I was curious.

Would I be correct in considering a point and a circle inverses of each other?

And by that same token, couldn't one consider a point in space and a sphere inverses of each other?

Definition of a Circle: all the points equally distant from a single point in a single plane.

Definition of a Sphere: All the points equally distant from a single point in co-ordinate space.

For all such things I'd use orthogonal holistic heuristics. And wave my arms about alot.

Heh.

I was thinking later on that perhaps the inverse of a circle (or sphere) would be everything outside of it. (A.K.A. hit the invert selection button in photoshop.)

So instead of walling from without, you'd be walling from within.