Linus Nielsen Feltzing wrote:
Mike Holden wrote:
But that's precisely what "proportional" means - linearly proportional!
To be proportional, the two values have to be always at exactly the same
ratio, such as y = x * 2.
Well, it can also be exponentially or logarithmically proportional, as
far as I know.
Linus
A proportion is usually written in the form
y = kx + c
where k is called the "constant of proportionality".
A "proportionality" can be expressed by almost any function; the
definition of "proportional" however implies a linear function. One
possible more "general" equation might be
y = F(x) = Px + c
where P is some polynomial in some other variable, with P generally a
constant, or close to constant, for the range of values we are
interested in. This is really a "function" in two variables:
e.g.,
P(q) = s^2 + 2s + 3
y = xs^2 + 2xs + 3x + c
If s is close to 1.0 and we can assume it *stays* there, then it becomes
y = x + 2x + 3x + c
y = 6x + c
If it can be represented by an exponential, logarithmic, harmonic or
some other function, it is not strictly a "proportion", but that is just
nitpicking. It is still useful to make statements like "a is
proportional to the square root of b".
a = k(b^0.5) + c, where c == 0
And if we *know* the function that approximates the value, we can use
it, whatever it is.
At any rate, we know what you mean when you say "proportional".
:)
--Mark Allums
