The extreme polygons for the self Chebyshev radius of the boundary
| Autor: | Nikitenko, Evgenii V., Nikonorov, Yurii G. |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1556/012.2023.04297 |
| Popis: | The paper is devoted to some extremal problems for convex polygons on the Euclidean plane, related to the concept of self Chebyshev radius for the polygon boundary. We consider a general problem of minimization of the perimeter among all $n$-gons with a fixed self Chebyshev radius of the boundary. The main result of the paper is the complete solution of the mentioned problem for $n=4$: We proved that the quadrilateral of minimum perimeter is a so called magic kite, that verified the corresponding conjecture by Rolf Walter. Comment: 42 pages, 22 figures, added some comments and sources in the bibliography |
| Databáze: | arXiv |
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