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Lack of relative monotonicity among various measures of trihedral angles

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Abstract

We consider the various measures on trihedral angles that have appeared in the literature and we show that no two of these measures are monotone with respect to each other. In other words, for any measures f, g, there exist trihedral angles α, β, γ, θ such that f(α) >  f(β), g(α) <  g(β), f(γ) >  f(θ), g(γ) >  g(θ). This is done through an elementary and systematic method based on multivariable calculus.

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Authors and Affiliations

  1. Mathematics Department, Yarmouk University, Irbid, Jordan

    Mowaffaq Hajja

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  1. Mowaffaq Hajja
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Correspondence to Mowaffaq Hajja.

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This work is supported by a research grant from Yarmouk University.

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Hajja, M. Lack of relative monotonicity among various measures of trihedral angles. J. Geom. 103, 237–246 (2012). https://doi.org/10.1007/s00022-012-0120-8

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  • DOI: https://doi.org/10.1007/s00022-012-0120-8

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