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The Real Projective Plane

  • H. S. M. Coxeter
  • George Beck

Table of contents

  1. Front Matter
    Pages i-xiv
  2. H. S. M. Coxeter, George Beck
    Pages 1-11
  3. H. S. M. Coxeter, George Beck
    Pages 12-24
  4. H. S. M. Coxeter, George Beck
    Pages 25-38
  5. H. S. M. Coxeter, George Beck
    Pages 39-54
  6. H. S. M. Coxeter, George Beck
    Pages 55-72
  7. H. S. M. Coxeter, George Beck
    Pages 73-91
  8. H. S. M. Coxeter, George Beck
    Pages 92-104
  9. H. S. M. Coxeter, George Beck
    Pages 105-125
  10. H. S. M. Coxeter, George Beck
    Pages 126-146
  11. H. S. M. Coxeter, George Beck
    Pages 147-154
  12. H. S. M. Coxeter, George Beck
    Pages 155-168
  13. H. S. M. Coxeter, George Beck
    Pages 169-199
  14. Back Matter
    Pages 200-227

About this book

Introduction

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.

Keywords

Area Congruence Erlang Invariant Mathematica Pascal addition configuration correlation form projective geometry proof proving theorem transformation

Authors and affiliations

  • H. S. M. Coxeter
    • 1
  • George Beck
    • 2
  1. 1.Department of MathematicsUniversity of TorontoTorontoCanada
  2. 2.TorontoCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-2734-2
  • Copyright Information Springer-Verlag New York, Inc. 1993
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-7647-0
  • Online ISBN 978-1-4612-2734-2
  • Buy this book on publisher's site