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Briggs, W., Cochran, L. and Gillett, B. (2015) Cochran, Lyle. In: Gillett, B., Ed., Calculus, 2nd Edition, Pearson Education, New York, 527-536.

has been cited by the following article:

• 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.