 In , Boris Delone and Dmitry Faddeev showed that binary cubic forms with integer coefficients can be used to parametrize orders in cubic fields.Their work was generalized in to include all cubic rings, giving a discriminant-preserving bijection between orbits of a GL(2, Z)-action on the space of integral binary cubic forms and cubic rings up to isomorphism.The classification of real cubic forms formula_1 is linked to the classification of umbilical points of surfaces.