Why attempt to find 'b' in golden ratio ends up with odd results? Imagine that you have a line segment which is divided into larger and smaller segment. You want to find a golden ratio for the longer segment $a$, and shorter one $b$. As you know the phi number which equals to $1.618$ and let's say you know the $b$ parameter, you try to write $1.618 = a/b = (a + b) / a$. However, no matter what you'll do - you can never get the proper result for $b$ if for example $a = 3,82$ and you perform : $1.618 = 3.82 / b$, then divide both sides by $1/3.82$ and then divide $1.618$ by $3.82$ in order to get $b$ result. Why is this happening?
 A: 
However, how can I know the values of 'a' and 'b' if all I know is just the fact that phi is 1.618 ?

You can't; you only know that the ratio of $a$ to $b$ is 1.618...; basically, this is a reflection of the fact that there are many rectangles with these proportions, but choosing the scale is left entirely up to you; that is you can choose any $a$ you want.
In the example you give, setting $a = 3.82$ makes 
$$
1.618... = 3.82/b\\ \Rightarrow b = 3.82/1.618... = 2.361...
$$
You can check this is consistent with the other equation:
$$
(a + b)/a = (6.18...)/3.82 = 1.618...
$$
A: Since you are looking from an aesthetic point of view for your 'logo example' as opposed to a more mathematical interpretation we can build a couple easy to use functions starting with, 
$$\frac{width}{height}=\frac{\phi}{1}$$(with $\phi$ being equal to 1.618...)
If you have a known height for the logo and want to know what the width should be you can use,
$${width}={\phi}*{height}$$
And if you know the width but need the height,
$${height}=\frac{width}{\phi}$$
Hope this helps!
