Question: people say that manhole covers are circular because they're the only shape that can't be turned to fall through itself. Am I right that this is also true of equalateral triangles?
Actually, is it true of all the regular polygons with an odd number of sides, since they don't have a "hypotenuse" (meaning here that there is no internal line that can be drawn from one vertex to another that is longer than any other internal dimension. I'm explaining this badly. But a counter example would be the diagonal on a square being linger than its width. That is not what a hypotenuse is, please tell me if there is a word.)
Of course you aren't going to make a pentagonal manhole cover, but is this saying just a misconstrued version of something like "why are manhole covers circles and not squares"?
Despite having taught high school geometry, I never TOOK high school geometry. Maybe I will try a proof.... I remember proofs, right?
