Hyperbolic geometry studies spaces of constant negative curvature, where the parallel postulate is replaced and geodesics exhibit exponential divergence. This framework underpins a rich theory of ...

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 ...

We have built a world of largely straight lines – the houses we live in, the skyscrapers we work in and the streets we drive on our daily commutes. Yet outside our boxes, nature teams with frilly, ...

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, ...

On a Thursday night in Ithaca, New York, Daina Taimina, an ebullient blond mathematician at Cornell University, sits at her kitchen table with her husband, David Henderson, a Cornell professor of ...

Math just met "warp drive" in a virtual reality headset to transport anyone who dons the visor to a reality twisted by hyperbolic geometry. The program was co-created by Sabetta Matsumoto, a physicist ...

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 ...