MathGroup Archive 2004

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Gauss Egregium theorem


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.


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