# The inverse Kakeya problem

```@article{Cabello2022TheIK,
title={The inverse Kakeya problem},
author={Sergio Cabello and Otfried Cheong and Michael Gene Dobbins},
journal={Periodica Mathematica Hungarica},
year={2022},
volume={84},
pages={70-75}
}```
• Published 18 December 2019
• Mathematics
• Periodica Mathematica Hungarica
We prove that the largest convex shape that can be placed inside a given convex shape  \$\$Q \subset \mathbb {R}^{d}\$\$ Q ⊂ R d in any desired orientation is the largest inscribed ball of  Q . The statement is true both when “largest” means “largest volume” and when it means “largest surface area”. The ball is the unique solution, except when maximizing the perimeter in the two-dimensional case.

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