  In this article I conduct a short review of the proofs of the area inside a
circle. These include intuitive as well as rigorous analytic proofs. This
discussion is important not just from mathematical view point but also because
pedagogically the calculus books still today use circular reasoning to prove
the area inside a circle (also that of an ellipse) on this important historical
topic, first illustrated by Archimedes. I offer an innovative approach, through
introduction of a theorem, which will lead to proving the area inside a circle
avoiding circular argumentation.
