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- Thread starter k312
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x,y,z are the coordinates

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Thanks for the post

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Fredrik

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"x,y,z" isn't a coordinate system. Those are just variable names that might possibly represent the components of a coordinate system on a 3-dimensional manifold. Your manifold (the surface defined by the equation z=y) is 2-dimensional.x,y,z are the coordinates

A coordinate system on an n-dimensional manifold is a function from an open subset of the manifold into [itex]\mathbb R^n[/itex]. If this is differential geometry, you need to use a coordinate system. Did you look at the post I linked to to see how the partial derivatives are defined?

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Just think about it, k312: would the limit quotient make sense in your standard surface.?

What would we mean, by e.g., ||h||->0 , etc. This is why , when we work with manifolds,

most of the work is done in R^n and then brought back/ pulled back into the manifold,

as Fredrik described, by using charts.

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