# About the Blaschke-Santalo diagram of area, perimeter and moment of inertia

arXiv: https://arxiv.org/abs/2307.11658 · HTML: https://mlsanity.com/paper/2307.11658/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jul 2023.

## Built on by (most cited first, 1 of 1)

- [Numerical exploration of the range of shape functionals using neural networks](https://mlsanity.com/paper/2602.14881/) (2026)

## Abstract (arXiv)

We study the Blaschke-Santal'o diagram associated to the area, the perimeter, and the moment of inertia. We work in dimension 2, under two assumptions on the shapes: convexity and the presence of two orthogonal axis of symmetry. We discuss topological and geometrical properties of the diagram. As a by-product we address a conjecture by P'olya, in the simplified setting of double symmetry.