KnowraHyperbolic planeLinked fromLinked fromThe 9 pages that link to Hyperbolic plane, each with the reason it gives.All 9Broader topic 4Related 3Compared with 2Riemannian manifoldBroader topic: It contrasts sharply with the sphere through its negative curvature and geodesic geometry.Parallel postulateBroader topic: Its geometry realizes the case where many parallels pass through an exterior point.Euclidean planeCompared with: Its parallel behavior differs from the Euclidean plane’s unique parallel.Nikolai LobachevskyBroader topic: It is the setting for the geometric properties Lobachevsky studied.Riemann sphereCompared with: Its noncompact geometry contrasts with the sphere’s compact positive-curvature geometry.PseudosphereRelated: The pseudosphere locally matches its geometry but omits regions needed for a complete model.Hyperbolic triangleRelated: The triangle’s sides and interior angles are measured within this curved plane.Selberg trace formulaBroader topic: It is the basic space on which the groups in the classical formula act.Hjelmslev's theoremRelated: The theorem concerns triangles embedded in this fixed-curvature plane.