Geodesic
Covering Discs in Minkowski Planes
Canadian mathematical bulletin, Tome 52 (2009) no. 3, pp. 424-434

Voir la notice de l'article provenant de la source Cambridge

DOI

We investigate the following version of the circle covering problem in strictly convex (normed or) Minkowski planes: to cover a circle of largest possible diameter by $k$ unit circles. In particular, we study the cases $k\,=\,3$ , $k\,=\,4$ , and $k\,=\,7$ . For $k\,=\,3$ and $k\,=\,4$ , the diameters under consideration are described in terms of side-lengths and circumradii of certain inscribed regular triangles or quadrangles. This yields also simple explanations of geometric meanings that the corresponding homothety ratios have. It turns out that basic notions from Minkowski geometry play an essential role in our proofs, namely Minkowskian bisectors, $d$ -segments, and the monotonicity lemma.
DOI : 10.4153/CMB-2009-046-2
Mots-clés : 46B20, 52A21, 52C15, affine regular polygon, bisector, circle covering problem, circumradius, d-segment, Minkowski plane, (strictly convex) normed plane 
Martini, Horst; Spirova, Margarita. Covering Discs in Minkowski Planes. Canadian mathematical bulletin, Tome 52 (2009) no. 3, pp. 424-434. doi: 10.4153/CMB-2009-046-2
@article{10_4153_CMB_2009_046_2,
     author = {Martini, Horst and Spirova, Margarita},
     title = {Covering {Discs} in {Minkowski} {Planes}},
     journal = {Canadian mathematical bulletin},
     pages = {424--434},
     year = {2009},
     volume = {52},
     number = {3},
     doi = {10.4153/CMB-2009-046-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2009-046-2/}
}
TY  - JOUR
AU  - Martini, Horst
AU  - Spirova, Margarita
TI  - Covering Discs in Minkowski Planes
JO  - Canadian mathematical bulletin
PY  - 2009
SP  - 424
EP  - 434
VL  - 52
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2009-046-2/
DO  - 10.4153/CMB-2009-046-2
ID  - 10_4153_CMB_2009_046_2
ER  - 
%0 Journal Article
%A Martini, Horst
%A Spirova, Margarita
%T Covering Discs in Minkowski Planes
%J Canadian mathematical bulletin
%D 2009
%P 424-434
%V 52
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2009-046-2/
%R 10.4153/CMB-2009-046-2
%F 10_4153_CMB_2009_046_2

Cité par Sources :