Finite Minkowski planes of type 20 with respect to homotheties

Methods to Construct Shortest Trees in Banach-Minkowski Planes

Operations Research Proceedings - Operations Research Proceedings 1994 ◽

10.1007/978-3-642-79459-9_60 ◽

1995 ◽

pp. 329-334

Author(s):

Dietmar Cieslik

Keyword(s):

Minkowski Planes

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Covering Discs in Minkowski Planes

Canadian Mathematical Bulletin ◽

10.4153/cmb-2009-046-2 ◽

2009 ◽

Vol 52 (3) ◽

pp. 424-434 ◽

Cited By ~ 2

Author(s):

Horst Martini ◽

Margarita Spirova

Keyword(s):

Essential Role ◽

Covering Problem ◽

Minkowski Geometry ◽

Minkowski Planes ◽

Strictly Convex ◽

Unit Circles ◽

Circle Covering ◽

Monotonicity Lemma

AbstractWe 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.

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Angle Measures and Bisectors in Minkowski Planes

Canadian Mathematical Bulletin ◽

10.4153/cmb-2005-048-0 ◽

2005 ◽

Vol 48 (4) ◽

pp. 523-534 ◽

Cited By ~ 13

Author(s):

Nico Düvelmeyer

Keyword(s):

Unit Circle ◽

Minkowski Plane ◽

Arc Length ◽

Area Measure ◽

Angular Measure ◽

Minkowski Planes ◽

Length Measure

AbstractWe prove that a Minkowski plane is Euclidean if and only if Busemann's or Glogovskij's definitions of angular bisectors coincide with a bisector defined by an angular measure in the sense of Brass. In addition, bisectors defined by the area measure coincide with bisectors defined by the circumference (arc length) measure if and only if the unit circle is an equiframed curve.

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