Projective Geometry

With 71 illustrations

H.S.M Coxeter

162 pages, parution le 01/01/1987 (2^eme édition)

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Résumé

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 Chapter 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.

Written for:
Undergraduate mathematics students

Introduction
Triangles and Quadrangles
The Principle of Duality
The Fundamental Theorem and Pappus's Theorem
One-dimensional Projectivities
Two-dimensional Projectivities
Polarities
The Conic
The Conic, Continued
A Finite Projective Plane
Parallelism
Coordinates

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	H.S.M Coxeter
Parution	01/01/1987
Édition	2^eme édition
Nb. de pages	162
Format	15,5 x 23,5
Couverture	Broché
Poids	310g
Intérieur	Noir et Blanc
EAN13	9780387406237
ISBN13	978-0-387-40623-7