Area inside a Circle: Intuitive and Rigorous Proofs

• 作者: Vali Siadat
• 来源期刊: 美国计算数学期刊(英文)
• 学科: 数学
• 关键词: Area Circle ELLIPSE CIRCULAR REASONING Intuitive PROOF Rigorous PROOF
• 年，卷（期）: 2017,（1）
• 页码范围: 102-108
• 页数: 7页
• 分类号: O1

摘要

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.