In our mind’s eye, the universe seems to go on forever. But using geometry we can explore a variety of three-dimensional shapes that offer alternatives to “ordinary” infinite space. When you gaze out ...

Dependencies are identified in two recently proposed first-order axiom systems for plane hyperbolic geometry. Since the dependencies do not specifically concern hyperbolic geometry, our results yield ...

In mathematics, hyperbolic geometry is a non-Euclidean geometry, meaning that the parallel postulate of Euclidean geometry is rejected. The parallel postulate in Euclidean geometry states, for two ...

Mathematicians often comment on the beauty of their chosen discipline. For the non-mathematicians among us, that can be hard to visualise. But in Prof Caroline Series’s field of hyperbolic geometry, ...

Reducing redundant information to find simplifying patterns in data sets and complex networks is a scientific challenge in many knowledge fields. Moreover, detecting the dimensionality of the data is ...

Hyperbolic space is a Pringle-like alternative to flat, Euclidean geometry where the normal rules don’t apply: angles of a triangle add up to less than 180 degrees and Euclid’s parallel postulate, ...

Geometry may be one of the oldest branches of mathematics, but it’s much more than a theoretical subject. It’s part of our everyday lives, says Professor Jennifer Taback, and key to understanding many ...

Sokoban a', since to that obtained a completely different gaming experience by the spherical stage 'hyperbolic number' appeared, I tried actually playing. The top page of hyperbolic geometry looks ...