The Tree in Pythagoras' Garden

Autor/inn/en	Mack, John; Czernezkyj, Vic
Titel	The Tree in Pythagoras' Garden
Quelle	In: Australian Senior Mathematics Journal, 24 (2010) 2, S.58-63 (6 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0819-4564
Schlagwörter	Geometric Concepts; Mathematics Instruction; Theories; Validity; Mathematical Logic; Problem Solving; Equations (Mathematics); Secondary School Mathematics + Suchen Sie Ihr Suchwort? Elementare Geometrie; Mathematics lessons; Mathematikunterricht; Theory; Theorie; Gültigkeit; Mathematical logics; Mathematische Logik; Problemlösen; Equations; Mathematics; Gleichungslehre
Abstract	This geometrical account of primitive Pythagorean triples was stimulated by a remark of Douglas Rogers on a recent paper by Roger Alperin (Alperin, 2005). Rogers, in commenting on this paper, noted that Fermat in the 17th century had posed a challenge problem on Pythagorean triples that suggested he knew how to construct a sequence of them, possibly via a geometrical method (Fermat, 1643). Rogers himself gave an expanded version of such a method and from this has come the present investigation. In this article, the authors discuss Pythagoras' theorem and describe Fermat's challenge to his correspondents, which was to find six "Primitive Pythagorean Triples" (PPTs) in which the two legs differed in value by 1. The authors show that given any right-angled triangle with sides forming a PPT, they can associate with each side a new right-angled triangle, likewise with sides forming a PPT. (Contains 3 figures.) (ERIC).
Anmerkungen	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
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2021/2/06