On cross-section measures in Minkowski spaces.
Gennadiy Averkov (2003)
Extracta Mathematicae
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Displaying similar documents to “On Reuleaux triangles in Minkowski planes.”
On cross-section measures in Minkowski spaces.
On the Busemann area in Minkowski spaces.
Schneider, Rolf (2001)
Beiträge zur Algebra und Geometrie
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On boundary arcs joining antipodal points of a planar convex body.
Averkov, Gennadiy (2006)
Beiträge zur Algebra und Geometrie
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Illumination of direct sums of two convex figures.
Baladze, E.D., Boltyanski, V.G. (2006)
Beiträge zur Algebra und Geometrie
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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 .
Two optimization problems for convex bodies in the -dimensional space.
Hernández Cifre, María A., Salinas, Guillermo, Segura Gomis, Salvador (2004)
Beiträge zur Algebra und Geometrie
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On isoperimetric inequalities in Minkowski spaces.
Martini, Horst, Mustafaev, Zokhrab (2010)
Journal of Inequalities and Applications [electronic only]
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Circumscribed simplices of minimal mean width.
Böröczky, Károly, Schneider, Rolf (2007)
Beiträge zur Algebra und Geometrie
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Mazur-Ulam Theorem
Artur Korniłowicz (2011)
Formalized Mathematics
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The Mazur-Ulam theorem [15] has been formulated as two registrations: cluster bijective isometric -> midpoints-preserving Function of E, F; and cluster isometric midpoints-preserving -> Affine Function of E, F; A proof given by Jussi Väisälä [23] has been formalized.
The Aleksandrov-Fenchel type inequalities for volume differences.
Zhao, Chang-jian, Bencze, Mihály (2010)
Balkan Journal of Geometry and its Applications (BJGA)
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Affine Independence in Vector Spaces
Karol Pąk (2010)
Formalized Mathematics
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In this article we describe the notion of affinely independent subset of a real linear space. First we prove selected theorems concerning operations on linear combinations. Then we introduce affine independence and prove the equivalence of various definitions of this notion. We also introduce the notion of the affine hull, i.e. a subset generated by a set of vectors which is an intersection of all affine sets including the given set. Finally, we introduce and prove selected properties...