Disagree, because a polygon has to have sides to be a polygon. A circle has no defined sides to categorise it as such. A circle is a closed system, but can be seen as a cycle that lasts until the world ends. Like infinity, a circle is infinite by definition because it goes on forever. Like the polygon comparison, a circle is technically in a different category. Infinity is typically described as a time full of endless possibilities while a circle is just that, a cycle that will repeat itself over the course of forever.
So still disagree on that argument. Please tell me this is for a Philosophy class or something, because having this as a math problem is horrible.