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Geometry: A Comprehensive Course (Dover Books on Mathematics) Paperback – December 1, 1988

4.1 out of 5 stars 42 customer reviews

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Product Details

  • Series: Dover Books on Mathematics
  • Paperback: 464 pages
  • Publisher: Dover Publications (December 1, 1988)
  • Language: English
  • ISBN-10: 0486658120
  • ISBN-13: 978-0486658124
  • Product Dimensions: 6.5 x 0.9 x 9.2 inches
  • Shipping Weight: 1.4 pounds (View shipping rates and policies)
  • Average Customer Review: 4.1 out of 5 stars  See all reviews (42 customer reviews)
  • Amazon Best Sellers Rank: #216,131 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

Format: Paperback
This text - comprised of detailed accounts of Euclidean, Affine, and Projective geometries, a thorough discussion of the Poincare model of hyperbolic geometry, and a motivating chapter on Algebraic geometry - is remarkable for its clarity and simplicity. Very little is initially expected of the reader - a sound knowledege of linear algebra, complex arithmetic and trigonometry - and the proof style is not too formal. Considering the level of detail of its treatment (it's a little more than twice the length of Coxeter's Geometry Revisited, which shares a similar selection of topics) it is ideal for undergraduates or those looking for a good, inexpensive text for self study.

Throughout the text the author emphasizes the use of basic algebraic techniques as an aid to finding clear and simple proofs. In more than one case a result is proved several times, each proof illustrating a different technique. In the first chapter, the utility of the vector approach is highlighted by using vector arithmetic, inner-products and exterior algebra to prove several classic theorems of plane geometry. In later chapters elementary group theory, Moebius transformations and linear algebra are used extensively in the discussions of the mappings of the Euclidean plane, of the mappings of the inversive plane, and of projective geometry respectively.

Basically, this is a good, detailed undergraduate introduction to geometry. It's perhaps a little less entertaining than Coxeter's introductory geometry books but it has a much friendlier price-tag.
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Format: Paperback
I would not recommend this as a first book. I started in Chapter One and the author's proofs seem sometimes too terse and sometimes confusing to me. Another drawback to this book is that it has no answers to the exercises.

There are some good written introductory books. It depends on your goals. Books like Foundations of Geometry (Dover Books on Mathematics) (has no solutions to the exercises that I know) by Wylie. The more I read this book, the more and more I am coming to like Geometry and appreciate the subject. Another nice first book to study alongside Wylie's is Euclidean Geometry and Transformations (Dover Books on Mathematics) by Dodge which has hints and answers, but seems more advanced than Wylie. Wylie's is an axiomatic approach, and I'm liking Wylie's book much more than Dodge's, but Dodge seems more of an analytic and algebraic approach to Euclid. Wylie's other book Introduction to Projective Geometry (Dover Books on Mathematics) (has answers in back to odd exercises I believe) is analytic and algebraic and is not like the "Foundations" book in writing and clarity. It is an advanced text and you will need some mathematical maturity and experience I think to study it even though it has "Introduction" in the Title. It's nice to "shift gears" and go back and forth between the two approaches, axiomatic and analytic/algebraic, since they are complementary.
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Format: Paperback
A wonderful book, value for money! If you are learning geometry for interest or to prepare for competitions such as IMO, then this book is for you! The theorems and diagrams are complete and straight to the point. The author presents the informations in a succinct manner; thus it is easy for one to follow and comprehend. I guess it may be one of the most complete book on geometry in the market!
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Format: Paperback
I purchased this book to provide a second source of information for a college senior/ graduate level geometry class. It was quite helpful at times in giving second explanations of topics covered in class at a price significantly less than the class textbook. The book is comprehensive, and reasonably well written for a math book. One drawback was that it does not discuss Poincare's upper half plane model of hyperbolic geometry, only Poincare's disc model is covered. Inversions are well covered, and one could use this information to map from the disc model to the upper half plane model, so this was not a serious omission. I have no regrets about buying this book.
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Format: Paperback Verified Purchase
An interesting book covering multiple topics not usually contained in the same book, this goes quite well logically from Euclidean Geometry to natural generalizations in affine and projective geometry. To finish it off, we have one of the more classical non-euclidean geometries through a discussion (nowhere near complete, though) of hyperbolic geometry. It is an easily accessible and interesting read for a prospective math education major. It is of little interest, however, to any other audience.

My biggest issue, though clearly seen if one were to use the table of contents, is that this is not comprehensive at either the college or high school levels. This assumes a STRONG background in both co-ordinate geometry and synthetic geometry (involving proofs). It also assumes familiarity with linear algebra, complex numbers and trigonometry. Moreover, the material moves quickly and leaves some of its developments as exercises as opposed to actually fully developing and discussing the material.

The material on hyperbolic geometry is woefully small (does not cover upper half plane model and no hyperbolic trigonometry) and incomplete as to make one wonder why it should be included until one realizes the price is low enough to be happy with so much other material, and the projective and affine geometry mentioned in this book isn't very general at all. A developed discussion of elliptic and spherical geometry is also missing. While a great introduction, the book doesn't go anywhere near in depth enough, and even wide enough, to be comprehensive.

Another issue I have with this book is that its coverage of Euclidean geometry is rather boring and covers few of the more classical and widely used theorems in math contests.
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