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 ...

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, ...

Even the most brilliant innovators get their inspiration from somewhere. For the Dutch graphic artist M.C. Escher, such a creative impetus came from a particular illustration in a 1957 mathematical ...

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 ...

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 ...

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, ...

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 ...