As a side note the set S = {re H : N(x) =1} forms a group under multiplication and can be identified with the 3 sphere $3 C R* by the function D : H - R D(a + bi + cj + dk) = (a, b, c, d) where o(H) = R4 and $(S) = $3 C R4 Furthermore the unit quaternions can be written in matrix form and there exists an isomor- phism S ~ SU(2)