Two fundamental invariances are known as Gauss theorem http://en.wikipedia.org/wiki/Divergence_theorem and Stokes’ theorem http://en.wikipedia.org/wiki/Stokes_theorem. The former is also known as divergence theorem which requires the existence of a closed surface (having an inside and an outside) and the smoothness of its exterior normals and satisfying the property of orientability http://en.wikipedia.org/wiki/Orientability. Stokes’ theorem requires the existence of a two-sided surface bounded by a smooth closed curve. Since one-sided Möbius bands are not orientable, their implied invariance property asserts that closed surfaces cannot possibly exist in nature therefore totally disqualifying the validity of Gauss theorem and partially crippling Stokes’ theorem.


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