Meaning of hyperbolic geometry

hyperbol'ic geom'etry

Pronunciation: [key]
— Geom. Geom.
  1. the branch of non-Euclidean geometry that replaces the parallel postulate of Euclidean geometry with the postulate that two distinct lines may be drawn parallel to a given line through a point not on the given line. Cf. Riemannian geometry.
Random House Unabridged Dictionary, Copyright © 1997, by Random House, Inc., on Infoplease.