[roundsquare]

Why does smallest in terms of absolute value matter? In any event, I can define the circle via the center and r/2 or center and r/4, etc... I don't see any value in caring about the absolute value.

As for dimensionality, how are you using the word? No matter what, we need 3 numbers to define a circle in R^2. Two numbers define its position and one number defines it size. I don't see what you're getting at. If you mean that because radius is a measure of length (one dimension) and area is a measure of area (two dimensions) then I have two questions: 1) Why does that matter? Its still just a single number. 2) Even if it does matter, why is radius more fundamental than diameter.