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Perspectives on Projective Geometry: A Guided Tour Through Real and Complex Geometry (Hardback)

Perspectives on Projective Geometry: A Guided Tour Through Real and Complex Geometry (Hardback)

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Condition

LIKE NEW: This book is in excellent, like-new condition. It was printed on acid-free paper.

Product Details

Continued from the back cover: "In particular, [this book] 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 the 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."

Chapters

  1. Pappos's Theorem: Nine Proofs and Three Variations
Part I. Projective Geometry
  1. Projective Planes
  2. Homogeneous Coordinates
  3. Lines and Cross-Ratios
  4. Calculating with Points on Lines
  5. Determinants
  6. More on Bracket Algebra
Part II. Working and Playing with Geometry
  1. Quadrilateral Sets and Liftings
  2. Conics and Their Duals
  3. Conics and Perspectivity
  4. Calculating with Conics
  5. Projective d-space
  6. Diagram Techniques
  7. Working with Diagrams
  8. Configurations, Theorems, and Bracket Expressions
Part III. Measurements
  1. Complex Numbers: A Primer
  2. The Complex Projective Line
  3. Euclidean Geometry
  4. Euclidean Structures from a Projective Perspective
  5. Cayley-Klein Geometries
  6. Measurements and Transformations
  7. Cayley-Klein Geometries at Work
  8. Circles and Cycles
  9. Non-Euclidean Geometry: A Historical Interlude
  10. Hyperbolic Geometry
  11. Selected Topics in Hyperbolic Geometry
  12. What We Did Not Touch
The book concludes with References and Index.
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AUTHOR: Richter-Gebert;Jürgen
PUBLISHER: Springer
ISBN-13: 9783642172854
ISBN-10: 3642172857
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Perspectives on Projective Geometry: A Guided Tour Through Real and Complex Geometry (Hardback)
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