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, ...

“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 ...

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 ...

Researchers have built an electronic array on a microchip that simulates particle interactions in a hyperbolic plane, a geometric surface in which space curves away from itself at every point. Atomic ...

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 ...

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 ...