
Journal of Convex Analysis 31 (2024), No. 1, 051058 Copyright Heldermann Verlag 2024 The Centroid BanachMazur 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 [Abstractpdf] Let $C$ and $D$ be convex bodies in the Euclidean space $E^d$. We define the centroid BanachMazur distance $\delta_{BM}^{\rm cen} (C, D)$ similarly to the classic BanachMazur 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: BanachMazur distance, centroid BanachMazur distance, convex body, centroid, parallelogram, triangle. MSC: 52A21; 46B20, 52A10. [ Fulltextpdf (156 KB)] for subscribers only. 