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 |
| _version_ | 1798014215349338112 |
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| author | Mostafa Ghandehari Horst Martini |
| author_facet | Mostafa Ghandehari Horst Martini |
| author_sort | Mostafa Ghandehari |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T15:14:59Z |
| format | Article |
| id | doaj.art-81a19697d33e4432b192ba9b0b24a112 |
| institution | Directory Open Access Journal |
| issn | 0213-8743 2605-5686 |
| language | English |
| last_indexed | 2024-04-11T15:14:59Z |
| publishDate | 2019-06-01 |
| publisher | University of Extremadura |
| record_format | Article |
| series | Extracta Mathematicae |
| spelling | doaj.art-81a19697d33e4432b192ba9b0b24a1122022-12-22T04:16:31ZengUniversity of ExtremaduraExtracta Mathematicae0213-87432605-56862019-06-01341On self-circumferences in Minkowski planesMostafa Ghandehari0Horst Martini1Department of Mathematics, University of Texas at Arlington, TX 76019, U.S.A.Faculty of Mathematics, University of Technology, 09107 Chemnitz, GermanyThis 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.https://publicaciones.unex.es/index.php/EM/article/view/72GaugeMinkowski geometrynormed planepolygonal gaugesRadon curveself-circumference |
| spellingShingle | Mostafa Ghandehari Horst Martini On self-circumferences in Minkowski planes Extracta Mathematicae Gauge Minkowski geometry normed plane polygonal gauges Radon curve self-circumference |
| title | On self-circumferences in Minkowski planes |
| title_full | On self-circumferences in Minkowski planes |
| title_fullStr | On self-circumferences in Minkowski planes |
| title_full_unstemmed | On self-circumferences in Minkowski planes |
| title_short | On self-circumferences in Minkowski planes |
| title_sort | on self circumferences in minkowski planes |
| topic | Gauge Minkowski geometry normed plane polygonal gauges Radon curve self-circumference |
| url | https://publicaciones.unex.es/index.php/EM/article/view/72 |
| work_keys_str_mv | AT mostafaghandehari onselfcircumferencesinminkowskiplanes AT horstmartini onselfcircumferencesinminkowskiplanes |