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  • © 1993

The Real Projective Plane

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  • ISBN: 978-1-4612-2734-2
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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xiv
  2. A Comparison of Various Kinds of Geometry

    • H. S. M. Coxeter, George Beck
    Pages 1-11
  3. Incidence

    • H. S. M. Coxeter, George Beck
    Pages 12-24
  4. Order and Continuity

    • H. S. M. Coxeter, George Beck
    Pages 25-38
  5. One-Dimensional Projectivities

    • H. S. M. Coxeter, George Beck
    Pages 39-54
  6. Two-Dimensional Projectivities

    • H. S. M. Coxeter, George Beck
    Pages 55-72
  7. Conics

    • H. S. M. Coxeter, George Beck
    Pages 73-91
  8. Projectivities on a Conic

    • H. S. M. Coxeter, George Beck
    Pages 92-104
  9. Affine Geometry

    • H. S. M. Coxeter, George Beck
    Pages 105-125
  10. Euclidean Geometry

    • H. S. M. Coxeter, George Beck
    Pages 126-146
  11. Continuity

    • H. S. M. Coxeter, George Beck
    Pages 147-154
  12. The Introduction of Coordinates

    • H. S. M. Coxeter, George Beck
    Pages 155-168
  13. The Use of Coordinates

    • H. S. M. Coxeter, George Beck
    Pages 169-199
  14. Back Matter

    Pages 200-227

About this book

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

  • Department of Mathematics, University of Toronto, Toronto, Canada

    H. S. M. Coxeter

  • Toronto, Canada

    George Beck

Bibliographic Information

  • Book Title: The Real Projective Plane

  • Authors: H. S. M. Coxeter, George Beck

  • DOI: https://doi.org/10.1007/978-1-4612-2734-2

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York, Inc. 1993

  • Hardcover ISBN: 978-0-387-97889-5

  • Softcover ISBN: 978-1-4612-7647-0

  • eBook ISBN: 978-1-4612-2734-2

  • Edition Number: 3

  • Number of Pages: XIV, 227

  • Additional Information: Originally published by Cambridge University Press

  • Topics: Geometry

Buying options

eBook USD 64.99
Price excludes VAT (USA)
  • ISBN: 978-1-4612-2734-2
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book USD 84.99
Price excludes VAT (USA)