The circle is a subset of the infinite polygons.
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A circle can be a polygon. Sometimes a circle can be a polygon that has infinite number of sides.
A circle is NOT a polygon, because a polygon is composed of straight line segments, and a polygon DOES NOT have rounded sides. BUT! I read this on the internet, that SOMETIMES a circle is considered a polygon with infinite number of sides.
Theoretically, there are an infinite number of sides a polygon could have. It will never turn into a circle.
There is no limit to the number of sides that a polygon can have. Mathematically, a circle is equivalent to a polygon with an infinite number of sides.
A circle could be considered to have "no sides" in theory, however under this definition it is not a polygon. Also, a circle could be considered to have infinite sides. You could consider a point to be a no-sided polygon, but it's a stretch.