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 $\operatorname{div} \operatorname{curl} F = 0$.
What is an intuitive explanation for $\operatorname{div} \operatorname{curl} F = 0$?
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multivariable-calculus
intuition
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2See this similar MO question: http://mathoverflow.net/questions/21881/how-should-one-present-curl-and-divergence-in-an-undergraduate-multivariable-calc – 2011-03-14
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0Strang points out in his CSE book that div curl = 0 is the transpose of curl grad = 0. – 2015-08-11