hyperbolic space | Lobachevsky-Bolyai-Gauss geometry

A non-Euclidean geometry, also called Lobachevsky-Bolyai-Gauss geometry, having constant sectional curvature -1. This geometry satisfies all of Euclid's postulates except the parallel postulate, which is modified to read: For any infinite straight line L and any point P not on it, there are many other infinitely extending straight lines that pass through P and which do not intersect L.

elliptic geometry | Euclidean geometry | hyperbolic metric | Klein-Beltrami model | non-Euclidean geometry | pseudosphere | Schwarz-Pick lemma