Download PDF The Real Projective Plane, by H.S.M. Coxeter
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The Real Projective Plane, by H.S.M. Coxeter
Download PDF The Real Projective Plane, by H.S.M. Coxeter
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Along with many small improvements, this revised edition contains van Yzeren's new proof of Pascal's theorem (§1.7) and, in Chapter 2, an improved treatment of order and sense. The Sylvester-Gallai theorem, instead of being introduced as a curiosity, is now used as an essential step in the theory of harmonic separation (§3.34). This makes the logi cal development self-contained: the footnotes involving the References (pp. 214-216) are for comparison with earlier treatments, and to give credit where it is due, not to fill gaps in the argument. H.S.M.C. November 1992 v Preface to the Second Edition Why should one study the real plane? To this question, put by those who advocate the complex plane, or geometry over a general field, I would reply that the real plane is an easy first step. Most of the prop erties are closely analogous, and the real field has the advantage of intuitive accessibility. Moreover, real geometry is exactly what is needed for the projective approach to non· Euclidean geometry. Instead of introducing the affine and Euclidean metrics as in Chapters 8 and 9, we could just as well take the locus of 'points at infinity' to be a conic, or replace the absolute involution by an absolute polarity.
- Sales Rank: #3545391 in Books
- Brand: Brand: Springer
- Published on: 1993-01-01
- Original language: English
- Number of items: 1
- Dimensions: 9.25" h x .55" w x 6.10" l, .76 pounds
- Binding: Paperback
- 227 pages
- Used Book in Good Condition
Most helpful customer reviews
28 of 29 people found the following review helpful.
standard reference. NOT for highschool students.
By Xah Lee
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
3 of 5 people found the following review helpful.
The REAL one !!!
By André Gargoura
The unbeatable book on projective geometry and the basis of Coxeter's treatment of non-euclidean geometries.
I've discovered that book while reading Hofstadter's " Le ton beau de Marot" and found it to be a little marvel.
Coxeter's other book "Projective Geometry" is not a duplication, rather a good complement.
Those books are part of Coxeter's geometry SUM : Introduction to Geometry, The real Projective Plane, Projective Geometry, Geometry Revisited, Non-Euclidean Geometry... to be included in the collection of anyone interested in mathematics.
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