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By James W. Anderson

The geometry of the hyperbolic airplane has been an lively and engaging box of mathematical inquiry for many of the earlier centuries. This e-book offers a self-contained creation to the topic, delivering the reader with a company clutch of the strategies and strategies of this gorgeous zone of arithmetic. themes lined contain the higher half-space version of the hyperbolic aircraft, Möbius differences, the overall Möbius staff and the subgroup maintaining course size within the higher half-space version, arc-length and distance, the Poincaré disc version, convex subsets of the hyperbolic airplane, and the Gauss-Bonnet formulation for the world of a hyperbolic polygon and its purposes. This up-to-date moment variation additionally good points: an multiplied dialogue of planar versions of the hyperbolic aircraft coming up from complicated research; the hyperboloid version of the hyperbolic aircraft; a short dialogue of generalizations to better dimensions; many new exercises.

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