Another interesting "angle" on them is as
-dimensional vector subspaces of an
-dimensional vector space without considering the plane
. This has the same VC-dimension (
) even if the points can be chosen anywhere rather than on the hyperplane
. Since no points on a ray can be separated, this is essentially the same as them acting on, say, a unit sphere, which has dimension
. Half of this sphere is also the same as our plane
by projection along the rays.