Show that S^2 is a 2 sheeted cover of {R}^3 (S^2 = {(x,y,z)| x^2 + y^2 + z^2 = 1}) {RP}^ 2 where S^2 is the unit sphere in Solution As it is a unit sphere. Hence its radius is 1. The centre of the sphere is (0,0,0) Let a point on the sphere be (x,y,z) The equation is (x-0)^2+(y-0)^2+(z-0)^2=r^2 x^2+y^2+z^2= 1 ..............Proved.