Projective Geometry - Paperback

EAN (ISBN-13): 9780387406237
ISBN (ISBN-10): 0387406239
Hardcover
Paperback
Publishing year: 2004
Publisher: Springer
162 Pages
Weight: 0,308 kg
Language: eng/Englisch

Book in our database since 2007-05-18T09:24:06+01:00 (London)
Detail page last modified on 2024-03-10T04:35:14+00:00 (London)
ISBN/EAN: 9780387406237

ISBN - alternate spelling:
0-387-40623-9, 978-0-387-40623-7
Alternate spelling and related search-keywords:
Book author: harold coxeter, staudt, von see, coxe, desargues
Book title: projective geometry coxeter

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Information from Publisher

Author: H.S.M. Coxeter
Title: Projective Geometry
Publisher: Springer; Springer US
162 Pages
Publishing year: 2003-10-09
New York; NY; US
Printed / Made in
Weight: 0,570 kg
Language: English
48,14 € (DE)
49,49 € (AT)
53,50 CHF (CH)
POD
XII, 162 p.

BC; Geometry; Hardcover, Softcover / Mathematik/Geometrie; Geometrie; Verstehen; Geometry

1 Introduction.- 1.1 What is projective geometry?.- 1.2 Historical remarks.- 1.3 Definitions.- 1.4 The simplest geometric objects.- 1.5 Projectivities.- 1.6 Perspectivities.- 2 Triangles and Quadrangles.- 2.1 Axioms.- 2.2 Simple consequences of the axioms.- 2.3 Perspective triangles.- 2.4 Quadrangular sets.- 2.5 Harmonic sets.- 3 The Principle of Duality.- 3.1 The axiomatic basis of the principle of duality.- 3.2 The Desargues configuration.- 3.3 The invariance of the harmonic relation.- 3.4 Trilinear polarity.- 3.5 Harmonic nets.- 4 The Fundamental Theorem and Pappus’s Theorem.- 4.1 How three pairs determine a projectivity.- 4.2 Some special projectivities.- 4.3 The axis of a projectivity.- 4.4 Pappus and Desargues.- 5 One-dimensional Projectivities.- 5.1 Superposed ranges.- 5.2 Parabolic projectivities.- 5.3 Involutions.- 5.4 Hyperbolic involutions.- 6 Two-dimensional Projectivities.- 6.1 Projective collineations.- 6.2 Perspective collineations.- 6.3 Involutory collineations.- 6.4 Projective correlations.- 7 Polarities.- 7.1 Conjugate points and conjugate lines.- 7.2 The use of a self-polar triangle.- 7.3 Polar triangles.- 7.4 A construction for the polar of a point.- 7.5 The use of a self-polar pentagon.- 7.6 A self-conjugate quadrilateral.- 7.7 The product of two polarities.- 7.8 The self-polarity of the Desargues configuration.- 8 The Conic.- 8.1 How a hyperbolic polarity determines a conic.- 8.2 The polarity induced by a conic.- 8.3 Projectively related pencils.- 8.4 Conics touching two lines at given points.- 8.5 Steiner’s definition for a conic.- 9 The Conic, Continued.- 9.1 The conic touching five given lines.- 9.2 The conic through five given points.- 9.3 Conics through four given points.- 9.4 Two self-polar triangles.- 9.5 Degenerate conies.- 10 A Finite Projective Plane.- 10.1 The idea of a finite geometry.- 10.2 A combinatorial scheme for PG(2, 5).- 10.3 Verifying the axioms.- 10.4 Involutions.- 10.5 Collineations and correlations.- 10.6 Conies.- 11 Parallelism.- 11.1 Is the circle a conic?.- 11.2 Affine space.- 11.3 How two coplanar lines determine a flat pencil and a bundle.- 11.4 How two planes determine an axial pencil.- 11.5 The language of pencils and bundles.- 11.6 The plane at infinity.- 11.7 Euclidean space.- 12 Coordinates.- 12.1 The idea of analytic geometry.- 12.2 Definitions.- 12.3 Verifying the axioms for the projective plane.- 12.4 Projective collineations.- 12.5 Polarities.- 12.6 Conics.- 12.7 The analytic geometry of PG(2, 5).- 12.8 Cartesian coordinates.- 12.9 Planes of characteristic two.- Answers to Exercises.- References.