From Symmetry to Monotonicity
Bernd Kawohl, David Krej\v{c}i\v{r}\'ik
TL;DR
This paper presents a shorter proof of a monotonicity property of a one-dimensional function, utilizing symmetry properties of a related two-dimensional surface, simplifying the original argument.
Contribution
It provides an alternative, more concise proof of a known monotonicity result by connecting it to symmetry properties in higher dimensions.
Findings
The proof reduces the problem to symmetry analysis of a 2D surface.
It simplifies the original proof of the monotonicity property.
The approach offers a new perspective on the problem.
Abstract
We offer an alternative and shorter proof to a result by Jan J.Ub{\o}e about monotonicity properties of a one-dimensional function that appeared in the Mathematical Intelligencer in 2015. Our proof is based on reducing the problem to symmetry properties of a two-dimensional surface.
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