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the real projective plane coxeter [pdf]

# The Real Projective Plane by H. S. M. Coxeter, George Beck

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The Real Projective Plane written by H. S. M. Coxeter, George Beck .
Along with many small improvements, this revised edition contains van Yzeren's new proof of Pascal's theorem (§1.7) and, in
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

Book Detail :-
Title: The Real Projective Plane
Edition:
Author(s): H. S. M. Coxeter, George Beck
Publisher: Springer-Verlag New York
Series:
Year: 1993
Pages: 235
Type: PDF
Language: English
ISBN: 978-1-4612-7647-0,978-1-4612-2734-2
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The author Harold Scott MacDonald "Donald" Coxeter , CC, FRS, FRSC (1907–2003) British-born Canadian geometer. He is regarded as one of the greatest geometers of the 20th century.
Coxeter was born in Kensington to Harold Samuel Coxeter and Lucy (née Gee). His father had taken over the family business of Coxeter & Son, manufacturers of surgical instruments and compressed gases (including a mechanism for anaesthetising surgical patients with nitrous oxide), but was able to retire early and focus on sculpting and baritone singing; Lucy Coxeter was a portrait and landscape painter who had attended the Royal Academy of Arts. A maternal cousin was the architect Sir Giles Gilbert Scott. He worked for 60 years at the University of Toronto and published twelve books.
Since 1978, the Canadian Mathematical Society have awarded the Coxeter–James Prize in his honor. He was made a Fellow of the Royal Society in 1950 and in 1997 he was awarded their Sylvester Medal. In 1990, he became a Foreign Member of the American Academy of Arts and Sciences and in 1997 was made a Companion of the Order of Canada. In 1973 he received the Jeffery–Williams Prize. A festschrift in his honour, The Geometric Vein, was published in 1982. It contained 41 essays on geometry, based on a symposium for Coxeter held at Toronto in 1979.

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Book Contents :- The Real Projective Plane written by H. S. M. Coxeter, George Beck cover the following topics.
1. A Comparision of Various Kinds of Geometry
2. Incidence
3. Order and Continuity
4. One Dimensional Projectivities
5. Two Dimensional Projectivities
6. Conices
7. Projectivities on a Conic
8. Affine Geometry
9. Euclidean Geometry
10. Continuity
11. The Introduction of Coordinates
12. The use of Coordinates
Appendix 1 The Complex Projective Plane
Appendix 2 How to Use Mathematica by George Beck
Bibiography
Index

Note:-

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