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arXiv · 2210.16150

The centroid Banach-Mazur distance between the parallelogram and the triangle

Marek Lassak
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Abstract

Let $C$ and $D$ be convex bodies in the Euclidean space $E^d$. We define the centroid Banach-Mazur distance $δ_{BM}^{\rm cen} (C, D)$ similarly to the classic Banach-Mazur distance $δ_{BM} (C, D)$, but with the extra requirement that the centroids of $C$ and an affine image of $D$ coincide. We prove that for the parallelogram $P$ and the triangle $T$ in $E^2$ we have $δ_{BM}^{\rm cen} (P, T) = \frac{5}{2}$.

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Marek Lassak. 2022-10-28. The centroid Banach-Mazur distance between the parallelogram and the triangle. https://arxiv.org/abs/2210.16150

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