**ERIC Number:**EJ891793

**Record Type:**Journal

**Publication Date:**2010

**Pages:**5

**Abstractor:**ERIC

**Reference Count:**12

**ISBN:**N/A

**ISSN:**ISSN-0045-0685

Leaning on Socrates to Derive the Pythagorean Theorem

Percy, Andrew; Carr, Alistair

Australian Mathematics Teacher, v66 n2 p8-12 2010

The one theorem just about every student remembers from school is the theorem about the side lengths of a right angled triangle which Euclid attributed to Pythagoras when writing Proposition 47 of "The Elements". Usually first met in middle school, the student will be continually exposed throughout their mathematical education to the formula b2 + c2 = a2, where "a" is the length of the hypotenuse. It is so important in school mathematics and in mathematical thinking that the student deserves to be able to derive the Pythagorean theorem with an appropriate degree of rigour. The aim of the authors, in this article, is to provide a repertoire of derivations that range from the visual and geometrical to the algebraic and, in doing so, expose the interconnectedness of many parts of the school curriculum. They begin by "allowing students to explore concrete examples". The simple case for a right isosceles triangle is easily seen to be true by construction. The construction can then generalised to any right-angled triangle. The student performs "dissections and recombinations of shapes", requiring no algebra or non-geometric manipulation. (Contains 6 figures and 1 footnote.)

Descriptors: Foreign Countries, Geometric Concepts, Geometry, Mathematics Education, Intermode Differences, Learning Modalities, Mathematical Logic, Validity, Experiential Learning

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:**Secondary Education

**Audience:**Teachers

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A

**Identifiers - Location:**Australia