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Means, Milne’s inequality, and quadrilateral area

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Abstract

We discuss Milne’s inequality and apply it to the sides of a convex quadrilateral to derive an approximation to the area of the quadrilateral via arithmetic and harmonic means of pairs of opposite sides.

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References

  1. Alsina, C., Nelsen, R.B.: A Cornucopia of Quadrilaterals. American Mathematical Society, Providence, RI (2020)

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  2. Bullen, P.: Dictionary of Inequalities, 2nd edn. CRC Press, Boca Raton, FL (2015)

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  3. Milne, E.A.: Note on Rosseland’s integral for the stellar absorption coefficient. Mon. Not. R. Astron. Soc. 85, 979–984 (1925)

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Authors and Affiliations

  1. Universitat Politècnica de Catalunya, Diagonal 649, 08028, Barcelona, Spain

    Claudi Alsina

  2. Lewis & Clark College, 615 S. Palatine Hill Rd., Portland, OR, 97219, USA

    Roger B. Nelsen

Authors
  1. Claudi Alsina
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  2. Roger B. Nelsen
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Corresponding author

Correspondence to Roger B. Nelsen.

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To our colleague and friend János Aczél, in memoriam.

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Alsina, C., Nelsen, R.B. Means, Milne’s inequality, and quadrilateral area. Aequat. Math. 95, 623–627 (2021). https://doi.org/10.1007/s00010-021-00823-9

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  • DOI: https://doi.org/10.1007/s00010-021-00823-9

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