Thomas Eshuis wrote: What even is a finite circle? Or an infinite circle for that matter?
Sloppy words on my behalf. A perfect circle of finite radius is imaginable but cannot be manufactured or found in nature. A perfect circle of infinite radius looks like a straight line, close up.
I can see the first notion, but how can something have a truly infinite radius? That would mean there'd be no end to it.
Correct, it may be imaginable but that depends on the limits of imagination, I guess.
Edit to add...
Talking of limits to imagination (and not necessarily limited to infinite circles)... The hyperbolic geometry of the Poincaré disk encloses an infinite area within a finite circle as can be seen in the following tube:
There are thousands of linked pages to Poincaré's disk and I'm sure even a cursory glance at a few will help. The most well known examples are in the Circle Limit works of M.C.Escher, e.g.
