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 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 ...

Margaret Wertheim gave a talk for the Australian Mathematical Sciences Institute at their 2016 annual Summer School. We have built a world of largely straight lines – the houses we live in, the ...

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 ...

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, ...

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 ...