**ERIC Number:**EJ779100

**Record Type:**Journal

**Publication Date:**2007

**Pages:**3

**Abstractor:**ERIC

**Reference Count:**2

**ISBN:**N/A

**ISSN:**ISSN-0819-4564

Pythagorean and Heronian Triangles

de Mestre, Neville; Marrows, Barney

Australian Senior Mathematics Journal, v21 n2 p21-23 2007

The basic Pythagorean theorem for right-angled triangles is well-known in mathematical terms as a[squared]+b[squared]+c[squared] were "a," "b," and "c" are the lengths of the sides of the triangle with "c" as the hypotenuse. When "a," "b," and "c" are all integers and obey this equation, they are referred to as a Pythagorean triple. One property of right-angled triangles based on Pythagorean triples is that their areas are always integers. Triangles that are right-angled and have integer sides and areas are referred to as Heronian triangles. These are called as such, because they depend on the rationalization of the formula for the area of a triangle given by Heron, a first century Egyptian engineer from Alexandria. In this article, the authors describe how Pythagorean triples and Heronian triangles are generated. (Contains 1 figure and 1 table.)

Descriptors: Geometric Concepts, Mathematical Formulas, Validity, Mathematical Logic, Mathematics Instruction, Geometry

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:**N/A

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A