Please use this identifier to cite or link to this item:
http://hdl.handle.net/10662/9841
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. |
URI: | http://hdl.handle.net/10662/9841 |
DOI: | 10.17398/2605-5686.34.1.19 |
Appears in Collections: | Extracta Mathematicae Vol. 34, nº 1 (2019) |
Files in This Item:
File | Description | Size | Format | |
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2605-5686_34_1_19.pdf | 296,24 kB | Adobe PDF | View/Open |
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