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arXiv · 2006.07259

Relating Symmetrizations of Convex Bodies: Once More the Golden Ratio

René Brandenberg·Katherina von Dichter·Bernardo González Merino
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Abstract

We show that for any Minkowski centered planar convex compact set $C$ the Harmonic mean of $C$ and $-C$ can be optimally contained in the arithmetic mean of the same sets if and only if the Minkowski asymmetry of $C$ is at most the golden ratio $(1+\sqrt{5})/2 \approx 1.618$. Moreover, the most asymmetric such set that is (up to a linear transformation) a special pentagon, which we call the golden house.

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René Brandenberg, Katherina von Dichter, Bernardo González Merino. 2020-06-12. Relating Symmetrizations of Convex Bodies: Once More the Golden Ratio. https://arxiv.org/abs/2006.07259

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