More generally, a smooth quadric (degree 2) hypersurface "X" of any dimension "n" is rational, by stereographic projection. (For "X" a quadric over a field "k", "X" must be assumed to have a "k"-rational point; this is automatic if "k" is algebraically closed.) To define stereographic projection, let "p" be a point in "X". Then a birational map from "X" to the projective space formula_23 of lines through "p" is given by sending a point "q" in "X" to the line through "p" and "q". This is a birational equivalence but not an isomorphism of varieties, because it fails to be defined where "q" = "p" (and the inverse map fails to be defined at those lines through "p" which are contained in "X").