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, ...

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 ...

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 ...

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 ...

Hyperbolic geometry originated in the 19th century, when mathematicians questioned the necessity of the parallel postulate in Euclidean geometry and discovered the hyperbolic plane ℍ², which satisfied ...

Geometry boasts a rich and captivating history within the realm of mathematics. In its early development, it was deeply rooted in practical observation used to describe essential concepts such as ...

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, ...

The crinkled edges of a lettuce leaf curve and expand in a shape that has perplexed mathematicians for centuries. Those curves -- an example of a high-level geometry concept called the hyperbolic ...

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 ...

Complex hyperbolic geometry studies spaces that combine the rich structure of complex manifolds with the intriguing features of hyperbolic curvature. At its heart lies the complex hyperbolic space, a ...