On arithmetic-geometric-mean polynomials. Issue 1 (2nd January 2017)

• Record Type: Journal Article
• Authors: Griffiths, Martin; MacHale, Des
• Is Part Of: International journal of mathematical education in science and technology. Volume 48:Issue 1(2017)
• Page Start: 111
• Page End: 117
• Publication Date: 2017-01-02
• Subjects: arithmetic-geometric mean -- inequalities -- multivariate polynomials; Mathematics -- Study and teaching -- Periodicals; Mathematics -- Periodicals; 510.07
• DOI: 10.1080/0020739X.2016.1172740
• Languages: English
• ISSNs: 0020-739X

Abstract

ABSTRACT: We study here an aspect of an infinite set P of multivariate polynomials, the elements of which are associated with the arithmetic-geometric-mean inequality. In particular, we show in this article that there exist infinite subsets of P for which every element may be expressed as a finite sum of squares of real polynomials. Some of the mathematics discussed here would be suitable as extension material for senior pre-university students and first-year undergraduates.