**ERIC Number:**EJ867343

**Record Type:**Journal

**Publication Date:**2009

**Pages:**12

**Abstractor:**ERIC

**Reference Count:**0

**ISBN:**N/A

**ISSN:**ISSN-0819-4564

An Ordinary but Surprisingly Powerful Theorem

Sultan, Alan

Australian Senior Mathematics Journal, v23 n2 p47-58 2009

Being a mathematician, the author started to wonder if there are any theorems in mathematics that seem very ordinary on the outside, but when applied, have surprisingly far reaching consequences. The author thought about this and came up with the following unlikely candidate which follows immediately from the definition of the area of a rectangle as length multiplied by width. The author refers to this theorem as Ordinary Theorem (OT). In this article, the author illustrates this ordinary but powerful theorem, and describes how important this seemingly ordinary theorem really is. The author also shows a treasure trove hidden in this theorem that is of almost all the familiar theorems one learns in high school, some of whose proofs are elusive. The author ends this article by leaving a question for one to ponder, "Should the area of a right triangle be taught as a fundamental concept in high school?" (Contains 9 figures.)

Descriptors: Fundamental Concepts, High Schools, Geometric Concepts, Mathematical Logic, Validity, Mathematics Instruction, Secondary School Mathematics, Mathematical Concepts, Problem Solving

Australian Association of Mathematics Teachers (AAMT). GPO Box 1729, Adelaide 5001, South Australia. Tel: +61-8-8363-0288; Fax: +61-8-8362-9288; e-mail: office@aamt.edu.au; Web site: http://www.aamt.edu.au

**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**High Schools

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A