Perspectives on Projective Geometry

A Guided Tour Through Real and Complex Geometry

  • Jürgen Richter-Gebert

Table of contents

  1. Front Matter
    Pages i-xxii
  2. Jürgen Richter-Gebert
    Pages 3-31
  3. Projective Geometry

    1. Front Matter
      Pages 33-33
    2. Jürgen Richter-Gebert
      Pages 35-46
    3. Jürgen Richter-Gebert
      Pages 47-66
    4. Jürgen Richter-Gebert
      Pages 67-78
    5. Jürgen Richter-Gebert
      Pages 79-92
    6. Jürgen Richter-Gebert
      Pages 93-107
    7. Jürgen Richter-Gebert
      Pages 109-123
  4. Working and Playing with Geometry

    1. Front Matter
      Pages 125-127
    2. Jürgen Richter-Gebert
      Pages 129-143
    3. Jürgen Richter-Gebert
      Pages 145-166
    4. Jürgen Richter-Gebert
      Pages 167-187
    5. Jürgen Richter-Gebert
      Pages 189-207
    6. Jürgen Richter-Gebert
      Pages 209-225
    7. Jürgen Richter-Gebert
      Pages 227-246
    8. Jürgen Richter-Gebert
      Pages 247-267
    9. Jürgen Richter-Gebert
      Pages 269-292
  5. Measurements

    1. Front Matter
      Pages 293-296
    2. Jürgen Richter-Gebert
      Pages 297-309

About this book

Introduction

Projective geometry is one of the most fundamental and at the same time most beautiful branches of geometry. It can be considered the common foundation of many other geometric disciplines like Euclidean geometry, hyperbolic and elliptic geometry or even relativistic space-time geometry. This book offers a comprehensive introduction to this fascinating field and its applications. In particular, it explains how metric concepts may be best understood in projective terms. One of the major themes that appears throughout this book is the beauty of the interplay between geometry, algebra and combinatorics. This book can especially be used as a guide that explains how geometric objects and operations may be most elegantly expressed in algebraic terms, making it a valuable resource for mathematicians, as well as for computer scientists and physicists. The book is based on the author’s experience in implementing geometric software and includes hundreds of high-quality illustrations.

Keywords

Cayley-Klein Geometries Geometric Operations Hyperbolic Geometry Invariant Theory Projective Geometry

Authors and affiliations

  • Jürgen Richter-Gebert
    • 1
  1. 1.Zentrum Mathematik (M10), LS GeometrieTU MünchenGarchingGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-17286-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-17285-4
  • Online ISBN 978-3-642-17286-1
  • About this book