You're hired! SVP of Aerospace Engineering. How many people do you need under you, killer?

Most manholes are round because that is the most practical shape such that the cover cannot fall in. There are actually other shapes, but they are usually hinged and most costly.

I've never thought about it, but a circle of the correct size has no less reason to not fall in than say a square or triangle of the appropriate size. I.e. if it's smaller than the hole, it'll most likely fall in.

My theory: They're heavy, so making it a circle at least eliminates the need to "align" it when putting it back. You can basically just drag it using a hook and it'll slot itself into place.

But manhole covers are always bigger than the hole. Otherwise, they'd fall in at installation and the problem would be immediately obvious.

The point here is more that a circle has the same diameter regardless of orientation. There's no way to rotate it to make it fit through a hole it couldn't before, like you can do with a rectangle.

This is also true of a triangle, and indeed there are triangular manholes.

Aren't the altitudes/heights of a triangle shorter than its sides?

The height of an equilateral triangle is about 87% of the length of one of its sides.

True. Whether they fit through the hole depends on how thick they are.

You might be interested in reading about Prince Rupert's cube. https://news.ycombinator.com/item?id=16399079

In particular from https://en.wikipedia.org/wiki/Prince_Rupert%27s_cube

> In geometry, Prince Rupert's cube (named after Prince Rupert of the Rhine) is the largest cube that can pass through a hole cut through a unit cube, i.e. through a cube whose sides have length 1, without splitting the cube into two pieces. Its side length is approximately 6% larger than that of the unit cube through which it passes. The problem of finding the largest square that lies entirely within a unit cube is closely related, and has the same solution.

That 6% larger is the key.

Man hole covers aren't flat discs nor thin cylinders, but are truncated cones. The diameter of the bottom of the cover is smaller than the top. There is no way for a cone to fall through an opening smaller than the widest diameter end.

The difference is that this "appropriate size" (= cost of materials) is smaller for circles than it is for any other shape.

Sorry, confused here on why the pothole variant is more objective? If anything, the manhole cover one seems pretty clear cut?

Potholes are naturally occurring. For any particular pothole, there is a reason it took whatever shape it did.

The only real constraint operating on manholes is that they fit the opening. Unless you can produce a design document specifying the requirements for the manhole you're looking at, there isn't really a "why".

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