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I am aware of an intuitive explanation for $\operatorname{curl} \operatorname{grad} F = 0$ (a block placed on a mountainous frictionless surface will slide to lower ground without spinning), and was wondering if there were a similar explanation for $\operatorname{div} \operatorname{curl} F = 0$.

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    See this similar MO question: http://mathoverflow.net/questions/21881/how-should-one-present-curl-and-divergence-in-an-undergraduate-multivariable-calc2011-03-14
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    Strang points out in his CSE book that div curl = 0 is the transpose of curl grad = 0.2015-08-11

5 Answers 5