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Thread: A Question About Curves

  1. #1 A Question About Curves 
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    Suppose that you know the area underneath a curve. Let the height of the curve be 'x' and the length of the curve be 'y'. How many possible solutions are there such that x divided by y is always a whole number, and the curve so formed has an area exactly equal to the one you have been given?


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  3. #2 Re: A Question About Curves 
    . DrRocket's Avatar
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    Quote Originally Posted by Liongold
    Suppose that you know the area underneath a curve. Let the height of the curve be 'x' and the length of the curve be 'y'. How many possible solutions are there such that x divided by y is always a whole number, and the curve so formed has an area exactly equal to the one you have been given?
    What do you mean by THE height of a curve ? Why is height restricted ?

    Is there some reason that you are reversing the traditinal roles of "x" and "y" ? -- there is nothing wrong about that, but it is a bit unusual.

    Finally, does this have anything to do with a homework or test problem ?

    Your question is not clear, but I am pretty sure that if one could state it precisely the answer would be c, the cardinality of the continuum.


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  4. #3  
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    This doesn't have anything to do with a homework question; it's just a question I've been thinking aobut.

    For this curve, let us assume that it resembles the crest of a wave. By height, I meant then the maximum height it reaches, and the length of this curve is not the total length of the curve, but instead the length it has from a Euclidean viewpoint.

    It resembles something like this:
    _ is the maximum height (x)
    / \
    / \
    / \
    / \
    / \
    ------------- is the length (y)

    As for why I chose to reverse the traditional roles, that was because I am more comfortable with them.

    EDIT: It dpesn't seem to have come out quite right...
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  5. #4  
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    i'm not sure exactly what the question is.

    perhaps you could form a few equations and go from there

    the length of a curve is given by the integral of (sqrt(1+(dy/dx)^2)) dx = *y*

    the peak of your wave would be given by dy/dx = 0 which occurs at point *x*

    it is confusing that you changed the general convention. so my equations are formed from general convention
    everything is mathematical.
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