Terms in a geometric mean equation

[liometopum]

In a geometric mean equation, say 2 x 8 = 16, or a x b = c, what are the words we would use to describe the numbers or terms? Specifically, if you know 'a' and 'c', what do you call 'b'?

For example, in a normal multiplication, a x b = c, 'a' is the multiplicand, 'b' is the multiplier, and 'c' is the product. What do you call the terms in a geometric mean equation? Calling them multiplicand and multiplier seems out of place, as it adds some sort of priority to one of the factors.

If you reverse it, and want to know what one of the missing multipliers is... e.g. what is 'a' if you know 'b' and 'c', so that a= c/b then what do you call 'a'? And what term describes the relation between 'a' and 'b'? A sentence such as:" 'a' is the geometric mean partner of 'b' for the product 'c' (or square of the geometric mean)" is clunky and probably not well stated.

The Wikipedia article, http://en.wikipedia.org/wiki/Geometric_mean, does give terminology. Is there a proper terminology?

 

[andrewkirk]

There is no special term to use. The best way to put it will vary by the context in which the geometric mean is being used.

For instance, if they are samples from a population, and we know all the sample values except one, and we know the geo mean, we would call it the 'missing data point'.

If they are price relatives (aka prels: term in finance for 1 plus the investment earnings in a period) and we know all the prels except one in a time series and we know the accumulation, which is related to the geo mean, we would call it the 'missing prel' or maybe 'unknown return'.

In your example above, you can just call 'a' the 'ratio' of c to b, or the 'quotient' if you prefer'.

 

[liometopum]

Thank you andrewkirk.
Maybe " 'a' is the geometric mean multiplier of 'b' for the geometric mean."
This gives priority to the known unit(s), and, in the example of only two terms, let's the reader assume the geometric mean is the square root of the product. That approach keeps the sentence tighter.