Position of the centroid of a planar convex body

Marek Lassak

Position of the centroid of a planar convex body

Functional Analysis 2022-12-22 v4 Metric Geometry

Authors: Marek Lassak

Abstract

It is well known that any planar convex body $A$ permits to inscribe an affine-regular hexagon $H_A$ . We prove that the centroid of $A$ belongs to the homothetic image of $H_A$ with ratio $\frac{4}{21}$ and the center in the center of $H_A$ . This ratio cannot be enlarged.

Keywords

planar convex body centroid affine-regular hexagon homothetic image convex geometry

Cite

@article{arxiv.2202.01815,
  title  = {Position of the centroid of a planar convex body},
  author = {Marek Lassak},
  journal= {arXiv preprint arXiv:2202.01815},
  year   = {2022}
}

Comments

8 pages, 1 figure

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