Through a field called geometric topology, mathematicians like me study all possible spaces in all dimensions. Whether trying ...

An AI method enables the generation of sharp, high-quality 3D shapes that are closer to the quality of the best 2D image models. Previous approaches typically generated blurry or cartoonish 3D shapes.

A research team from the Aerospace Information Research Institute (AIR) of the Chinese Academy of Sciences has developed a ...

Shape The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else By Jordan Ellenberg Illustrated. 463 pages. Penguin Press. $28.

Euclidean geometry is the branch of mathematics describing shapes and the spatial relationships between objects in two-dimensional (2D) and three-dimensional (3D) settings. The rules of Euclidean ...

A 150-year-old theory about an otherworldly shape proposed by Lord Kelvin, one of history's greatest physicists, has finally been put to the test — and his conjecture is now in doubt.