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 cross section of a chambered nautilus shell shows the newly defined shape, the "soft cell," repeating outward in a spiral. FlamingPumpkin via Getty Images When humans cover a space using tiles of ...

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 ...

How few corners can a shape have and still tile the plane?” mathematician Gábor Domokos asked me over pizza. His deceptively simple question was about the geometry of tilings, also called ...

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