Hyperbolic Games vs The Matrix Mentor

The Hyperbolic Games are similar in spirit to the Torus Games, but played on curved surfaces. Most people will want to start with the Torus Games instead, which offer a selection of easily playable games, designed for children ages 10 and up, all implemented in multi-connected spaces in 2 and 3 dimensions. The Hyperbolic Games, by contrast, are for math students — advanced undergraduates and beginning graduate 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: - 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.

Are matrices getting you down? Don’t worry… THE MATRIX MENTOR IS HERE TO HELP The Matrix Mentor provides a visual understanding of linear transformations. Where others may teach you the mathematical rules that can be hard to remember, our playground provides a visual and interactive demonstration of the inner workings. SCARED OF MATRICES? DON'T BE! At its core, The Matrix Mentor is a visual learning tool, designed to bring matrices from an abstract mathematical concept to a concrete application. Whether you think about vectors as 3D points or a RGB color value, the fundamentals hold true. - Experiment with different types of transformations - Discover how matrices interact with a given vector, or a whole grid of points - Develop your intuitive sense for reading matrices and linear transformations Do yourself a favour, and start playing with The Matrix Mentor today!