Projective Geometry [Paperback]

H.S.M. Coxeter (Author)

Book Description

Publication Date: October 9, 2003 | ISBN-10: 0387406239 | ISBN-13: 978-0387406237 | Edition: 2nd

In Euclidean geometry, constructions are made with ruler and compass. Projective geometry is simpler: its constructions require only a ruler. In projective geometry one never measures anything, instead, one relates one set of points to another by a projectivity. The first two chapters of this book introduce the important concepts of the subject and provide the logical foundations. The third and fourth chapters introduce the famous theorems of Desargues and Pappus. Chapters 5 and 6 make use of projectivities on a line and plane, respectively. The next three chapters develop a self-contained account of von Staudt's approach to the theory of conics. The modern approach used in that development is exploited in Chapter 10, which deals with the simplest finite geometry that is rich enough to illustrate all the theorems nontrivially. The concluding chapters show the connections among projective, Euclidean, and analytic geometry.

Editorial Reviews

From the Back Cover

In Euclidean geometry, constructions are made with a ruler and compass. Projective geometry is simpler: its constructions require only a ruler. In projective geometry one never measures anything, instead, one relates one set of points to another by a projectivity. This classic book introduces the important concepts of the subject and provides the logical foundations, including the famous theorems of Desargues and Pappus and a self-contained account of von Staudt's approach to the theory of conics. The modern approach used in this account is then utilized to deal with the simplest finite geometry that is rich enough to illustrate all the theorems nontrivially. The book concludes by demonstrating the connections among projective, Euclidean, and analytic geometry. From the reviews of Projective Geometry: ...The book is written with all the grace and lucidity that characterize the author's other writings. ...  -T. G. Room, Mathematical Reviews This is an elementary introduction to projective geometry based on the intuitive notions of perspectivity and projectivity and, formally, on axioms essentially the same as the classical ones of Vebber and Young...This book is an excellent introduction. - T. G. Ostrom, Zentralblatt

Product Details

• Paperback: 174 pages
• Publisher: Springer; 2nd edition (October 9, 2003)
• Language: English
• ISBN-10: 0387406239
• ISBN-13: 978-0387406237
• Product Dimensions: 9.2 x 6.1 x 0.5 inches
• Shipping Weight: 9.6 ounces (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #708,463 in Books (See Top 100 in Books)

More About the Author

Discover books, learn about writers, read author blogs, and more.

Customer Reviews

Most Helpful Customer Reviews

15 of 20 people found the following review helpful:

4.0 out of 5 stars Good Concise Coverage of Synthetic Projective Geometry, February 7, 2007

By 

R. Schultz - See all my reviews
(REAL NAME)   

This review is from: Projective Geometry (Paperback)

Coxeter provides good coverage of the fundamental concepts of synthetic projective geometry. This is a good introductory book. The examples provided are clear. Coxeter's style is concise. Topics such as Desargues theorem , Pappus's theorem and conics are covered. The solutions to some exercises can be found in the back of the book. The book addresses finite geometries and analytic projective with a chapter on each.