Projective Geometry, 2E by H.S.M. Coxeter
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Projective Geometry, 2E written by
H.S.M. Coxeter .
In Euclidean geometry, constructions are made with ruler and compass. Projective geometry is simpler: its constructions require only a ruler. In projective geometry one never measures anything, instead, one relates one set of points to another by a projectivity. The first two chapters of this book introduce the important concepts of the subject and provide the logical foundations. The third and fourth chapters introduce the famous theorems of Desargues and Pappus. Chapters 5 and 6 make use of projectivities on a line and plane, repectively. The next three chapters develop a self-contained account of von Staudt's approach to the theory of conics. The modern approach used in that development is exploited in
10, which deals with the simplest finite geometry that is rich enough to illustrate all the theorems nontrivially. The concluding chapters show the connections among projective, Euclidean, and analytic geometry.
Why should one study Pappian geometry? To this question, put by enthusiasts for ternary rings, The author reply that the classical projective plane is an easy first step. The theory of conics is beautiful in itself and provides a natural introduction to algebraic geometry.
Apart from the correction of many small errors, the changes made in this revised edition are chiefly as follows. Veblen's notation Q(ABC, DEF) for a quadrangular set of six points has been replaced by the "permutation symbol" (AD) (BE) (CF), which indicates more immediately that there is an involution interchanging the points on each pair of opposite sides of the quadrangle. Although most of the work is in the projective plane, it has seemed worth while (in Section 3.2) to show how the Desargues configuration can be derived as a section of the "complete 5-point" in space. Section 4.4 emphasizes the analogy between the configurations of Desargues and Pappus.
Book Detail :-
Title: Projective Geometry
Author(s): H.S.M. Coxeter
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About Author :-
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 :-
Projective Geometry, 2E written by
cover the following topics.
2. Triangles and Quadrangles
3. The Principle of Duality
4. The Fundamental Theorem and Pappus's Theorem
5. One-dimensional Projectivities
6. Two-dimensional Projectivities
8. The Conic
9. The Conic, Continued
10. A Finite Projective Plane
Answers to Exercises
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