Tangent segments in Minkowski planes.
Wu, Senlin (2008)
Beiträge zur Algebra und Geometrie
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Displaying similar documents to “-measures in Minkowski planes.”
Tangent segments in Minkowski planes.
A new type of orthogonality for normed planes
Horst Martini, Margarita Spirova (2010)
Czechoslovak Mathematical Journal
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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 .
Some Generalization of Nearaffine Planes
Jan Jakóbowski (2005)
Bulletin of the Polish Academy of Sciences. Mathematics
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There are three kinds of Benz planes: Möbius planes, Laguerre planes and Minkowski planes. A Minkowski plane satisfying an additional axiom is connected with some other structure called a nearaffine plane. We construct an analogous structure for a Laguerre plane. Moreover, our description is common for both cases.
Extending Nearaffine Planes to Hyperbola Structures
Kinga Cudna-Salmanowicz, Jan Jakóbowski (2007)
Bulletin of the Polish Academy of Sciences. Mathematics
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H. A. Wilbrink [Geom. Dedicata 12 (1982)] considered a class of Minkowski planes whose restrictions, called residual planes, are nearaffine planes. Our study goes in the opposite direction: what conditions on a nearaffine plane are necessary and sufficient to get an extension which is a hyperbola structure.
On the stability of the unit circle with minimal self-perimeter in normed planes
Horst Martini, Anatoly Shcherba (2013)
Colloquium Mathematicae
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We prove a stability result on the minimal self-perimeter L(B) of the unit disk B of a normed plane: if L(B) = 6 + ε for a sufficiently small ε, then there exists an affinely regular hexagon S such that S ⊂ B ⊂ (1 + 6∛ε) S.
Lower levels of Euclidean planes.
Quaisser, Erhard (1998)
Beiträge zur Algebra und Geometrie
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Minkowski planes with Miquelian pairs.
Kroll, Hans-Joachim, Matraś, Andrzej (1997)
Beiträge zur Algebra und Geometrie
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Minimum Steiner Trees in Normed Planes.
Ding-Zhu Du, Biao Gao, R. L. Graham, Zi-Cheng Liu, Peng-Jun Wan (1993)
Discrete & computational geometry
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A universal construction for projective Hjelmslev planes of level
G. Hanssens, H. Van Maldeghem (1989)
Compositio Mathematica
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On the size of maximal caps in .
Metsch, K. (2003)
Advances in Geometry
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Points and Triangles in the Plane and Halving Planes in Space.
H. Edelsbrunner, B. Chazelle, L.J. Guibas, M. Sharir, R. Wenger, B. Aronov (1991)
Discrete & computational geometry
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Orthogonality in normed linear spaces: a classification of the different concepts and some open problems.
Carlos Benítez Rodríguez (1989)
Revista Matemática de la Universidad Complutense de Madrid
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Orthogonality in inner products is a binary relation that can be expressed in many ways without explicit mention to the inner product of the space. Great part of such definitions have also sense in normed linear spaces. This simple observation is at the base of many concepts of orthogonality in these more general structures. Various authors introduced such concepts over the last fifty years, although the origins of some of the most interesting results that can be obtained for these generalized...
On (a,b,c,d)-orthogonality in normed linear spaces
C.-S. Lin (2005)
Colloquium Mathematicae
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We first introduce a notion of (a,b,c,d)-orthogonality in a normed linear space, which is a natural generalization of the classical isosceles and Pythagorean orthogonalities, and well known α- and (α,β)-orthogonalities. Then we characterize inner product spaces in several ways, among others, in terms of one orthogonality implying another orthogonality.