In mathematics, the Veronese surface is an algebraic surface in five-dimensional projective space. It is the embedding of the projective plane according to the linear system of divisors given by the conic sections. In more algebraic language, it is the same to say that the mapping

: f ( x : y : z ) = ( x 2: y 2: z 2: yz : xz : xy )

gives the transformation applied to homogeneous coordinates.