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Angle Measures and Bisectors in Minkowski Planes

  Published:2005-12-01
 Printed: Dec 2005
  • Nico Düvelmeyer
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Abstract

\begin{abstract} We 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.
Keywords: Radon curves, Minkowski geometry, Minkowski planes, angular bisector, angular measure, equiframed curves Radon curves, Minkowski geometry, Minkowski planes, angular bisector, angular measure, equiframed curves
MSC Classifications: 52A10, 52A21 show english descriptions Convex sets in $2$ dimensions (including convex curves) [See also 53A04]
Finite-dimensional Banach spaces (including special norms, zonoids, etc.) [See also 46Bxx]
52A10 - Convex sets in $2$ dimensions (including convex curves) [See also 53A04]
52A21 - Finite-dimensional Banach spaces (including special norms, zonoids, etc.) [See also 46Bxx]
 

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