Paradox: Circular Rooms and Corners I don't know why this popped into my head, but it did and so now I'm going to put it in all of your heads too. Does a perfectly circlular room have NO corners; or INFINITE corners? Of course, first we have to define "corner". Is being 90 degrees a requirement? Would a 1 degree angle constitute a corner? After all, two straight lines come together at an angle. A shallow angle but still an angle. Then, if 1 degree works, what about 0.000002 degrees? Couldn't a circle possibly be a bazillion shallow corners between a bazillion sides, that as the number approaches infinity the shape looks more and more like the perfect circle? OR..... Would a truly perfect circular room actually be curved on the smallest, most infinitely small microscopic level, thereby having no straight segments with which to form a corner? This flies in the face of the notion that all curves are merely a large number of small, straight segments joined by a large number of extremely shallow angles. What do you think?