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© 2013

Symmetry and Pattern in Projective Geometry

Textbook

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

  1. 1.BangaloreIndia

Bibliographic information

Reviews

From the reviews:

“Here, readers meet a slice of geometry, intermediate between elementary Euclidean and modern algebraic, where first come the objects, extraordinary, surprising, and intriguing. By meeting and literally seeing these special objects, specifically linear configurations and various projective varieties of low dimension and low degree, undergraduates can--perhaps for the first time--really experience mathematics as a phenomenological science. … Summing Up: Highly recommended. Upper-division undergraduates through researchers/faculty.” (D. V. Feldman, Choice, Vol. 51 (2), October, 2013)

“The book under review presents an introduction to projective geometry as well as some preliminary results on algebraic geometry and finite geometries. … This is a well-illustrated, self-contained textbook on projective geometry. Both the basics and the significant facts are presented in an original manner. The book is intended for undergraduate students in mathematics and computer science.” (Georgi Hristov Georgiev, Mathematical Reviews, September, 2013)

“The author wanted to convey some of the fascination he feels for the subject. … Nice figures, some in color, illustrate perspective. … this is a nice introduction for those with an interest in geometry.” (Arthur Gittleman, Computing Reviews, July, 2013)