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Introduction to Geometry Paperback – March 9, 1989

ISBN-13: 978-0471504580 ISBN-10: 0471504580 Edition: 2nd

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Introduction to Geometry + Geometry Revisited (New Mathematical Library) + Challenging Problems in Geometry (Dover Books on Mathematics)
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Product Details

  • Paperback: 496 pages
  • Publisher: Wiley; 2nd edition (March 9, 1989)
  • Language: English
  • ISBN-10: 0471504580
  • ISBN-13: 978-0471504580
  • Product Dimensions: 5.8 x 0.9 x 9.1 inches
  • Shipping Weight: 1.7 pounds (View shipping rates and policies)
  • Average Customer Review: 4.1 out of 5 stars  See all reviews (12 customer reviews)
  • Amazon Best Sellers Rank: #229,705 in Books (See Top 100 in Books)

Editorial Reviews

From the Publisher

This classic work is now available in an unabridged paperback edition. The Second Edition retains all the characterisitcs that made the first edition so popular: brilliant exposition, the flexibility permitted by relatively self-contained chapters, and broad coverage ranging from topics in the Euclidean plane, to affine geometry, projective geometry, differential geometry, and topology. The Second Edition incorporates improvements in the text and in some proofs, takes note of the solution of the 4-color map problem, and provides answers to most of the exercises.

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Most Helpful Customer Reviews

53 of 56 people found the following review helpful By Craig Matteson HALL OF FAMETOP 1000 REVIEWER on January 10, 2004
Format: Paperback
This is a wonderful book. It isn't for mathematical beginners, but it isn't opaque either. It requires a student to think, experiment and to learn by puzzling things out in one's mind rather than simple memorization and regurgitation. Nor does it follow the all too common modern method of over simplifying things to allow people to pretend they have learned math while only dabbling in a few basic topics.
This book is amply illustrated with many exercises (answers are provided at the back for all the exercises). The book also has some humor and wit with the quotes it distributes throughout the book to help liven things up.
There is also a list of helpful references and an index. When reading the book, don't be afraid of going to a dictionary or the web or some other math books for clarification of some terms or more basic concepts. It is essential to have everything clear in your mind before moving on or you will stumble. As in all math, it is like a building with the next stage being built on the present one which is built on the previous one. You can't skip steps very successfully very often.
This is a great volume to have in your library, but even better to work through.
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70 of 79 people found the following review helpful By Charles R. Williams on July 22, 2000
Format: Paperback
A better title for this book would be "Advanced Topics in Geometry". The chapters are pretty much self-contained.
This book presumes a thorough, rigorous knowledge of high school geometry such as you might get in a college geometry course designed for future teachers along with considerable mathematical maturity.
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29 of 31 people found the following review helpful By D. Briggs on June 27, 2000
Format: Paperback
This is Coxeter best book. Introduction to Geometry covers a wide range of topics and is the first book that I will look at for any geometry topic. It is now a little dated but only in the topics that it does not cover. Like all of Coxeter works each topic is clear and to the point. If you only buy one book on geometry this is it.
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10 of 10 people found the following review helpful By Benjamin Crowell on August 23, 2009
Format: Paperback Verified Purchase
This is the best book I've seen covering geometry at this level. Coxeter was known as an apostle of visualization in geometry; many other books that cover this material just give you page after page of symbols with no diagrams. He motivates all the topics well, and lays out the big picture for the reader rather than just presenting a compendium of facts. This is a survey of a huge field, but he does a great job of focusing on the most important results. As other reviewers have noted, this book is not "introductory" in the sense of high school geometry; it's introductory in the sense of being the kind of book a college math major would use in his/her first upper-division geometry course. It doesn't presuppose a great deal of mathematical knowledge, but it probably isn't a book that one could appreciate without having already developed quite a high level of mathematical maturity.
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14 of 16 people found the following review helpful By Redmond Geek on March 10, 2012
Format: Paperback
This is one of those books that's listed in the bibliography of almost every other geometry text I've read -- and rightly so. Reading through it, you'll find some absolute gems of geometric insight. So why am I giving it only three stars? Primarily because it misrepresents itself as an "Introduction," which it isn't. It's much more like one of those fast-paced "ten countries in five days" package tours offerred by various travel agents. In a mere 412 pages, Coxeter zips through a vast number of topics -- each of them actually a specialty area in the larger field of geometry. It simply isn't possible for a book of this length to give the reader any kind of serious grounding in this material.

In addition, some of the topics are ones at which Coxeter himself admitted he wasn't very skilled. During his career, his main areas of interest were symmetry, n-dimensional Euclidean geometry, projective geometry, and higher-dimensional polygons. Things like topology and differential geometry were outside his territory, so the treatment of these topics in "Introduction" is not as engaging as his discussion of various isometries.

This book originally grew out of a set of lectures that Coxeter gave to college-level math majors and math teachers. By all accounts, Coxeter was a very lively and engaging teacher; I imagine it must have been wonderful to listen to those lectures, and then have Coxeter's own lecture notes (i.e., this book) as a reminder of everything that he said. Unfortunately, I don't think the book stands as well on its own as a teacher; it needs Coxeter himself to fill in the gaps between the words and bring it to life.
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5 of 5 people found the following review helpful By malfalfa on April 14, 2011
Format: Paperback
The only reason I give it a 4/5 is because the diagrams need to be labeled. It's pretty hard to keep up with the conversation when the author refers to a poorly labeled complex diagram. I think Coxeter's other book does a great job and you can download it for free or buy it for under $10. It is a great introduction to college level geometry; and introduction because it doesn't really go into too much depth, but is not shallow either. I would recommend it, but buy it used because it's just not one of those books you'll constantly look back at for help in the future...it's pretty much a one read and that's it.
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