The Centroid Banach-Mazur Distance between the Parallelogram and the Triangle

M. Lassak

Journal of convex analysis, Tome 31 (2024) no. 1, pp. 51-58

Résumé

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 $\delta_{BM}^{\rm cen} (P, T) = \frac{5}{2}$.

Détail

Classification : 52A21, 46B20, 52A10
Mots-clés : Banach-Mazur distance, centroid Banach-Mazur distance, convex body, centroid, parallelogram, triangle