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Math Help - Creating a ten step log scale function

  1. #1
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    Creating a ten step log scale function

    I'm working with a set range of numbers for area, ranging from 0.01 km^2 to 4 km^2. I'm trying to set up a function that will allow me to have ten steps between 0.01 and 4 but that will not be equidistant, as the impact of area in my case is not linear. Anyone have a suggestion on how to do this?
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  2. #2
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    Re: Creating a ten step log scale function

    There are infinitely many ways to do this. I think in order to give you better advice, we need to know more context. What do these numbers represent? You use units of area. The area of what object?

    The first thought that came to my mind was to think of the problem as a graphical problem in two dimensions. You essentially want to have a function taking the set {0,1,...,10} to the desired partition of [0.01,4]. So draw the problem as a graph problem in two dimensions, and see if something doesn't suggest itself (I don't exactly know what that would be - this is not a rhetorical question).
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  3. #3
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    Re: Creating a ten step log scale function

    The numbers represent the spatial resolution. of radar "bin" coverage (ranging from 0.01 to 4 km^2 based on distance from the center of the radar). I don't think the 'relative' value is linear for the two quantities. I don't know just what an 'accurate' non-linear relationship would be, but I don't think a spatial resolution of 0.5 sq km, for example, is 4 times the value of a 2.0 sq km resolution. I thought a log scale might be a decent representation to have some kind of non-linear relationship.
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