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The Fixed Points of the Transformation
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absolute adjacent region algebraic curve algebraic relation angle A1 becomes belongs boundary Cayleyan circles orthogonal closed surface coefficients congruent points congruent sides consider constants corresponding curve diametral planes discontinuous group Dist distance doubly periodic functions elliptic geometry exceptional points finite number fixed circles fixed points formation Fuchsian group function F(z funda fundamental region Funktionen genus given region Gott group of linear Hence hyperbolic identical transformation infinite infinity integral inverse with respect Koebe linear transformation loxodromic Math mental region modular group number of inversions number of poles octahedron one-to-one origin parabolic point Poincare point congruent pole of H(z polygon principal circle rational functions real axis reflections region congruent Riemann's surface rotations Section shaded region shaded triangle simple automorphic function simply connected singularities sphere straight line tangent Theorem tion trans triangle functions Ueber unchanged uniformised by means upper half-plane vertex vertices z-plane zz'-plane