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 intersection of these convex hulls is called a Radon point of the set.

Two sets of four points in the plane (the vertices of a square and an equilateral triangle with its centroid), the multipliers solving the system of three linear equations for these points, and the Radon partitions formed by separating the points with positive multipliers from the points with negative multipliers.

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.