Gauss Egregium theorem

*To*: mathgroup at smc.vnet.net*Subject*: [mg48126] Gauss Egregium theorem*From*: mathma18 at hotmail.com (Narasimham G.L.)*Date*: Fri, 14 May 2004 00:12:25 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

From classical surface theory, when E,F,G,e,f,g are coefficients of first and second fundamental forms,can it be shown/verified that (e*g - f^2) depends on E,F,G and partial derivatives alone? Can hand differentiation and algebraic expression calculations (bit laborious) be simpler by using symbolic computation on Mathematica ? Suppose someone had a hunch that (e*g - f^2) was connectable to the variables E,F,G and derivatives and did not know how exactly it is done, i.e., by means of which relation of equality, can Mathematica help find it out by simplification or by any other way ? Differentiating, especially by a computer, should be easier than integration :).. Gauss termed finding this not so obvious result of differentiation and algebraic simplification an excellent result.. a Theorem.