Question

Why can't the mean proportional be negative?

Answer 1

"mean proportional"
??
not sure what you mean

Answer 2

like average ratio

Answer 3

when a/b = b/d, then b is the mean proportional.

Answer 4

oops, i mean a/b=b/c. not that it makes a difference.

Answer 5

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

Answer 6

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

Answer 7

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.

Answer 8

Thanks for answering, btw. :) And i find it amusing we both have the same name almost, dumb cow and dumb duck :D

Answer 9

But the question is still unanswered :/

Answer 10

i agree, sorry I don't have a sophisticated mathematical reason for you
I have never considered it before

Answer 11

oh. thanks anyhow :]

Answer 12

http://regentsprep.org/Regents/math/geometry/GP12/LMeanP.htm

look at definition.
It is just positive by definition

Answer 13

oh!. i didn't know that.

Answer 14

am i allowed to ask now, why they defined it to be positive? :P

Answer 15

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

Answer 16

ah. how come it has to be a function?

Answer 17

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

Answer 18

I didn't comprehend fully.....but ah, thanks anyway. I'll keep asking why forever lol.