On self-circumferences in Minkowski planes
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University of Extremadura
2019-06-01
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| Series: | Extracta Mathematicae |
| Subjects: | |
| Online Access: | https://publicaciones.unex.es/index.php/EM/article/view/72 |
| Summary: | 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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| ISSN: | 0213-8743 2605-5686 |