About the Book
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 64. Chapters: Hyperbolic function, Non-Euclidean geometry, Gyrovector space, SL2(R), Apollonian gasket, Split-quaternion, Triangle group, Poincare half-plane model, Fuchsian group, Hyperbolic space, Hyperbolic angle, Poincare metric, Hyperboloid model, Hilbert's theorem, Anosov diffeomorphism, Hyperbolization theorem, Schwarz lemma, Hyperbolic coordinates, Beltrami-Klein model, Rips machine, Poincare disk model, Mostow rigidity theorem, (2,3,7) triangle group, Hyperbolic motion, Pair of pants, Hypercycle, Hyperbolic triangle, Uniform tilings in hyperbolic plane, Hyperbolic tree, Angle of parallelism, Tameness theorem, Ultraparallel theorem, Hyperbolic 3-manifold, Macbeath surface, Saccheri quadrilateral, Ending lamination theorem, Caratheodory metric, Hjelmslev transformation, Weeks manifold, Picard horn, Hyperbolic Dehn surgery, Schoen-Yau conjecture, Geometric finiteness, Ideal triangle, Earthquake map, Bolza surface, Fuchsian model, The geometry and topology of three-manifolds, Upper half-plane, Double limit theorem, Complex geodesic, Hyperbolic manifold, Geometric topology, Hyperbolic law of cosines, Cusp neighborhood, Gieseking manifold, Arithmetic hyperbolic 3-manifold, Meyerhoff manifold, Non-positive curvature, Horocycle, Pleated surface, Tame manifold, Schwarz-Ahlfors-Pick theorem, Margulis lemma, Non-Euclidean crystallographic group, Apollonian sphere packing, Lambert quadrilateral, Hyperbolic volume, Horoball, Kleinian model, Bryant surface. Excerpt: A gyrovector space is a mathematical concept for studying hyperbolic geometry in analogy to the way vector spaces are used in Euclidean geometry. This vector-based approach has been developed by Abraham Albert Ungar from the late 1980s onwards. These gyrovectors can be used to unify the study of Euclidean and hyperbolic geometry. Soon after special relativity was developed...
