UID:
almahu_9947366704102882
Umfang:
1 online resource (341 p.)
ISBN:
1-281-76642-9
,
9786611766429
,
0-08-087311-1
Serie:
Pure and applied mathematics ; 3
Inhalt:
Projective geometry and projective metrics
Anmerkung:
Description based upon print version of record.
,
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
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II. 13. Collineations of ConicsII. 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
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IV. 26. Angles and Motions in Euclidean GeometryIV. 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
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V. 38. The Elliptic Line Element . Length and AreaV. 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
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VI. 51. Hyperbolic Spheres, Limit Spheres, and Equidistant SurfacesVI. 52. The Hyperbolic Group of Motions; VI. 53. Elliptic Geometry in Space; VI. 54. The Line Element of Elliptic Space; Bibliography; Index
,
English
Weitere Ausg.:
ISBN 0-12-374580-2
Sprache:
Englisch
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