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, ...

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, ...

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 ...

One hypothesis about the shape of the universe is that the universe is in the space of Euclidean geometry and flat. In Euclidean geometry, it is assumed that straight lines extend everywhere, planes ...

Building on previous work that realized Euclidean lattice models using circuit quantum electrodynamics (QED) and interconnected networks of superconducting microwave resonators, researchers at ...