On self-circumferences in Minkowski planes
doi:10.17398/2605-5686.34.1.19
Keywords:
Gauge, Minkowski geometry, normed plane, polygonal gauges, Radon curve, self-circumference, self-perimeterAbstract
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.
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