It makes sense that the number of dimensions ends up somewhere, but I think there's no particularly obvious a priori reason why it should be a denominator. For

It makes sense that the number of dimensions ends up somewhere, but I think there's no particularly obvious a priori reason why it should be a denominator. For example, the length of the long diagonals of a unit cube in n dimensions depends on the dimension, but it's \sqrt n, not anything divided by n (well, it's n^{3/2} divided by n, but that's not much use). Of course one can fill in why in this case it happens to be the dimension in the denominator—several sibling posts, particularly gniv's (https://news.ycombinator.com/item?id=36562093 https://news.ycombinator.com/item?id=36562093), have done so nicely—but I was responding specifically to the disclaimer: > I don't give a rat's ass if there's a proof or not connecting the two. I'm not a mathematician, but it makes sense from a calculus perspective that the number of dimensions ends up as a divisor. which seemed to suggest that it should be obvious without mathematical reasoning.