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How do you visualize the exterior derivative of differential forms?

I imagine differential forms to be some sort of (oriented) line segments, areas, volumes etc. That is if I imagine a two-form, I imagine two vectors, constituting a parallelogram.

So I think provided I can imagine a field of oriented line segments, with exterior derivative I should imagine an appropriate field of oriented areas.

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    http://mathoverflow.net/questions/21024/what-is-the-exterior-derivative-intuitively2012-10-03

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