On arithmetic-geometric-mean polynomials

• Martin Griffiths ^[1] ; Des MacHale ^[2]
  1. [1] University of Essex

     University of Essex

     Colchester District, Reino Unido

     
  2. [2] University College Cork

     University College Cork

     Irlanda

     
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 48, Nº. 1, 2017, págs. 111-117
• Idioma: inglés
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• Resumen

  • We study here an aspect of an infinite set 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 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.