A polygon with very many sides has the same circumference/area as a circle with the same radius, so is a circle just a polygon with a lot of sides?

This is part of the study of geometry.

Yes, a circle is technically a polygon "with a lot of sides", but that "a lot" would actually lean more towards the concept of infinity; a circle is a polygon with an infinitely large amount of sides.

By reducing the size of the measurement, or increasing the accuracy (in this case by increasing sides), one gets a result closer to the actual one.

This concept has been reused for the creation of other fields of mathematics, such as calculus.

a reflection across the x-axis , followed by the by a reflection across the y-axis , and then a scale dilation of 0.5 .