# Thread: A Question About Curves

1. 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?

2.

3. 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.

4. 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...

5. 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

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