In two dimensions, it’s the Reuleaux triangle: an equilateral triangle with curved arcs connecting each corner, creating a shape with a constant width but a smaller area than a circle. Now, a team of ...

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 ...

Have you ever wondered why the cover of a manhole is nearly always round? Why isn’t it oval or square? Reuleaux curve based on an equilateral triangle. Reuleaux curves based on the pentagon (top) and ...

Mathematicians are “reinventing the wheel” by giving it a new shape. Their newly imagined wheel looks like a many-dimensional guitar pick, and it could theoretically roll in ways beyond our ...