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ERIC Number: EJ906702
Record Type: Journal
Publication Date: 2010
Pages: 6
Abstractor: ERIC
Reference Count: 3
ISSN: ISSN-0819-4564
The Tree in Pythagoras' Garden
Mack, John; Czernezkyj, Vic
Australian Senior Mathematics Journal, v24 n2 p58-63 2010
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.)
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:; Web site:
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Secondary Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A