Which polygon has infinite sides?

If a point moves in plane such that its distance remains constant from a fixed point then the figure obtained is called circle.

Or we can define circle as the collection of points which are equidistant from fixed points. However there is another way to describe circle: It is a polygon made up of infinite sides.

But how can we prove that?

As we all know that earth is a big sphere but to us, humans, it is like a plane surface. The reason behind this is that are considering very very small part of the surface. So if we consider infinitesimal part then it can be considered as made up of infinite planes.

Similarly a circle can be defined as a polygon of infinite sides.

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No, it cannot be so defined. A polygon, by definition has straight sides. As the number of sides of a polygon approach infinity (under certain conditions), the shape approaches a circle: in the limit but it can never actually be a circle.