Elementary Geometry in Hyperbolic Space
eBook - PDF

Elementary Geometry in Hyperbolic Space

  1. 236 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Elementary Geometry in Hyperbolic Space

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Yes, you can access Elementary Geometry in Hyperbolic Space by Werner Fenchel in PDF and/or ePUB format, as well as other popular books in Mathematics & Geometry. We have over one million books available in our catalogue for you to explore.

Information

Publisher
De Gruyter
Year
2011
Print ISBN
9783110117349
eBook ISBN
9783110849455
Edition
1
Topic
Mathematics
Subtopic
Geometry
Index
Mathematics

Table of contents

  1. I. Preliminaries
  2. 1. Quaternions
  3. 2. The hyperbolic functions
  4. 3. Trace relations
  5. 4. The fractional linear group and the cross ratio
  6. Notes to Chapter I
  7. II. The Möbius Group
  8. 1. Similarity transformations
  9. 2. The extended space. Orientation. Angular measure
  10. 3. Inversion
  11. 4. Circle- and sphere-preserving transformations
  12. 5. The Möbius group of the upper half-space
  13. Notes to Chapter II
  14. III. The Basic Notions of Hyperbolic Geometry
  15. 1. Lines and planes. Convexity
  16. 2. Orthogonality
  17. 3. The invariant Riemannian metric
  18. 4. The hyperbolic metric
  19. 5. Transformation to the unit ball
  20. Notes to Chapter III
  21. IV. The Isometry Group of Hyperbolic Space
  22. 1. Characterization of the isometry group
  23. 2. Classification of the motions
  24. 3. Reversals
  25. 4. The isometry group of a plane
  26. 5. The spherical and cylindric surfaces
  27. Notes to Chapter IV
  28. V. Lines
  29. 1. Line matrices
  30. 2. Oriented lines
  31. 3. Double crosses
  32. 4. Transversals
  33. 5. Pencils and bundles of lines
  34. Notes to Chapter V
  35. VI. Right-Angled Hexagons
  36. 1. Right-angled hexagons and pentagons
  37. 2. Trigonometric relations for right-angled hexagons
  38. 3. Trigonometric relations for polygons in a plane
  39. 4. Determination of a hexagon by three of its sides
  40. 5. The amplitudes of a right-angled hexagon
  41. 6. Transversals of a right-angled hexagon
  42. 7. The bisectors and radii of a right-angled hexagon
  43. 8. The medians of a right-angled hexagon
  44. 9. The altitudes of a right-angled hexagon
  45. Notes to Chapter VI
  46. VII. Points and Planes
  47. 1. Point and plane matrices
  48. 2. Incidence and orthogonality
  49. 3. Distances and angles
  50. 4. Pencils of points and planes
  51. 5. Bundles of points and planes
  52. 6. Tetrahedra
  53. Notes to Chapter VII
  54. VIII. Spherical Surfaces
  55. 1. Equations of spherical surfaces
  56. 2. An invariant of a pair of spherical surfaces
  57. 3. The power of a point with respect to a spherical surface
  58. 4. The radical plane of a pair of spherical surfaces
  59. 5. Linear families of spherical surfaces
  60. Notes to Chapter VIII
  61. IX. Area and Volume
  62. 1. Various coordinate systems
  63. 2. Area
  64. 3. Volume of some bodies of revolution
  65. 4. Volume of polyhedra
  66. Notes to Chapter IX
  67. References
  68. Index