These games are more challenging than the Torus Games because they combine a multi-connected topology with a non-Euclidean geometry. Mathematically they illustrate the following: - The hyperbolic plane, as a live scrollable object. - The under-appreciated fact that the 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). Players may pinch-to-zoom to pass from one to the other, or stop to view the model from any other distance. - The strong — but also under-appreciated — correspondence between the hyperbolic plane and an ordinary sphere. In particular, central projection of the sphere corresponds to the Beltrami-Klein model of the hyperbolic plane, and stereographic projection of the sphere corresponds to the Poincaré disk model of the hyperbolic plane. - The Klein quartic surface, viewed with its natural geometry. The sudoku puzzles take full advantage of the Klein quartic’s tremendous amount of symmetry.
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