PL EN

Preferencje
Język
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo

## Colloquium Mathematicum

2007 | 107 | 2 | 273-285
Tytuł artykułu

### Circumradius versus side lengths of triangles in linear normed spaces

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Given a planar convex body B centered at the origin, we denote by ℳ ²(B) the Minkowski plane (i.e., two-dimensional linear normed space) with the unit ball B. For a triangle T in ℳ ²(B) we denote by $R_B(T)$ the least possible radius of a Minkowskian ball enclosing T. We remark that in the terminology of location science $R_B(T)$ is the optimum of the minimax location problem with distance induced by B and vertices of T as existing facilities (see, for instance, [HM03] and the references therein). Using methods of linear algebra and convex geometry we find the lower and upper bound of $R_B(T)$ for the case when B is an arbitrary planar convex body centered at the origin and T ⊆ ℳ ²(B) is an arbitrary triangle with given Minkowskian side lengths a₁, a₂, a₃. We also obtain some further results from the geometry of triangles in Minkowski planes, which are either corollaries of the main result or statements needed in the proof of the main result.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
273-285
Opis fizyczny
Daty
wydano
2007
Twórcy
autor
• Institute of Algebra and Geometry, Faculty of Mathematics, Otto-von-Guericke University of Magdeburg, Universitätsplatz 2, D-39106 Magdeburg, Germany
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory