Czechoslovak Mathematical Journal

, Volume 60, Issue 2, pp 339–349 | Cite as

A new type of orthogonality for normed planes

  • Horst Martini
  • Margarita Spirova
Article
First Online:
Received:

Abstract

In this paper we introduce a new type of orthogonality for real normed planes which coincides with usual orthogonality in the Euclidean situation. With the help of this type of orthogonality we derive several characterizations of the Euclidean plane among all normed planes, all of them yielding also characteristic properties of inner product spaces among real normed linear spaces of dimensions d ⩾ 3.

Keywords

chordal orthogonality Feuerbach circle inner product space James orthogonality Minkowski plane normed linear space normed plane orthocentricity Wallace line 

MSC 2010

46B20 46C15 52A21 
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Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2010

Authors and Affiliations

  • Horst Martini
    • 1
  • Margarita Spirova
    • 1
  1. 1.Fakultät für MathematikTU ChemnitzChemnitzGermany

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