UID:
almahu_9947360003002882
Format:
Online-Ressource (xi, 225 p)
,
ill
Edition:
Online-Ausg. Palo Alto, Calif ebrary 2011 Electronic reproduction; Available via World Wide Web
ISBN:
0899254934 (U.S.)
,
3110117347
,
9783110117349
Series Statement:
De Gruyter studies in mathematics 11
Content:
Elementary Geometry in Hyperbolic Space
Note:
Includes bibliographical references and index
,
2. An invariant of a pair of spherical surfaces3. The power of a point with respect to a spherical surface; 4. The radical plane of a pair of spherical surfaces; 5. Linear families of spherical surfaces; Notes to Chapter VIII; IX. Area and Volume; 1. Various coordinate systems; 2. Area; 3. Volume of some bodies of revolution; 4. Volume of polyhedra; Notes to Chapter IX; References; Index.
,
4. Determination of a hexagon by three of its sides5. The amplitudes of a right-angled hexagon; 6. Transversals of a right-angled hexagon; 7. The bisectors and radii of a right-angled hexagon; 8. The medians of a right-angled hexagon; 9. The altitudes of a right-angled hexagon; Notes to Chapter VI; VII. Points and Planes; 1. Point and plane matrices; 2. Incidence and orthogonality; 3. Distances and angles; 4. Pencils of points and planes; 5. Bundles of points and planes; 6. Tetrahedra; Notes to Chapter VII; VIII. Spherical Surfaces; 1. Equations of spherical surfaces.
,
I. Preliminaries; 1. Quaternions; 2. The hyperbolic functions; 3. Trace relations; 4. The fractional linear group and the cross ratio; Notes to Chapter I; II. The Möbius Group; 1. Similarity transformations; 2. The extended space. Orientation. Angular measure; 3. Inversion; 4. Circle- and sphere-preserving transformations; 5. The Möbius group of the upper half-space; Notes to Chapter II; III. The Basic Notions of Hyperbolic Geometry; 1. Lines and planes. Convexity; 2. Orthogonality; 3. The invariant Riemannian metric; 4. The hyperbolic metric; 5. Transformation to the unit ball.
,
Notes to Chapter IIIIV. The Isometry Group of Hyperbolic Space; 1. Characterization of the isometry group; 2. Classification of the motions; 3. Reversals; 4. The isometry group of a plane; 5. The spherical and cylindric surfaces; Notes to Chapter IV; V. Lines; 1. Line matrices; 2. Oriented lines; 3. Double crosses; 4. Transversals; 5. Pencils and bundles of lines; Notes to Chapter V; VI. Right-Angled Hexagons; 1. Right-angled hexagons and pentagons; 2. Trigonometric relations for right-angled hexagons; 3. Trigonometric relations for polygons in a plane.
Additional Edition:
ISBN 9783110849455
Language:
English
DOI:
10.1515/9783110849455
URL:
http://www.degruyter.com/doi/book/10.1515/9783110849455
