What is the relationship betwenn RP^2 and CP? Espesicially, why are their stenographic representations different? As far as I understand the stenographic representation for RP^2 goes like that: a sphere with antipodal points identified is put above the R^2 plane, lines through the origin of the sphere cut the R^2 plane and project the sphere to the plane and so on. Whereas, the stenographic representation for CP is: take a sphere, cut it in the middle with the R^2 plane and take lines starting from the north pole projecting from the sphere to the plane. And take lines starting from the south pole projecting from the sphere to the other side of the plane. Plus, transistion functions connecting these two mappings.