Projective Geometry and Projective Metrics
Projective Geometry and Projective Metrics
Academic Press
Published on 29. August 2011
331 pages
978-0-08-087311-4 (ISBN)
Description
Projective Geometry and Projective Metrics
More details
Persons
Content
- Front Cover
- Projective Geometry and Projective Metrics
- Copyright Page
- TABLE OF CONTENTS
- Preface
- Chapter I. The Projective Plane
- I. 1. Ideal Points
- I. 2. The Projective Plane
- I. 3. Projective Coordinates
- I. 4. The Content of Projective Geometry. Duality Principle
- I. 5. Groups of Transformations. Projectivities
- I. 6. Cross Ratio . Intervals
- I. 7. Perspectivities
- I. 8. The Projectivities of Line on Itself
- I. 9. Collineations
- Exercises
- Chapter II. Polarities And Conic Sections
- II. 10. Polarities
- II. 11. Conic Sections
- II. 12. The Theorems of Steiner and Pascal
- II. 13. Collineations of Conics
- II. 14. Pencils of Conics
- Exercises
- Chapter III. Affine Geometry
- III. 15. The Content of Affine Geometry . The Affine Group
- III. 16. The Affine Theory of Conics
- III. 17. Convex Sets
- III. 18. The Equiaffine Group . Area
- Exercises
- Chapter IV. Projective Metrics
- IV. 19. Metric Spaces
- IV. 20. Segment, Straight Lines, Great Circles . Projective- Metric Spaces
- IV. 21. Perpendiculars in Open Two-Spaces
- IV. 22. Motions
- IV. 23. Motions of Open Two-Spaces
- IV. 24. Minkowskian Geometry
- IV. 25. Reflections in Minkowskian Geometry . Euclidean Geometry
- IV. 26. Angles and Motions in Euclidean Geometry
- IV. 27. The Euclidean Theory of Conics
- IV. 28. Hilbert's Geometry
- IV. 29. Motions and Area in Hilbert Geometry . Definition of Hyperbolic Geometry
- Exercises
- Chapter V. Non-Euclidean Geometry
- V. 30. Hyperbolic Trigonometry
- V. 31. Length and Area
- V. 32. Equidistant Curves and Limit Circles
- V. 33. Some Synthetic Properties of Hyperbolic Geometry
- V. 34. The Group of Hyperbolic Motions
- V. 35. Weierstrass Coordinates
- V. 36. Definition of Elliptic Geometry
- V. 37. Elliptic Trigonometry . Relation of Elliptic and Spherical Geometry
- V. 38. The Elliptic Line Element . Length and Area
- V. 39. Cayley's Method
- Exercises
- Chapter VI. Spatial Geometry
- VI. 40. Three-Dimensional Projective Space
- VI. 41. Collineations of the Projective Space
- VI. 42. Line Coordinates . Linear Complexes
- VI. 43. Polarities and Quadrics
- VI. 44. Linear Congruences and Reguli
- VI. 45. Affine Geometry in Space
- VI. 46. Convex Sets in Space
- VI. 47. Three-Dimensional Projective-Metrics
- VI. 48. Minkowskian Geometry in Space
- VI. 49. Euclidean Geometry in Space
- VI. 50. Hilbert's Geometry in Space . Hyperbolic Geometry
- VI. 51. Hyperbolic Spheres, Limit Spheres, and Equidistant Surfaces
- VI. 52. The Hyperbolic Group of Motions
- VI. 53. Elliptic Geometry in Space
- VI. 54. The Line Element of Elliptic Space
- Bibliography
- Index
