The Real Projective Plane (Hardcover)

~ (Author), G. Beck (Contributor) "1.1 Introduction. The ordinary geometry taught in school, dealing with circles, angles, parallel lines, similar triangles and so on, is called Euclidean geometry because it..." (more)
Key Phrases: quadrangular involution, degenerate polarity, harmonic net, Alex Rosenberg, Blaise Pascal (more...)

Editorial Reviews

Product Description

This introduction to projective geometry can be understood by anyone familiar with high school geometry and algebra. The restriction of real geometry of two dimensions allows every theorem to be illustrated in a diagram. The subject is, in a sense, even simpler than Euclid, whos constructions involved a ruler and a compass: here we have constructions using rulers alone. A strict axiomatic treatment is followed only to the point of letting the student see how it is done, but then relaxed to avoid becoming tedious. After two introductory chapters, the concept of conntinuity is introduced by means of an unusual, but intuitively acceptable axiom. Subsequent chapters then treat one- and two-dimensional projectivities, conics, affine geometry, and Euclidean geometry. Chapter 10 continues the discussion of continuity at a more sophisticated level, and the remaining chapters introduce coordinates and their uses. An appendix by George Beck describes Mathematica scripts that can generate illustrations for several chapters; they are provided on a diskette included with the book. (both PC and Macintosh versions are available.

Product Details

• Hardcover: 222 pages
• Publisher: Springer; 3rd edition (December 23, 1992)
• Language: English
• ISBN-10: 0387978895
• ISBN-13: 978-0387978895
• Product Dimensions: 9.5 x 6.4 x 0.8 inches
• Shipping Weight: 1.3 pounds
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon.com Sales Rank: #2,312,537 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

21 of 22 people found the following review helpful:

5.0 out of 5 stars standard reference. NOT for highschool students., August 21, 2001

By	Xah Lee (Mountain View, CA USA) - See all my reviews

This book teaches the basics of projective geometry from an abstract and axiomatic approach. The book claims that any bright highschool student should be able to understand it, but it's more likely that a 3rd year undergraduate math major will have difficulty digesting the book by himself. This is because its axiomatic approach, plus it is written extremely succinctly. If you are going to read this book on your own, some experience with modern math and history of geometry is a good pre-requisite. The book by itself is an excellent work. I believe it is the only modern, strictly axiomatic approach to projective geometry of real plane. This is a standard reference to projective geometers. The software that accompanies the book is of no utility. It is written in 1993 era, requires you to have Mathematica, is not useful, and also because it comes in an early 90s 5.5" floppy disk. (I think it's on mathsource.com) If you want to learn projective geometry with some computer software enhancement, I highly suggest CabriGeometry II or The Geometer's Sketchpad, Cinderella or other similar ones. Note that projective geometry of lower dimensions is essentially theory of conic sections. Anyone who are serious about conics should study projective geometry. Projective Geometry in the 18th century were thought as the top most parent of all geometry and highly exhorted. --Xah Lee