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Is it good to say

the smaller the parameter is, the outer the curve.

or alternatively,

the bigger the parameter is, the inner the curve.

I don't feel they are natural. What do you think?

I am not sure if "outer" and "inner" here can be used as the comparative degree form of adjectives "out" and "in"? Can "out" and "in" be adjectives?

Thanks!

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  • I may not be completely understanding the question, but could you say "the greater the curve" and "the lesser/smaller the curve"?
    – nxx
    Commented Feb 5, 2014 at 1:23
  • By "parameter" you mean the horizontal X axis, right? And by "bigger curve" I'm assuming you mean the "roundness" or a curve, right? Are you trying to describe [A] the way any single curve behaves (they all behave similarly) or are you trying to describe [B] some relationship between the three curves: for example, at x=1, the three curves are all bunched up together, while at x=1.25, the curves are separated from each other... are you trying to describe this [B]?
    – CoolHandLouis
    Commented Feb 5, 2014 at 11:34
  • @CoolHandLouis: the parameter is $\Phi$ (Φ) and I try to describe the relations between the curves.
    – Tim
    Commented Feb 5, 2014 at 11:36
  • Instead of "inner" or "outer" you could just say "further in" and "further out".
    – hairboat
    Commented Feb 5, 2014 at 14:33
  • Though this will not answer your curvature question, in my opinion, it would be more natural to write in a technical paper: The larger Φ values give the larger ω values than the smaller Φ values.
    – Damkerng T.
    Commented Feb 5, 2014 at 17:01

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I think you're intuition is telling you the right thing: those don't sound natural. One way to say it might be,

The greater the parameter, the greater the value of Y with respect to X.

although that sounds a bit technical. If you wanted a more informal way to say it, you could try,

The curves move higher on the graph as the parameter increases.

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If you want to avoid technical-sounding explanations, you can just say "the bigger the parameter is, the flatter the curve is." Alternatively, "the smaller the parameter is, the more rounded the curve is." (It's more accurate to say that the curve is rounded than to say it's round.) Less formally, you can say "the bigger the parameter, the flatter the curve." "Is" is implied in this case.

Now, out and in are prepositions, and outer and inner are adjectives. So, outer and inner are not comparatives of out and in, although they look as if they are. (The comparatives of outer and inner are "more outer" and "more inner".)

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The smaller the parameter, the bigger the curvature.
The larger the parameter, the smaller the curvature.
The (concave) graph flattens-out at about 1.3 and above.

The slope-of-the-graph (aka "the curve") flattens-out at about 1.3 and above. So you might be trying to say something like, "We see the effect of <SomeTechnicalThing> where the curve flattens-out at higher values of the parameter."

A more complete description might be, "The variable slope is always negative, decreasing (concave) at smaller X values and flattens-out (becomes linear) at about 1.3 and above."

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  • I think the O.P. is trying to describe the relationship between the three lines, not the shape of any one particular line. Also, when speaking of the place where a curve flattens out, a relatively common expression is knee of the curve.
    – J.R. ♦
    Commented Feb 5, 2014 at 11:04
  • @JR - I have reservations about answering these technical questions in ELL. Should we be doing more to get people to provide more context first? So we can know better what their needs are in asking so we can answer better? I was on the fence whether or not to vote this one closed since it was so techy/mathy.
    – CoolHandLouis
    Commented Feb 5, 2014 at 11:22
  • Feel free to leave comments imploring O.P.'s to add a little more context to their questions. That way, it won't seem like I'm the sole curmudgeon with an axe to grind. :^)
    – J.R. ♦
    Commented Feb 5, 2014 at 11:59

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