Why Can’t a Round Manhole Cover Fall Through Its Own Opening?

A round manhole cover has a straightforward geometric advantage: however it is rotated, its width remains its diameter. If a rigid circular cover matches a circular opening, there is no narrower orientation through which it can pass. A square cover is different. Because the opening’s diagonal is longer than its side, a square cover can potentially be stood up and angled so that one edge enters along the diagonal.

The relevant property is called constant width: the distance between two parallel supporting lines is the same in every direction. A circle has constant width, but it is not the only such shape. A Reuleaux triangle, formed from three circular arcs, also has constant width. So the familiar claim that a cover cannot fall through its opening and therefore must be circular is too strong. Circles also have practical advantages: they can be rolled and do not need angular alignment. Even so, some installations use square or other covers.

The useful lesson is not merely an answer to a riddle. It is how a geometric property can provide an engineering margin of safety: if there is no narrower orientation, the cover is less likely to pass through its own opening.

https://mathworld.wolfram.com/CurveofConstantWidth.html
https://mathworld.wolfram.com/ReuleauxTriangle.html