is there such a thing as a circle, or just a multi sided shape whith many sides, that looks like a circle?

Answer 1

As the length of each side approaches zero, what's the difference?

Seriously, that's the way math handles this situation. Let epsilon be some tiny number >0, such that a polygon with side length less than epsilon is, for all practical purposes, a circle. No matter how small of an epsilon you give me, I can give you a polygon with side length smaller than that.

Answer 2

As n approaches infinity, a regular (all sides and angles equal) polygon with n sides begins to look more and more like a circle. However, since a circle is round, it does not have sides and no shape with sides can ever be a circle.

Answer 3

In a discrete space you have to go with the tiny sides. In a
continuous space your circle won't have straight sides.
The discrete case: It looks like a circle and you'll probably never be able to tell the difference but it's not a true circle
per definition.

Answer 4

a circle is made of archs, not lines.