TITLE:
Area inside a Circle: Intuitive and Rigorous Proofs
AUTHORS:
Vali Siadat
KEYWORDS:
Area, Circle, Ellipse, Circular Reasoning, Intuitive Proof, Rigorous Proof
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.7 No.1,
March
31,
2017
ABSTRACT: 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 use circular reasoning today 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 the introduction
of a theorem, which will lead to proving the area inside a circle avoiding
circular argumentation.