Symmetry and Pattern in Projective Geometry

  • Eric Lord

Table of contents

  1. Front Matter
    Pages I-XI
  2. Eric Lord
    Pages 27-41
  3. Eric Lord
    Pages 43-77
  4. Eric Lord
    Pages 79-113
  5. Eric Lord
    Pages 115-132
  6. Eric Lord
    Pages 133-144
  7. Eric Lord
    Pages 145-171
  8. Back Matter
    Pages 173-184

About this book

Introduction

Symmetry and Pattern in Projective Geometry is a self-contained study of projective geometry which compares and contrasts the analytic and axiomatic methods.The analytic approach is based on homogeneous coordinates. Brief introductions to Plücker coordinates and Grassmann coordinates are also presented.

This book looks carefully at linear, quadratic, cubic and quartic figures in two, three and higher dimensions. It deals at length with the extensions and consequences of basic theorems such as those of Pappus and Desargues. The emphasis throughout is on special configurations that have particularly interesting symmetry properties.
 
The intricate and novel ideas of H S M Coxeter, who is considered one of the great geometers of the twentieth century, are also discussed throughout the text. The book concludes with a useful analysis of finite geometries and a description of some of the remarkable configurations discovered by Coxeter.
 
This book will be appreciated by mathematics undergraduate students and those wishing to learn more about the subject of geometry. Subject and theorems that are often considered quite complicated are made accessible and presented in an easy-to-read and enjoyable manner. 

Keywords

analytic projective geometry axioms of projective geometry finite projective geometry homogeneous coordinates synthetic projective geometry

Authors and affiliations

  • Eric Lord
    • 1
  1. 1.BangaloreIndia

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4471-4631-5
  • Copyright Information Springer-Verlag London 2013
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4471-4630-8
  • Online ISBN 978-1-4471-4631-5
  • About this book
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