Ellipsoidal coordinates
that generalizes the two-dimensional elliptic coordinate system.by the equations where the following limits apply to the coordinates Consequently, surfaces of constantare hyperboloids of one sheet because the last term in the lhs is negative, and surfaces of constantare hyperboloids of two sheets because the last two terms in the lhs are negative.Using this function, the scale factors can be written Hence, the infinitesimal volume element equals and the Laplacian is defined by Other differential operators such asby substituting the scale factors into the general formulae found in orthogonal coordinates.are the usual polar and azimuthal angles of spherical coordinates, respectively.