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 ...

Two mathematicians have proved a long-standing conjecture that is a step on the way toward finding the worst shape for packing the plane. For centuries, mathematicians suspected that hexagonal tiles ...

When most people think of shapes, they imagine a triangle, a rectangle, or maybe even a fancier-sounding rhombus or trapezoid. But to mathematicians, shapes encompass a vast universe of surprising ...