Absolutely Australia's Lowest Prices

Shop over 1.5 Million Toys in our Huge New Range

Projective Geometry


Product Description
Product Details

Table of Contents

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.

Promotional Information

Springer Book Archives

Ask a Question About this Product More...
Write your question below:
Look for similar items by category
Home » Books » Science » Mathematics » Geometry » General
How Fishpond Works
Fishpond works with suppliers all over the world to bring you a huge selection of products, really great prices, and delivery included on over 25 million products that we sell. We do our best every day to make Fishpond an awesome place for customers to shop and get what they want — all at the best prices online.
Webmasters, Bloggers & Website Owners
You can earn a 5% commission by selling Projective Geometry on your website. It's easy to get started - we will give you example code. After you're set-up, your website can earn you money while you work, play or even sleep! You should start right now!
Authors / Publishers
Are you the Author or Publisher of a book? Or the manufacturer of one of the millions of products that we sell. You can improve sales and grow your revenue by submitting additional information on this title. The better the information we have about a product, the more we will sell!
Item ships from and is sold by Fishpond World Ltd.
Back to top