hyperbolic geometry

Meanings

1. A type of geometry that rejects the parallel postulate. Given a straight line L and a point p not on L, more than one straight line can be drawn through p without intersecting L.
2. A non-Euclidean geometry, that features the hyperbola as geodesic, and has constant negative curvature

Etymology

The terminology was introduced in 1871 by Felix Klein, who classified some non-Euclidean geometries as hyperbolisch (“hyperbolic”), elliptisch (“elliptical”), and parabolisch (“parabolic”).