be non-orientable. A matroid without any two-point lines is called a Sylvester matroid. Relatedly, the Kelly–Moser configuration with seven points and only three ordinary lines forms one of the forbidden minors for GF(4)-representable matroids. Distance geometry Another generalization of the Sylvester–Gallai theorem to arbitrary metric spaces was conjectured by and proved by . In this generalization, a triple of points in a metric space is defined to be collinear when the triangle inequality for these points is an equality, and a line is defined from any pair of points by repeatedly including additional points that are collinear with points already added to the line, until no more such points can be added. The generalization of Chvátal and Chen states that every finite metric space has a line that contains either all points or exactly two of the points. Notes References External links Proof presentation by Terence Tao at the 2013 Minerva Lectures Euclidean plane geometry Theorems in discrete geometry Matroid theory Articles containing proofs