Abstract: The Gaussian equation expression of surface theory is discussed.The direct explicit formula expression of Gaussian equation is derived by means of the matrix expression of the fundamental equation on curved surface.The derivation of Gaussian curvature simplified formula is discussed which discloses the discovery of Gaussian curvature implicit formula.The proof procedure of Gaussian equation of Liouville form is demonstrated.

Key words: fundamental equation of surface theory, matrix expression, Gaussian equation, Liouville form