English: An illustration of Radon's theorem for two sets of four points in the plane: the vertices of a square, and an equilateral triangle with its centroid. Each point is labeled with a weight, used as part of a proof of the theorem. The weighted sum of the points is (0,0), and the sum of the weights is zero, from which it can be shown that the convex hull of the points with positive weights intersects the convex hull of the points with negative weights.