The first person to offer a concrete interpretation of this system did so by interpretingstraight lines as geodesics on a surface of constant (*) negative curvature,
A conjecture put forth by Thurston states that the interior of an irreducible, atoroidal, sufficientlylarge compact 3-manifold is a manifold with this system. Models of this system include the upper halfplane model. The first person to offer a concrete interpretation of this system did so by interpretingstraight lines as geodesics on a surface of constant (*) negative curvature, the psuedosphere, and wasBeltrami. In this system, the area of a triangle is given by pi minus the sum of its interior angles; thus thesum of the interior angles of a triangle must always be less than pi. This system was discoveredindependently by both Bolyai and Lobachevsky. For 10 points, name this non-Euclidean geometry whichshares its name with a conic section.
A conjecture put forth by Thurston states that the interior of an irreducible, atoroidal, sufficientlylarge compact 3-manifold is a manifold with this system.
hyperbolic geometry [prompt on non-Euclidean geometry]