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

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

2. Projective Planes
3. Homogeneous Coordinates
4. Lines and Cross-Ratios
5. Calculating with Points on Lines
6. Determinants
7. More on Bracket Algebra

Part II. Working and Playing with Geometry

8. Quadrilateral Sets and Liftings
9. Conics and Their Duals
10. Conics and Perspectivity
11. Calculating with Conics
12. Projective d-space
13. Diagram Techniques
14. Working with Diagrams
15. Configurations, Theorems, and Bracket Expressions

Part III. Measurements

16. Complex Numbers: A Primer
17. The Complex Projective Line
18. Euclidean Geometry
19. Euclidean Structures from a Projective Perspective
20. Cayley-Klein Geometries
21. Measurements and Transformations
22. Cayley-Klein Geometries at Work
23. Circles and Cycles
24. Non-Euclidean Geometry: A Historical Interlude
25. Hyperbolic Geometry
26. Selected Topics in Hyperbolic Geometry
27. What We Did Not Touch

The book concludes with References and Index.