Geodesic
A new type of orthogonality for normed planes
Czechoslovak Mathematical Journal, Tome 60 (2010) no. 2, pp. 339-349 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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 $d\geq 3$.
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 $d\geq 3$.
Classification : 46B20, 46C15, 52A21
Keywords: chordal orthogonality; Feuerbach circle; inner product space; James orthogonality; Minkowski plane; normed linear space; normed plane; orthocentricity; Wallace line 
@article{CMJ_2010_60_2_a3,
     author = {Martini, Horst and Spirova, Margarita},
     title = {A new type of orthogonality for normed planes},
     journal = {Czechoslovak Mathematical Journal},
     pages = {339--349},
     year = {2010},
     volume = {60},
     number = {2},
     mrnumber = {2657953},
     zbl = {1224.46026},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2010_60_2_a3/}
}
TY  - JOUR
AU  - Martini, Horst
AU  - Spirova, Margarita
TI  - A new type of orthogonality for normed planes
JO  - Czechoslovak Mathematical Journal
PY  - 2010
SP  - 339
EP  - 349
VL  - 60
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/CMJ_2010_60_2_a3/
LA  - en
ID  - CMJ_2010_60_2_a3
ER  - 
%0 Journal Article
%A Martini, Horst
%A Spirova, Margarita
%T A new type of orthogonality for normed planes
%J Czechoslovak Mathematical Journal
%D 2010
%P 339-349
%V 60
%N 2
%U http://geodesic.mathdoc.fr/item/CMJ_2010_60_2_a3/
%G en
%F CMJ_2010_60_2_a3
Martini, Horst; Spirova, Margarita. A new type of orthogonality for normed planes. Czechoslovak Mathematical Journal, Tome 60 (2010) no. 2, pp. 339-349. http://geodesic.mathdoc.fr/item/CMJ_2010_60_2_a3/