ERIC Number: EJ769545
Record Type: Journal
Publication Date: 2005
Pages: 6
Abstractor: ERIC
Reference Count: 6
ISBN: N/A
ISSN: ISSN-0730-8639
A Description of a Family of Heron Quadrilaterals
Sastry, K. R. S.
Mathematics and Computer Education, v39 n1 p72-77 Win 2005
Mathematical historians place Heron in the first century. Right-angled triangles with integer sides and area had been determined before Heron, but he discovered such a "non" right-angled triangle, viz 13, 14, 15; 84. In view of this, triangles with integer sides and area are named "Heron triangles." The Indian mathematician Brahmagupta, born in 598, placed two right triangles along a common side to produce a non right-angled Heron triangle. Not content with that he extended his principle to generate cyclic (inscribable in a circle) quadrilaterals with integer sides, diagonals, and area. Such quadrilaterals are called "Brahmagupta quadrilaterals." Later mathematicians were intrigued by this technique, but Kummer analyzed the Brahmagupta principle and gave a complex construction to determine more general "Heron quadrilaterals," quadrilaterals with integer sides, diagonals, and area. It is highly desirable to have simpler constructions to determine Heron quadrilaterals. As a small step in this direction, this paper aims to propose a description of an infinite set of Heron quadrilaterals via "Heron angles." The author encourages everyone to provide constructions to generate Heron parallelograms, Heron trapezoids at least in infinite families if not a complete description. (Contains 3 figures.)
Descriptors: Professional Personnel, Numbers, Geometric Concepts, Geometry, Mathematics, History, Mathematical Concepts
MATYC Journal Inc. Mathematics and Computer Education, P.O. Box 158, Old Bethpage, NY 11804. Tel: 516-822-5475; Web site: http://www.macejournal.org
Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Identifiers: N/A

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