# Integral Geometry about the visual angle of a convex set

## TL;DR

This paper explores integral formulas related to the visual angle of convex sets, providing geometric interpretations and simplified proofs within the framework of Integral Geometry.

## Contribution

It offers a unified interpretation of classical formulas like Crofton, Hurwitz, and Masotti, and introduces simpler proofs using measure-theoretic approaches.

## Key findings

- Unified geometric interpretation of classical formulas
- Simplified proofs of integral formulas
- Enhanced understanding of visual angle measures

## Abstract

In this paper we deal with a general type of integral formulas of the visual angle, among them those of Crofton, Hurwitz and Masotti, from the point of view of Integral Geometry. The purpose is twofold: to provide an interpretation of these formulas in terms of integrals of densities with respect to the canonical measure in the space of pairs of lines and to give new simpler proofs of them.