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arXiv · 2008.01653

Banach-Mazur distances between parallelograms and other affinely regular even-gons

Marek Lassak
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Abstract

We show that the Banach-Mazur distance between the parallelogram and the affine-regular hexagon is $\frac{3}{2}$ and we conclude that the diameter of the family of centrally-symmetric planar convex bodies is just $\frac{3}{2}$. A proof of this fact does not seem to be published earlier. Asplund announced this without a proof in his paper proving that the Banach-Mazur distance of any planar centrally-symmetric bodies is at most $\frac{3}{2}$. Analogously, we deal with the Banach-Mazur distances between the parallelogram and the remaining affine-regular even-gons.

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Marek Lassak. 2020-08-04. Banach-Mazur distances between parallelograms and other affinely regular even-gons. https://arxiv.org/abs/2008.01653

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