On angular measures in Minkowski planes
type: Item
instance of: scholarly article
title: On angular measures in Minkowski planes
zbMATH Open document ID: 1246.46011
author: Andreas Fankhänel
published in: Beiträge zur Algebra und Geometrie
publication date: 2011-10-07T00:00:00Z
review text: Following ideas of Brass and Düvelmeyer, the author introduces a translation invariant angular measure for normed planes that has the property that if two James-orthogonal vectors form an angle of measure \({\pi\over 2}\), then the plane is Euclidean. This implication does not hold for Birkhoff orthogonality; it yields a more general class of norms whose unit circles suitably contain arcs which are pieces of Radon curves.
reviewed by: Horst Martini
Mathematics Subject Classification ID: 46B20
Mathematics Subject Classification ID: 52A21
zbMATH DE Number: 5955039
zbMATH Keywords: angular measure
zbMATH Keywords: Birkhoff orthogonality
zbMATH Keywords: James orthogonality
zbMATH Keywords: Radon curve
zbMATH Keywords: Thales' theorem
zbMATH Keywords: normed plane
zbMATH Keywords: Minkowski geometry
MaRDI profile type: Publication
full work available at URL: s13366-011-0011-4
OpenAlex ID: W1970687460
cites work: Characterizations of inner product spaces
cites work: Erdös distance problems in normed spaces
cites work: Angle Measures and Bisectors in Minkowski Planes
cites work: \(I\)-measures in Minkowski planes
cites work: Antinorms and Radon curves
cites work: The geometry of Minkowski spaces -- a survey. I
cites work: Q4716272
DOI: 10.1007/S13366-011-0011-4
description: scientific article; zbMATH DE number 5955039