There’s a story going around in mathematical circles, perhaps due to a 1971 article of Victor Klee, that Reuleaux triangles make a good shape for manhole covers. This is because, like the more common circular manhole covers, they can’t fall into the holes that they cover. However, circles have other useful properties: they roll more easily and you don’t have to align them very carefully with their holes. I can’t find any evidence that anyone anywhere has ever actually used a Reuleaux triangle shaped manhole cover.

A rounded triangular (but not Reuleaux triangle) valve cover on the UC Irvine campus

So what is that picture, you ask? I took it, and a batch of related photos from the UC Irvine campus, with the plan of replacing a similar photo that had been deleted from the Wikipedia Reuleaux triangle article over some licensing snafu. But it’s not a Reuleaux triangle manhole cover, for multiple reasons.

  1. The red rounded triangle that you see when you first look at the image is not the cover. It’s the plate onto which the cover fits. The actual cover is inset, and has the shape of a standard equilateral triangle with rounded corners.

  2. Reuleaux triangles have pointy corners. The corners of the base plate are rounded. You can see that they have a bigger radius of curvature, at the corner, than the rounded equilateral triangle of the cover.

  3. It’s not a manhole cover. It’s far too small for a man to fit through into a hole under it. It’s just a valve cover. That was also true of the old image that was deleted, of a valve cover in San Francisco. (I don’t remember if it also had the other flaws, but if it’s anything like these ones then yes.) Valve covers are small and light enough to be easily lifted and fitted into place; you don’t have to roll them, and there’s no deep hole for them to fall into.

So I think it’s far enough from being a good illustration of the manhole story that I’m not going to try to add it to the Wikipedia article. But I did at least find some pretty fallen Spring blossoms:

Utility cover with fallen Spring blossoms on the UC Irvine campus

If anyone does know of somewhere that uses actual Reuleaux triangle shaped manhole covers, please tell me where to find them.

(As usual see G+ for comments. This has been episode 3 of Things That Are Not Reuleaux Triangles. For episodes 1 and 2 see The shape of the Kresge Auditorium and Triforce string art respectively. Maybe some day I’ll continue the series with something about the Wankel rotary engine.)