Category: Geometric transversal theory

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
Helly's theorem
Helly's theorem is a basic result in discrete geometry on the intersection of convex sets. It was discovered by Eduard Helly in 1913, but not published by him until 1923, by which time alternative pro
Carathéodory's theorem (convex hull)
Carathéodory's theorem is a theorem in convex geometry. It states that if a point x of Rd lies in the convex hull of a set P, then x can be written as the convex combination of at most d + 1 points in
Radon's theorem
In geometry, Radon's theorem on convex sets, published by Johann Radon in 1921, states that any set of d + 2 points in Rd can be partitioned into two sets whose convex hulls intersect. A point in the
Shapley–Folkman lemma
The Shapley–Folkman lemma is a result in convex geometry with applications in mathematical economics that describes the Minkowski addition of sets in a vector space. Minkowski addition is defined as t