High Quality Content by WIKIPEDIA articles! In discrete geometry, Tverberg's theorem, first stated by Helge Tverberg (1966), 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 (d + 1)(r - 1) + 1 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 each of the subsets. The partition resulting from this theorem is known as a Tverberg partition.

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