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Title: On self-circumferences in Minkowski planes
Authors: Ghandehari, Mostafa
Martini, Horst
Keywords: Gauge;Minkowski geometry;Normed plane;Polygonal gauges;Radon curve;Self-circumference;Self-perimeter;Calibre;Geometría de Minkowski;Plano normado;Medidores poligonales;Curva de radón;Autoperímetro;Autocircunferencia
Issue Date: 2019
Publisher: Universidad de Extremadura
Abstract: This paper contains results on self-circumferences of convex figures in the frameworks of norms and (more general) also of gauges. Let δ(n) denote the self-circumference of a regular polygon with n sides in a normed plane. We will show that δ(n) is monotonically increasing from 6 to 2π if n is twice an odd number, and monotonically decreasing from 8 to 2π if n is twice an even number. Calculations of self-circumferences for the case that n is odd as well as inequalities for the self-circumference of some irregular polygons are also given. In addition, properties of the mixed area of a plane convex body and its polar dual are used to discuss the self-circumference of convex curves.
DOI: 10.17398/2605-5686.34.1.19
Appears in Collections:Extracta Mathematicae Vol. 34, nº 1 (2019)

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