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 ...

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 ...

The author discusses the fundamentals of plane hyperbolic geometry and describes a method for generating hyperbolic tilings by computer, based on the recently developed theory of automatic groups.

Our gallery gets to grips with hyperbolic space through mathematical artist Vi Hart’s visualisations in balloons, beads, clothes and more. See more in our gallery here. Receive a weekly dose of ...

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 ...