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"mean proportional" ?? not sure what you mean
like average ratio
when a/b = b/d, then b is the mean proportional.
oops, i mean a/b=b/c. not that it makes a difference.
oh ok , and to answer your question, not sure it can't be negative but it doesn't make a difference really a/b = b/c --> b^2 = ac --> b = +-sqrt(ac) usually ratios deal with lengths which by definition are always positive
example: say b = -3, a = 1, c = 9 -1/3 = -3/9 , the negative cancels out so the proportion is equivalent to 1/3 = 3/9
ah....i see. i understood that the negative cancels out (which is why i sort of asked the question, because my textbook says mean proportional can't be negative). and is it true, ratios are defined to be positive things?Thenn that would make sense.
Thanks for answering, btw. :) And i find it amusing we both have the same name almost, dumb cow and dumb duck :D
But the question is still unanswered :/
i agree, sorry I don't have a sophisticated mathematical reason for you I have never considered it before
oh. thanks anyhow :]
http://regentsprep.org/Regents/math/geometry/GP12/LMeanP.htm look at definition. It is just positive by definition
oh!. i didn't know that.
am i allowed to ask now, why they defined it to be positive? :P
It comes from the definition of a function y = +-sqrt(x) is not a function because it does not pass the vertical line test y = sqrt(x) is however, so the mean proportional is always positive
ah. how come it has to be a function?
http://en.wikipedia.org/wiki/Geometric_mean#cite_note-1 it applies only to positive numbers, and it wouldn't make sense if the mean of positive numbers were negative
I didn't comprehend fully.....but ah, thanks anyway. I'll keep asking why forever lol.