A convex body whose centroid and Santal\'o point are far apart

TL;DR

This paper presents a specific convex body example where the centroid and Santaló point are significantly separated, highlighting a notable geometric property.

Contribution

The authors construct an explicit convex body demonstrating a large distance between its centroid and Santaló point, providing insight into their spatial relationship.

Findings

Centroid and Santaló point can be far apart in convex bodies

Explicit example illustrating the separation

Contributes to understanding geometric properties of convex bodies

Abstract

We give an example of a convex body whose centroid and Santal\'o point are "far apart".