On equichordal curves

Abstract

SynopsisIn this paper we consider equichordal curves in ℝn. We extend the notion of chordal area to all equichordal curves and introduce a notion of *-chordal area. We establish results connected with the length, *-chordal area and extended chordal area. Moreover, we give a Crofton-type integral formula for plane equichordal curves and derive an isoperimetric inequality for *-chordal area. The paper is based on the results of F. J. Craveiro de Carvalho and S. A. Robertson [2].