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 ...

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 ...

Breakthroughs, discoveries, and DIY tips sent every weekday. Terms of Service and Privacy Policy. Hard as it may be to imagine, there’s a newly defined geometric ...

Mathematicians have long wondered how “shapes of constant width” behave in higher dimensions. A surprisingly simple construction has given them an answer. In 1986, after the space shuttle Challenger ...

Mathematicians have reinvented the wheel with the discovery of shapes that can roll smoothly when sandwiched between two surfaces, even in four, five or any higher number of spatial dimensions. The ...