Once upon a time there were plenty of square pegs jammed into round holes, but those dark times have passed. Now there is a special shape that allows people to drill square holes. This special ...

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 ...

No one knows how to find the smallest shape that can cover all other shapes of a certain width. But high school geometry is getting us closer to an answer. “Hey — I’ve got holes in some of my jeans.

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 ...

If you enjoyed this article, I’d like to ask for your support. Scientific American has served as an advocate for science and industry for 180 years, and right now may be the most critical moment in ...