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Thursday, January 7, 2016

HyperRogue and hyperbolic geometry

One mathematical field that I find particularly interesting and beautiful is hyperbolic geometry: it's the same as Euclidean geometry, but takes the axiom that for any line and any point outside of that line, there's more than one line passing through that point which doesn't intersect the given line. In the past, hyperbolic geometry has featured heavily in the works of mathematically inclined artists like M.C. Escher.

Recently, over the past few years, independent developer ZenoRogue has created a video game that utilizes hyperbolic geometry, by the name of HyperRogue. The game is in the roguelike genre, but rather than using turn-based game evolution on a square or hexagonal grid, the game is based on the truncated order-7 triangular tiling of the hyperbolic plane, often called the "hyperbolic soccer ball," which is what gives it all sorts of interesting non-Euclidean properties. Keep reading to watch a Center of Math original video of HyperRogue gameplay, along with commentary about how the mathematical properties of hyperbolic space affect the game.

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