Hyperbolic Games

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 Beltami-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).

Languages	English
License	Freeware (GNU General Public License)
FAQ	Geometry Games FAQ
Last update	17 May 2009 (Version 1.0) Improved hand cursor visibility on sphere Improved Help file and Study Questions
Download	Hyperbolic Games for Mac OS 10.4 or later (8.8 MB) Hyperbolic Games for Windows XP or later (8.7 MB) Hyperbolic Games Source Code (8.9 MB)

Questions? Contact Jeff Weeks.

This material is based upon work supported by the National Science Foundation under Grant No. 0822022. 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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