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## Main Question or Discussion Point

if the grad of the curl of a function is always zero does this mean the magnitude of the curl is constant? or am i way off here?

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if the grad of the curl of a function is always zero does this mean the magnitude of the curl is constant? or am i way off here?

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cristo

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edit: misread the question- sorry!

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uart

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Actually nolan I think you are mixing up two seperate properties of "curl" there to come to this misconception. The properties that you are thinking of are probably these two :

1. The

2. If a given function can be written as the

Note that neither of thse two things (taken seperately or together) imply what you have written.

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uart

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mathwonk

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that in turn is true by the FTC, which holds by the trivial fact that the derivative of the area function is the height functon, which holds trivially because the area of a rectangle is the base times the height.

on the other hand, sticking all these trivialities together, maybe we have a pathologically amazing theorem!

more interesting is the investigation of forms with zero curl which are not gradients, like dtheta.

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uart

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