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 ...

Hyperbolic knot theory concerns itself with the study of knots and links embedded in three‐dimensional spaces that admit hyperbolic structures. The geometry of a link complement—the manifold that ...

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 ...

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 ...

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, ...

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 ...

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 ...