Complex networks, ranging from biological systems to technological and social infrastructures, have long intrigued researchers with their intricate connectivity and emergent behaviours. Recent ...

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 ...

Complex hyperbolic geometry investigates spaces that combine the subtleties of complex structures with non‐Euclidean, negatively curved metrics, offering rich terrain for both theoretical exploration ...

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 ...

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 ...

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 ...

Atomic interactions in everyday solids and liquids are so complex that some of these materials’ properties continue to elude physicists’ understanding. Solving the problems mathematically is beyond ...

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, ...

This paper gives a quantitative version of Thurston's hyperbolic Dehn surgery theorem. Applications include the first universal bounds on the number of nonhyperbolic Dehn fillings on a cusped ...

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 ...