Integral Geometry about the visual angle of a convex set

2019/06/25 by Cufí, Julià, Gallego, Eduardo, Reventós, Agustí
#52A10 #53A04 #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1906.10374

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.

Related

• Integral Geometry of pairs of planes
• On the solid angle of a convex set
• Integral geometry of pairs of hyperplanes or lines
• On some relations between the Perimeter, the Area and the Visual Angle of a Convex Set
• Polygones convexes : le problème de la fin heureuse