| 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. |
| hyperbolic geometry | |
noun | |
| (mathematics) a non-Euclidean geometry in which the parallel axiom is replaced by the assumption that through any point in a plane there are two or more lines that do not intersect a given line in the plane; "Karl Gauss pioneered hyperbolic geometry" |
