Infinite points on its circumference would infer that it is a curve. A curve is a line that changes its direction continuously from point to point throughout its entire length.
I would say it has no sides.
"A curve is a line that changes its direction continuously from point to point throughout its entire length"
from point to point, huh? so theres a new bearing to each new point, and by deduction, straight lines in between points. how close are these points together?
of course, the idea of a "point" is an abstraction, so there need be no limit on how many there are, how small, and how close they are together. but no matter how far you zoom in, you will not escape the fact that there is a theoretical straight line, or "side", between each and every point. however, you might well concede that there is a level of scale beyond which all considerations of 'sides' become meaningless and not applicable to any useful purpose. so, i would not say it has no sides. it is most correct to say it is undefined.
Who defines a circle parametrically?
The answer is an engineer pretending to be a mathematician.