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The arithmetic mean - Geometric mean - Harmonic mean: Inequalities and a spectrum of applications

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Abstract

The Arithmetic Mean–Geometric Mean–Harmonic Mean inequality, AM–GM–HM inequality in short, is one of the fundamental inequalities in Algebra, and it is used extensively in olympiad mathematics to solve many problems. The aim of this article is to acquaint students with the inequality, its proof and various applications.

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Suggested Reading

  1. B J Venkatachala, Inequalities - An Approach Through Problems, Hindustan Book Agency.

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Authors and Affiliations

  1. Homi Bhabha Centre for Science Education, Tata Institute of Fundamental Research, Mumbai, India

    Prithwijit De

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  1. Prithwijit De
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Correspondence to Prithwijit De.

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De, P. The arithmetic mean - Geometric mean - Harmonic mean: Inequalities and a spectrum of applications. Reson 21, 1119–1133 (2016). https://doi.org/10.1007/s12045-016-0423-4

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  • DOI: https://doi.org/10.1007/s12045-016-0423-4

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