**ERIC Number:**EJ875472

**Record Type:**Journal

**Publication Date:**2004

**Pages:**9

**Abstractor:**As Provided

**ISBN:**N/A

**ISSN:**ISSN-0740-8404

Density of Primitive Pythagorean Triples

Killen, Duncan A.

AMATYC Review, v26 n1 p3-11 Fall 2004

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.

Descriptors: Computer Software, Regression (Statistics), College Mathematics, Two Year Colleges, Computer Uses in Education, Mathematical Concepts, Teaching Methods, Mathematics Instruction

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

**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**Two Year Colleges

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A