Tossup

A group is described by this adjective if every triangle on its Cayley graph is delta-thin, a concept introduced by Mikhael Gromov. By the uniformization theorem, this adjective describes every Riemann surface that isn’t the Riemann sphere (10[1])or the quotient of the complex plane by a discrete subgroup. (-5[1])In a model of a plane described by this adjective, a horocycle (-5[1])is the set of (10[2])points tangent to the boundary circle. A plane described by this adjective (10[1])is modeled by the Poincaré (“pwon-car-AY”) disk. (10[3])A (10[1])plane (-5[1])is described by this adjective if every point is a saddle point or if the plane has constant negative curvature. (10[3]-5[2])Triangles have angles that sum to (-5[1])less than 180 (10[2]-5[1])degrees in a geometry (10[1])described by this word (-5[1])that was introduced by Nikolai (10[1])Lobachevsky. For 10 points, name this adjective derived from a conic section with two non-connected (10[1])curves. (10[1])■END■ (10[6]0[1])

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