“The treatise itself, therefore, contains only twenty-four pagesthe most extraordinary two dozen pages in the whole history of thought!” “How different with BolyaiJnos and Lobachvski, who claimed at ...

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 ...

Complex hyperbolic geometry investigates spaces that combine the subtleties of complex structures with non‐Euclidean, negatively curved metrics, offering rich terrain for both theoretical exploration ...

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, ...

Euclidean geometry is the kind you were taught at school, the world of sines and cosines, and the square on the hypotenuse being equal to the squares on the other two sides. Its laws—first set out by ...

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, ...

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 ...

Tessellations aren’t just eye-catching patterns—they can be used to crack complex mathematical problems. By repeatedly ...

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 ...

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 ...