@Zinnia #198882
…what?
That’s units of measurements - conventions of physics -, not mathematics. And squaring, cubing, et cetera the unit of length is the best way, precisely because it’s a special case.
And in case you ask why the circle in mathematics is the one with r=1 rather than D=1 or A=1, the unit circle, besides being the totality of points at 1 away from a point (and the unit disk all points 1 or less), making it of special mathematical interest, is (or mmore specifically, its [1,1] quadrant is) fundamental to trigonometry, and there are certainly many more features of interest an actual mathematician could describe.
PS:
The 1-unit-of-length square/cube/n-cube is the special case ideal for definition because it is both the direct application of the concept of extending length towards higher dimensions and the easiest to construct, but all regular shapes are special cases. In real life, most things are irregular in shape. And furthermore, the irrational nature of π makes it ill-suited for defining a basic derived unit.