Tverberg'S Theorem

(Theory)

Logo of Tverberg's theorem
sciences
Theory since 1966
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What is Tverberg's theorem?

In discrete geometry, Tverberg's theorem, first stated by Helge Tverberg , is the result that sufficiently many points in d-dimensional Euclidean space can be partitioned into subsets with intersecting convex hulls. Specifically, for any set of points there exists a point x (not necessarily one of the given points) and a partition of the given points into r subsets, such that x belongs to the convex hull of all of the subsets. The partition resulting from this theorem is known as a Tverberg partition.

Technology Types

convex hullgeometric transversal theorypropositionstatementtheoremtheorems in convex geometrytheorems in discrete geometrytheory

Synonyms

Tverberg partitionTverberg partition theoremTverberg theoremTverberg's partition theorem

Translations

Satz von Tverberg (de)Теорема Тверберга (ru)

Tech Info


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