41. Other useful models of hyperbolic geometry exist in Euclidean space, in which the metric is not preserved. 42. These forms, based on non-Euclidean hyperbolic geometry , are known today as hyperboloids of revolution. 43. The geometry on rapidity space is inherited from the hyperbolic geometry on velocity space via the map stated. 44. Interactive geometry and analysis takes place in the realm of euclidean geometry, spherical geometry or hyperbolic geometry . 45. Several authors still consider " non-Euclidean geometry " and " hyperbolic geometry " to be synonyms. 46. The characteristic postulate of hyperbolic geometry says that there are at least two lines of the latter type. 47. In the late 1970s, William Thurston introduced hyperbolic geometry into the study of knots with the hyperbolization theorem. 48. These together with the subspace hyperplanes separating hemispheres are the hypersurfaces of the Poincar?disc model of hyperbolic geometry . 49. M�bius transformations are also isometries of the hyperbolic plane, so in hyperbolic geometry all Apollonian gaskets are congruent. 50. However, in spherical geometry and hyperbolic geometry , there are infinitely many different shapes of right isosceles triangles.
