Journal of Convex Analysis 31 (2024), No. 1, 051--058
Copyright Heldermann Verlag 2024
The Centroid Banach-Mazur Distance between the Parallelogram and the Triangle
Marek Lassak
Institute of Mathematics and Physics, University of Technology and Life Sciences, Bydgoszcz, Poland
lassak@pbs.edu.pl
[Abstract-pdf]
Let $C$ and $D$ be convex bodies in the Euclidean space $E^d$. We define the centroid Banach-Mazur distance $\delta_{BM}^{\rm cen} (C, D)$ similarly to the classic Banach-Mazur distance $\delta_{BM} (C, D)$, 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 $\delta_{BM}^{\rm cen} (P, T) = \frac{5}{2}$.
Keywords: Banach-Mazur distance, centroid Banach-Mazur distance, convex body, centroid, parallelogram, triangle.
MSC: 52A21; 46B20, 52A10.
[ Fulltext-pdf (156 KB)] for subscribers only.