Torus Games or Hyperbolic Games?
Torus Games

Most people will want to start with a different app, the Torus Games, which offers a selection of easily playable games for a broad audience, all implemented in multi-connected spaces in 2 and 3 dimensions. The Torus Games are available for free from the Torus Games web page.

Hyperbolic Games

By contrast the present app, the Hyperbolic Games, is for math students — advanced undergrads and beginning grad students. 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:

On the horizon…

A newer, easier Hyperbolic Pool app is at the planning stage. It will focus on hyperbolic geometry itself, without the distraction of a multi-connected topology and therefore with no repeating images. Instead, it will implement pool on a pentagonal pool table with all 90° angles. To bring out the relationships among the different geometries, it will also offer spherical pool on a triangular table with 90° angles, and Euclidean pool on a square table with 90° angles. This new app will run in 3D, presenting the pool table as a horizontal slice of the 3D space. (In mathematical terms, the pool table will be a cross-sectional slice of H³, E³ or S³.) If plans go as intended, the app will run in virtual reality, and will optionally include a real physical table to let players feel with their hands what they see with their eyes. (Yes, a square physical table can be made to match up with a virtual pentagonal one, but only locally!)

Still have a question? Submit it to the Geometry Games Contact Page for a more-or-less prompt reply.

The latest Hyperbolic Games are freely available at www.geometrygames.org/HyperbolicGames. The Hyperbolic Games may be freely distributed under the terms of the GNU General Public License.

© 2018 by Jeff Weeks