Density of Primitive Pythagorean Triples

Autor/in	Killen, Duncan A.
Titel	Density of Primitive Pythagorean Triples
Quelle	In: AMATYC Review, 26 (2004) 1, S.3-11 (9 Seiten) PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0740-8404
Schlagwörter	Computer Software; Regression (Statistics); College Mathematics; Two Year Colleges; Computer Uses in Education; Mathematical Concepts; Teaching Methods; Mathematics Instruction + Suchen Sie Ihr Suchwort? Regression; Regressionsanalyse; Computernutzung; Teaching method; Lehrmethode; Unterrichtsmethode; Mathematics lessons; Mathematikunterricht
Abstract	Based on the properties of a Primitive Pythagorean Triple (PPT), a computer program was written to generate, print, and count all PPTs greater than or equal to I[subscript x], where I[subscript x] is an arbitrarily chosen integer. The Density of Primitive Pythagorean Triples may be defined as the ratio of the number of PPTs whose hypotenuse is less than or equal to I[subscript x], to I[subscript x] (PPTs/I[subscript x]. The PPT Density for all PPTs with a primitive hypotenuse less than or equal to I[subscript x], remains rather stable, even as I[subscript x] is increased from 5 to 1,000,000. Using a TI-83 calculator, a linear regression correlation between the number of PPTs and the value of Ix, using 36 data points distributed between I[subscript x] = 1,000 and I[subscript x] = 1,000,000 was determined and the results are as shown: Number of PPTs = (0.1591543612)I[subscript x] - 0.726456424; r = 0.999999992. (As Provided).
Anmerkungen	American Mathematical Association of Two-Year Colleges. 5983 Macon Cove, Memphis, TN 38134. Tel: 901-333-4643; Fax: 901-333-4651; e-mail: amatyc@amatyc.org; Web site: http://www.amatyc.org
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10