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I recently got the book A geometrical approach to differential forms by David Bachman. At the moment the biggest issue i am having is just visualizing what the form should look like/ be. The calculations for a one form and a vector are pretty much the same for a dot product so should the form be visualized as a vector? if so where is it and why does it have such an odd notation if it cant be visualized as a vector then how should we (I) picture it?

Thanks for any help you can give me