December 6, 2013 | 2
What shape has a constant width, no matter how it’s oriented? While most of you would say a circle (and you’d be right), that’s not the only answer. Other shapes, like the Reuleaux triangle, also fit the mold. At the base, the triangle is shaped like an equilateral triangle, but each side curves on a circular arc.
In the video “Shapes and Solids of Constant Width,” Numberphile’s Steve Mould discusses and demonstrates the use of these shapes in more depth. In an attempt to see what could replace the wheel, he even tries to balance on a wooden board supported by 3-D shapes of constant width that aren’t circles.