This is a hyperbolic pseudosphere—made with nothing more than yarn and a crochet hook. Hyperbolic geometry describes surfaces that are negatively curved. If you're enjoying this article, consider ...

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 ...

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 ...

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 ...

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 ...

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 ...

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, ...