ERIC Number: EJ769627
Record Type: Journal
Publication Date: 2007
Pages: 3
Abstractor: ERIC
ISBN: N/A
ISSN: ISSN-0730-8639
EISSN: N/A
Primitive Pythagorean Triples: The 3, 4, 5 Connection
Skurnick, Ronald
Mathematics and Computer Education, v41 n1 p22-24 Win 2007
The Pythagorean Theorem, arguably one of the best-known results in mathematics, states that a triangle is a right triangle if and only if the sum of the squares of the lengths of two of its sides equals the square of the length of its third side. Closely associated with the Pythagorean Theorem is the concept of Pythagorean triples. A "Pythagorean triple" is a triple of numbers (a, b, c) such that a[squared] + b[squared] = c[squared], where a, b, and c, are positive integers. A simple way to prove this "3, 4, 5 connection (with respect to primitive Pythagorean triples)" involves a nice application of the notions of congruence and modular arithmetic from elementary number theory. This article provides the proof of primitive Pythagorean triples that is accessible to students who are familiar with, or are mathematically mature enough to understand its definition. This article concludes with a list of the 16 primitive Pythagorean triples.
Descriptors: Geometric Concepts, Arithmetic, Number Concepts, Mathematical Formulas, College Mathematics, Mathematics Instruction, Problem Solving, Mathematical Logic, Validity
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: Higher Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A