Think of a rectangular flag. When it is moved by the wind, we may think of the inferior border of the flag as drawing a curve in some plane. But, obviously, the area of the waving flag is the same of the rectangular flag.(adsbygoogle = window.adsbygoogle || []).push({});

So, if I draw a curve of length L in a plane, and I set up a fence of constant height H over said curve, I suppose its area is LH. But what is the rigorous justification?? Line integrals??

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# Area of a fence over a curve

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