Tangent segments in Minkowski planes.
Wu, Senlin (2008)
Beiträge zur Algebra und Geometrie
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Displaying similar documents to “A new type of orthogonality for normed planes”
Tangent segments in Minkowski planes.
-measures in Minkowski planes.
Fankhänel, Andreas (2009)
Beiträge zur Algebra und Geometrie
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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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Homological transformations in four-dimensional space.
C. Ernesto, S. Lindgren (1974)
Gaceta Matemática
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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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An alternative proof of Petty's theorem on equilateral sets
Tomasz Kobos (2013)
Annales Polonici Mathematici
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The main goal of this paper is to provide an alternative proof of the following theorem of Petty: in a normed space of dimension at least three, every 3-element equilateral set can be extended to a 4-element equilateral set. Our approach is based on the result of Kramer and Németh about inscribing a simplex into a convex body. To prove the theorem of Petty, we shall also establish that for any three points in a normed plane, forming an equilateral triangle of side p, there exists a fourth...
The Blasius function in the complex plane.
Boyd, John P. (1999)
Experimental Mathematics
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Upper estimates on self-perimeters of unit circles for gauges
Horst Martini, Anatoliy Shcherba (2016)
Colloquium Mathematicae
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Let M² denote a Minkowski plane, i.e., an affine plane whose metric is a gauge induced by a compact convex figure B which, as a unit circle of M², is not necessarily centered at the origin. Hence the self-perimeter of B has two values depending on the orientation of measuring it. We prove that this self-perimeter of B is bounded from above by the four-fold self-diameter of B. In addition, we derive a related non-trivial result on Minkowski planes whose unit circles are quadrangles. ...
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...