Similar in spirit to the Torus Games, the Hyperbolic Games add a new challenge: curvature. Players enjoy familiar games (maze, pool, sudoku) on hyperbolic, flat and spherical surfaces, while gaining first-hand experience with the effects of curvature (holonomy, geodesic convergence/divergence).
Unlike the Torus Games, which were designed for children ages 10 and up, the Hyperbolic Games are intended for college- and university-level geometry and topology classes. A set of Study Questions, accessible from the Hyperbolic Games' Help menu, introduces students to the concepts of holonomy and curvature, leading to a simple proof of the Gauss-Bonnet Theorem.
By letting the player vary his or her viewpoint, the Hyperbolic Games also highlight the under-appreciated fact that two traditional models of the hyperbolic plane are simply different views of the same fixed-radius surface in Minkowski space: the Beltrami-Klein model corresponds to a viewpoint at the origin (central projection) while the Poincaré disk model corresponds to a viewpoint one radian further back (stereographic projection).
Contact Jeff Weeks.
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This material is based upon work supported by the National Science Foundation under Grant No. 1136261. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.
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