling student that could accidentally waste valuable time re-creating the actual diagram to go along with the proof provided. An errata website would have been helpful, but I didn't see anything. Maybe next time.

All in all, this book was excellent, and completely changed my opinion of the "Idiot's Guides" series.