Editing Radon's theorem (section)

{{short description|Says d+2 points in d dimensions can be partitioned into two subsets whose convex hulls intersect}}
In [[geometry]], '''Radon's theorem''' on [[convex set]]s, published by [[Johann Radon]] in 1921, states that:<blockquote>Any set of d&nbsp;+&nbsp;2 points in '''[[real number|R]]'''<sup>d</sup> can be [[partition of a set|partitioned]] into two sets whose [[convex hull]]s intersect. </blockquote>A point in the intersection of these convex hulls is called a '''Radon point''' of the set.[[File:Radon coefficients.svg|thumb|300px|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''&nbsp;=&nbsp;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 segment]]s.