Ceva's and Menelaus' theorems for the -dimensional space.
Buba-Brzozowa, Malgorzata (2000)
Journal for Geometry and Graphics
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Displaying similar documents to “Self-similar simplices.”
Ceva's and Menelaus' theorems for the -dimensional space.
Gergonne and Nagel points for simplices in the -dimensional space.
Koźniewski, Edwin, Górska, Renata A. (2000)
Journal for Geometry and Graphics
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A note on intersections of simplices
David A. Edwards, Ondřej F. K. Kalenda, Jiří Spurný (2011)
Bulletin de la Société Mathématique de France
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We provide a corrected proof of [1, Théorème 9] stating that any metrizable infinite-dimensional simplex is affinely homeomorphic to the intersection of a decreasing sequence of Bauer simplices.
Polarity for a simplex
Sahib Ram Mandan (1966)
Czechoslovak Mathematical Journal
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The additivity of the volume and Sperner's lemma
W. Dębski (1990)
Colloquium Mathematicae
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The Self-Similarity of the Josephus Problem and its Variants
Masakazu Naito, Sohtaro Doro, Daisuke Minematsu, Ryohei Miyadera (2009)
Visual Mathematics
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Inequalities for inscribed simplex and applications.
Yang, Shiguo, Cheng, Silong (2006)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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Sperner's Lemma
Karol Pąk (2010)
Formalized Mathematics
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In this article we introduce and prove properties of simplicial complexes in real linear spaces which are necessary to formulate Sperner's lemma. The lemma states that for a function ƒ, which for an arbitrary vertex υ of the barycentric subdivision B of simplex K assigns some vertex from a face of K which contains υ, we can find a simplex S of B which satisfies ƒ(S) = K (see [10]).
On self-reciprocal functions in two variables
R. U. Verma (1971)
Annales Polonici Mathematici
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Combinatorial lemmas for polyhedrons I
Adam Idzik, Konstanty Junosza-Szaniawski (2006)
Discussiones Mathematicae Graph Theory
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We formulate general boundary conditions for a labelling of vertices of a triangulation of a polyhedron by vectors to assure the existence of a balanced simplex. The condition is not for each vertex separately, but for a set of vertices of each boundary simplex. This allows us to formulate a theorem, which is more general than the Sperner lemma and theorems of Shapley; Idzik and Junosza-Szaniawski; van der Laan, Talman and Yang. A generalization of the Poincaré-Miranda theorem is also...