Abstract

Let CC and DD be convex bodies in the Euclidean space EdE^d. We define the centroid Banach-Mazur distance δBMcen(C,D)\delta_{BM}^{\rm cen} (C, D) similarly to the classic Banach-Mazur distance δBM(C,D)\delta_{BM} (C, D), but with the extra requirement that the centroids of CC and an affine image of DD coincide. We prove that for the parallelogram PP and the triangle TT in E2E^2 we have δBMcen(P,T)=52\delta_{BM}^{\rm cen} (P, T) = \frac{5}{2}.

Author information

Contact details are reproduced from the original publication and may be historical.

Marek Lassak

Institute of Mathematics and Physics, University of Technology and Life Sciences, Bydgoszcz, Poland

lassak@pbs.edu.pl

Keywords

  • Banach-Mazur distance
  • centroid Banach-Mazur distance
  • convex body
  • centroid
  • parallelogram
  • triangle

Mathematics Subject Classification

52A21; 46B20, 52A10

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Suggested citation

M. Lassak. “The Centroid Banach-Mazur Distance between the Parallelogram and the Triangle.” Journal of Convex Analysis 31 (2024), No. 1, 51–58. https://doi.org/10.68381/jca31004

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Published by Heldermann Verlag, 2024. Rights now held by Banach Press LLC.