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 ...

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, ...

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 ...

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 ...

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 ...

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 ...

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 ...

This originally appeared in the July/August issue of Discover magazine as "Your Hyperbolic Mind." Support our science journalism by becoming a subscriber. The human brain is both a marvel and a ...