On The Integral Formulas Of Crofton And Hurwitz Relative To The Visual Angle Of A Convex Set

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Abstract

We provide a unified approach that encompasses some integral formulas for functions of the visual angle of a compact convex set due to Crofton, Hurwitz and Masotti. The basic tool is an integral formula that also allows us to integrate new functions of the visual angle. Also, we establish some upper and lower bounds for the considered integrals, generalizing, in particular, those obtained by Santaló for Masotti's integral.
Original languageEnglish
Pages (from-to)874-896
Number of pages23
JournalMathematika
Volume65
Issue number4
DOIs
Publication statusPublished - 1 Jan 2019

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