Hyperbolic Games vs Calcu

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.

Calcu-Logarithm performs calculations and helps user understand logarithms on advanced level: 1. Solves equation "y = log_a(x)” for “y”, “x”, and “a”, with relevant graphs. 2. Explains and illustrates how to compute log_e (x) from Taylor series. 3. Explains and illustrates how to compute log_10 (x) digit by digit (based on M.Goldberg algorithm). 4. Explains and provides proof of log_e definition as the integral of x inverse. 5. Simplifies logarithmic expressions and solves logarithmic equations with polynomials of up to 20th degree. 6. Includes virtual slide rule for multiplication and division. 7. Calculates, explains, and graphs logarithms of complex numbers. Developers welcome any feedback, please write to us at graphmath@aol.com. Please check out our other Math apps.