## Curves of Constant Width and Odd-Sided Reuleaux Polygons

A curve of constant width is a convex, two-dimensional shape that, when rotated inside a square, always makes contact with all four sides. A circle is the most obvious (but somewhat trivial) example. Some non-trivial examples are the odd-sided Reuleaux polygons â€” the first four of which are shown above. Since they donâ€™t have fixed axes of rotation, curves of constant width (except the circle) have few practical applications. One notable use of the Reuleaux triangle, though, is in drilling holes in the shape of a slightly rounded square (watch one of the triangleâ€™s vertices and notice the shape it traces out as it spins). On a less technical note, all curves of constant width are solutions to the brainteaser, â€śOther than a circle, what shape can you make a manhole cover such that it canâ€™t fall through the hole it covers?â€ť Mathematica code posted here. Additional source not linked above. ...