Hyperbolic Games
Free
2.1.4for iPhone, iPad and more
Age Rating
Hyperbolic Games Screenshots
About Hyperbolic Games
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.
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.
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What's New in the Latest Version 2.1.4
Last updated on Sep 4, 2020
Old Versions
Supports Wide Color displays
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Version History
2.1.4
Sep 4, 2020
Supports Wide Color displays
2.1.3
Apr 2, 2020
- Launch-screen format satisfies new App Store requirement
- Toolbar height adapts to default for iPhone or iPad
- Toolbar height adapts to default for iPhone or iPad
2.1.1
Nov 1, 2018
- Added screenshots for iPad Pro (3rd Gen)
2.1
Oct 26, 2018
- Updated for iOS 11 and 12
2.0
Feb 24, 2018
Hyperbolic Games FAQ
Click here to learn how to download Hyperbolic Games in restricted country or region.
Check the following list to see the minimum requirements of Hyperbolic Games.
iPhone
Requires iOS 12.0 or later.
iPad
Requires iPadOS 12.0 or later.
iPod touch
Requires iOS 12.0 or later.
Hyperbolic Games supports English