Radon's Theorem

In geometry, Radon's theorem on convex sets, named after Johann Radon, states that any set of d + 2 points in Rd can be partitioned into two (disjoint) sets whose convex hulls intersect. A point in the intersection of these hulls is called a Radon point of the set.

For example, in the case d = 2, any set of four points in the Euclidean plane can be partitioned in one of two ways. It may form a triple and a singleton, where the convex hull of the triple (a triangle) contains the singleton; alternatively, it may form two pairs of points that form the endpoints of two intersecting line segments.