In 1867, French mathematician Pierre Ossian Bonnet proved something that seemed like common sense: if you know how far apart ...

Can you drill a hole in a cube that an identical cube could fall through? Prince Rupert of the Rhine first asked this question in the 17th century, and he soon found out the answer is yes. One can ...

A 3D shape with all straight edges and flat faces is a polyhedron. Other 3D shapes with least one curved surface are not polyhedra. A 3D shape with regular polygonal faces, meeting at equal angles, is ...

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.

Physicists have turned a long-standing imaging workhorse into a kind of nanoscale chisel, using a razor-precise ion beam to ...