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) f(θ), g(γ) > g(θ). This is done through an elementary and systematic method based on multivariable calculus.
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