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Geometry Paperback – February 13, 2012

ISBN-13: 978-1107647831 ISBN-10: 1107647835 Edition: 2nd

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Product Details

  • Paperback: 602 pages
  • Publisher: Cambridge University Press; 2 edition (February 13, 2012)
  • Language: English
  • ISBN-10: 1107647835
  • ISBN-13: 978-1107647831
  • Product Dimensions: 9.4 x 7.5 x 1.2 inches
  • Shipping Weight: 2.8 pounds (View shipping rates and policies)
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (10 customer reviews)
  • Amazon Best Sellers Rank: #303,237 in Books (See Top 100 in Books)

Editorial Reviews

Review

'This is a textbook that demonstrates the excitement and beauty of geometry ... richly illustrated and clearly written.' Extrait de L'Enseignement Mathématique

'... this is a remarkable and nicely written introduction to classical geometry.' Zentralblatt MATH

'... could form the basis of courses in geometry for mathematics undergraduates. It will also appeal to the general mathematical reader.' John Stone, The Times Higher Education Supplement

'It conveys the beauty and excitement of the subject, avoiding the dryness of many geometry texts.' J. I. Hall, Mathematical Association of America

'To my mind, this is the best introductory book ever written on introductory university geometry ... readers are introduced to the notions of Euclidean congruence, affine congruence, projective congruence and certain versions of non-Euclidean geometry (hyperbolic, spherical and inversive). Not only are students introduced to a wide range of algebraic methods, but they will encounter a most pleasing combination of process and product.' P. N. Ruane, MAA Focus

'... an excellent and precisely written textbook that should be studied in depth by all would-be mathematicians.' Hans Sachs, American Mathematical Society

Book Description

Popular with students and instructors alike, this accessible and highly readable undergraduate textbook has now been revised to include end-of-chapter summaries, more challenging exercises, new results and a list of further reading. Complete solutions to all of the exercises are also provided in a new Instructors' Manual available online.

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Customer Reviews

4.5 out of 5 stars
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The book assumes minimal background in mathematics.
Shankar N. Swamy
The problems are not challenging enough to give you a real skill in all of these geometries, although they do become more challenging in later chapters.
J. J. K. Swart
Despite these limitations, Brannan et al. is a good and enjoyable book for anyone from high school through first-year graduate level in mathematics.
William A. Huber

Most Helpful Customer Reviews

51 of 51 people found the following review helpful By William A. Huber on May 6, 2003
Format: Paperback
A quarter century ago I noticed that some of the graduate physics students in my university were carrying around copies of Scientific American. Armed with that clue, I dug out every article on the newly discovered fundamental particles. Within the space of a week of fairly easy reading I was able to acquire a good sense of what this subject was all about. These articles explained the basic stuff our professors assumed we must know (but most of us surely didn't).
Brannan, Esplen, and Gray's Geometry accomplish for math what those Scientific American articles did for physics: speaking at a level accessible to anyone with a good high school education, they bring the interested reader up to speed in affine, projective, hyperbolic, inversive, and spherical geometry. They provide the simple explanations, diagrams, and computational details you are assumed to know-but probably don't-when you take advanced courses in topology, differential geometry, algebraic geometry, Lie groups, and more. I wish I had had a book like this when I learned those subjects.
Individual chapters of about 50 pages focus on distinct geometries. Each one is written to be studied in the course of five evenings: a week or two of work apiece. Although they build sequentially, just about any of them can be read after mastering the basic ideas of projective geometry (chapter 3) and inversive geometry (chapter 5). This makes the latter part of the book relatively accessible even to the less-committed reader and an effective handbook for someone looking for just an overview and basic formulas.
The approach is surprisingly sophisticated. The authors do not shy away from introducing and using a little bit of group theory, even at the outset. (Scientific American, even in its heyday, never dared do that.
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20 of 20 people found the following review helpful By J. J. K. Swart on February 16, 2003
Format: Paperback
This book gives a beautiful overview of geometry of 2 dimensions. All of the book is about many plane geometries I have heard of, but didn't really know. This book changed that.
The first chapter treats some basics about conics. The second chapter is on affine geometry. The third and fourth chapters are about projective geometry. In the fifth chapter you will be led through Inversive geometry which functions as a base for the sixth and seventh chapter. The sixth chapter has as itst title Non-Euclidean geometry, but it is in fact the Hyperbolic geometry of Boljay in a formulation of Henry Poincaré. The seventh chapter is about Spherical Geometry. In the eighth chapter all of these geometries are demonstrated to be special cases of the Kleinian vieuw of geometry: that is, every geometry can be seen as consisting of the invariants of a specific group of transformations of the 2 dimensional plane into itself. It is clearly demonstrated that this is less trivial than you would expect.
I learned two things from this book. The first is, that you can, in principle, prove every theorem of geometry by just using Euclidean geometry. But if you do this, the amount of work it takes can be very huge indeed. It is a far better strategy to try to determine what geometry is best suited for the problem at hand, and solve it within that geometry.
Since the book gives a very clear picture not only of the particular geometries, but also to how the geometries relate to each other, you have, as an extra bonus, insight in the level of abstraction and the scope of your theorem.
The second thing I learned is how you can use geometry to make concepts as simple as 'triangle' precise. What I mean is this: a right angle triangle is not the same as an equilateral triangle.
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16 of 18 people found the following review helpful By Shankar N. Swamy on January 2, 2005
Format: Paperback
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.
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