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Perspectives on Projective Geometry

A Guided Tour Through Real and Complex Geometry

By Jürgen Richter-Gebert

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This book provides a comprehensive introduction into the classical topic of projective geometry.  It   explains how metric concepts may be best understood in projective terms and explores the beauty of the interplay of geometry, algebra and combinatorics.

Full Description

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  • ISBN13: 978-3-6421-7285-4
  • 593 Pages
  • Publication Date: February 4, 2011
  • Available eBook Formats: PDF
Full Description
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.
Table of Contents

Table of Contents

  1. 1 Pappos's Theorem: Nine Proofs and Three Variations.
  2. 2 Projective Planes.
  3. 3 Homogeneous Coordinates.
  4. 4 Lines and Cross
  5. Ratios.
  6. 5 Calculating with Points on Lines.
  7. 6 Determinants.
  8. 7 More on Bracket Algebra.
  9. 8 Quadrilateral Sets and Liftings.
  10. 9 Conics and Their Duals.
  11. 10 Conics and Perspectivity.
  12. 11 Calculating with Conics.
  13. 12 Projective $d$
  14. space.
  15. 13 Diagram Techniques.
  16. 14 Working with diagrams.
  17. 15 Configurations, Theorems, and Bracket Expressions.
  18. 16 Complex Numbers: A Primer.
  19. 17 The Complex Projective Line.
  20. 18 Euclidean Geometry.
  21. 19 Euclidean Structures from a Projective Perspective.
  22. 20 Cayley
  23. Klein Geometries.
  24. 21 Measurements and Transformations.
  25. 22 Cayley
  26. Klein Geometries at Work.
  27. 23 Circles and Cycles.
  28. 24 Non
  29. Euclidean Geometry: A Historical Interlude.
  30. 25 Hyperbolic Geometry.
  31. 26 Selected Topics in Hyperbolic Geometry.
  32. 27 What We Did Not Touch.
  33. References.
  34. Index.

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