A Geometric Generalization of the Pythagorean Means

Greg Markowsky; Dylan Phung; David Treeby

doi:10.1080/0025570X.2022.2125729

A Geometric Generalization of the Pythagorean Means

Greg Markowsky
, Dylan Phung
, David Treeby

School of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

Abstract

Summary: Each of the Pythagorean means corresponds to the centroid of a region in the Cartesian plane. We show how this insight leads to a short proof of a result that generalizes the HM-GM-AM inequality.

Original language	English
Pages (from-to)	520-524
Number of pages	5
Journal	Mathematics Magazine
Volume	95
Issue number	5
DOIs	https://doi.org/10.1080/0025570X.2022.2125729
Publication status	Published - 30 Sept 2022

Keywords

Primary 26E60
Secondary 26D99

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10.1080/0025570X.2022.2125729

Cite this

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title = "A Geometric Generalization of the Pythagorean Means",

abstract = "Summary: Each of the Pythagorean means corresponds to the centroid of a region in the Cartesian plane. We show how this insight leads to a short proof of a result that generalizes the HM-GM-AM inequality.",

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AB - Summary: Each of the Pythagorean means corresponds to the centroid of a region in the Cartesian plane. We show how this insight leads to a short proof of a result that generalizes the HM-GM-AM inequality.

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A Geometric Generalization of the Pythagorean Means

Abstract

Keywords

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