(Embedding of P2(R) in R1). Let F:R3 → R* be given by F(x, y, z) = (x2 - y2, xy, xz, yz), (x, y, z) = p € R3. Let S2 CR3 be the unit sphere with the origin 0 € R3. Ob- serve that the restriction = F S2 is such that (p) = (−p), and consider the mapping : P2(R) → R1 given by