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D. A. Brannan
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Geometry 1st Edition

by David A. Brannan (Author), Matthew F. Esplen (Author), Jeremy J. Gray (Author)
4.5 4.5 out of 5 stars 17 ratings
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Geometry
Geometry
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This textbook demonstrates the excitement and beauty of geometry. The approach is that of Klein in his Erlangen program: a geometry is a space together with a set of transformations of that space. The authors explore various geometries: affine, projective, inversive, non-Euclidean and spherical. In each case they carefully explain key results and discuss the relationship among geometries. This richly illustrated and clearly written text includes full solutions to over 200 problems and is suitable both for undergraduate courses on geometry and as a resource for self study.
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  1. ISBN-10
    0521597870
  2. ISBN-13
    978-0521597876
  3. Edition
    1st
  4. Publisher
    Cambridge University Press
  5. Publication date
    April 13, 1999
  6. Language
    English
  7. Dimensions
    7.75 x 1.25 x 9.75 inches
  8. Print length
    512 pages
  9. See all details
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Editorial Reviews

Review

"...an excellent and precisely written textbook that should be studied in depth by all would-be mathematicians." Mathematical Reviews

"There are many things to like about this book. It conveys the beauty and excitement of the subject, avoiding the dryness of many geometry texts. I was very pleased to see the classification of conics developed in Chapters 1 through 4...The effort put in on the problems and answers is very impressive...The language is clear, with little to fear from Anglicisms...presentation is clean and pleasing to the eye...it raised in me a desire to teach elementary geometry again, something I have not felt or done in years." MAA Online

Book Description

Textbook for undergraduate courses on geometry or for self study that reveals the intricacies of geometry.

Product details

  • Publisher ‏ : ‎ Cambridge University Press; 1st edition (April 13, 1999)
  • Language ‏ : ‎ English
  • Paperback ‏ : ‎ 512 pages
  • ISBN-10 ‏ : ‎ 0521597870
  • ISBN-13 ‏ : ‎ 978-0521597876
  • Item Weight ‏ : ‎ 2.01 pounds
  • Dimensions ‏ : ‎ 7.75 x 1.25 x 9.75 inches
  • Customer Reviews:
    4.5 4.5 out of 5 stars 17 ratings

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D. A. Brannan

D. A. Brannan

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Customer reviews

4.5 out of 5 stars
4.5 out of 5
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17 global ratings

Top reviews from the United States

doodler
5.0 out of 5 stars Five Stars
Reviewed in the United States on September 30, 2015
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Wow, want a well written book. Provides a clear narrative and motivation behind the ideas and concepts.
One person found this helpful
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Shankar N. Swamy
5.0 out of 5 stars A Nice Introduction to Geometrys - Precise and Accurate!
Reviewed in the United States on January 2, 2005
This book is at the level of a freshman mathematics course.

Mainly deals with Affine, Projective, Inversive, Spherical and Non-Euclidean geometrys. The beauty of the book is in its accuracy. Someone has done a good job of technical editing! There is always a risk of getting things wrong when attempting to make mathematics accessible at a lower level. The authors seem to have avoided that pitfall with significant success. The subject matter is focused and to the point. At each point, it precisely explains what is intended and moves on without digressions.

I have had significant interests in geometries, and work in a area that uses some elementary projective geometry. At times I get asked some relatively simple questions such as "why do we need 4x4 matrices in Computer Graphics?" Often I just answer such questions to the minimum (" ... it makes applying translations easier ..."). I never proffer a deeper answer because most people I run into either have no background to understand a more technical explanation in terms of the algebra of projective planes or they don't care - they don't need to, for most of their work!. (Many of the computer graphics folks I have met think that the homogeneous coordinates is an ad-hok concept that was invented as a "trick"!)

Occasionally, I do run into some who are interested in knowing the analytical reasoning behind some of the transformations used everyday in computer graphics. This book demonstrated to me how to talk to some of those without having to use very abstract concepts of geometry. I read it first in 1999. I have revisited it since, many times for the nice figures they provide. First time, it took me about three "after work" months to study through the book - not bad at all for a 350+ pages mathematics book!

By looking at the diagrams in the book, I learned how to draw simple diagrams instead of abstract symbols to explain the concepts, theorems and problems. For a book that is as simple, the technical content is remarkably precise and accurate. The book assumes minimal background in mathematics.

Recommended for people interested in computer graphics and want to understand the transformations in there deeper (for whatever reason!), under-graduate students interested in geometry, and for anyone with a casual interest in geometry.
20 people found this helpful
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avniu
4.0 out of 5 stars "Who is who" in geometry
Reviewed in the United States on August 3, 2010
Verified Purchase
The book presents clearly several geometries in the spirit of Kleinean unifying view of geometry. It begins with a recapitulation of many important facts on conic sections, since conic sections played an extraordinary role in science over two thousand of years, and on the other hand the authors use conic sections as very representative geometric objects to explain transformations that specify affine, projective, inversive, non-Euclidean and spherical geometry. The key ideas, results and techniques that served as corner stone in the discovery and development of geometries are presented clearly and fluently using algebraic methods combined with rich illustrations, which provide the shortest path to the proofs and relationships between geometries. As an excellent example of this approach is the Joachimstal's notation for plane conics. The book can also serve as `who is who' in geometry. However, the book has no references to the literature, which would have been very useful for further reading.

Avni Pllana
4 people found this helpful
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J. Wrenholt
5.0 out of 5 stars My Favorite Geometry Book.
Reviewed in the United States on January 26, 2009
I have purchased and worked through several geometry books in the past year. This is, by far, the best one I've come across. It is modern, it is fun, and it is enlightening.

I love the clear worked out numerical examples. As I write geometric computer programs it gives me a way to check each function as I go along. It has an abundance of wonderful illustrations that help you understand the theorems and concepts.

I found this Geometry to be clearly and fully presented for an independent reader, and not just a supplement to some lecture course. There is a minimum amount of mathematical history included, but it is well-chosen and well-written.

Plus, I learned how to draw the tessellations of the Poincare disc, ala M.C. Escher. So that alone made it worth the price and the effort.

Definitely 5 stars.
6 people found this helpful
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Rovenski
5.0 out of 5 stars Geometry
Reviewed in the United States on July 20, 2007
It is a beautiful book to support University course
"Foundations of geometry" for undergraduate students.
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Murph
4.0 out of 5 stars interesting book
Reviewed in the United States on August 17, 2011
Verified Purchase
a class i took used this book, i sold the book after the class ended, for $70, but i'm looking for an opportunity to buy one back in a few years when the price goes down, so it must be a good book, alright. the graphics stick in your head, and the book develops a sense for geometry, it gives you more of a feel for how the math explains the geometry. prerequisites for understanding it might be just high school math, but then knowing some college math is also helpful of course, it was a while ago, but i remeber multivariable calculus and linear algebra in there
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Top reviews from other countries

KTS
4.0 out of 5 stars Four Stars
Reviewed in the United Kingdom on August 15, 2014
Verified Purchase
Good information
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