No perfect circles in space...

[Jehanne]

That's very true, but the point of my OP is that one cannot visualize the warping of space/time.

I think this is more a matter of practice than inability.

Most people don't spend any time really attempting to visualize four dimensional objects, let alone curved four dimensional manifolds. For that matter, even curved *three* dimensional manifolds are beyond what most people spend any time thinking about. That doesn't make them impossible to imagine. It just means you have to work a bit harder to do so.

But to answer the OP: yes, I find it quite easy to imagine 'circles' (meaning the set of points equidistant from some center point) to not have the 'circumference' (meaning the arc length of the boundary curve' equal to pi times the 'diameter' (twice the defining distance).

Among other possibilities is changing the definition of 'distance'. The standard Euclidean distance (based on the Pythagorean equation) is not the only possible 'metric', even in a 'flat' plane. The taxicab metric is another, perfectly usable measure of 'distance' and the 'circles' for the taxicab metric are actually 'squares' in two dimensions, 'octagons' in three dimensions, etc.

Other types of 'metric' can easily be used, and are used, when discussing general relativity. Again, no fundamental issue is found, but you have to keep track of the definitions a bit more closely.

In a 3d world/model, say, on a sphere, how do you imagine a geodesic (a circle) where C != 2r * pi?

P.S. A geodesic is, of course, just a path on a surface, in which case, it can be an arc.