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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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- Thread starter Castilla
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- #1

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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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HallsofIvy

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(Integral) [f(x) + H]dx - (Integral) f(x)dx = (Integral) Hdx.

And that is not LH, which is the obvious area of a flag of length L and heigth H when it is "at rest".

- #4

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I draw a smooth curve in the plane xy. I know its length, it is L. I "build" a fence over it, reaching the same height H for every point of the curve.

It is pretty obvious that this fence has area LH, but what is the rigorous justification? Do I need to go to line integrals to have it?

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