Algebra question / conversion of ranges Greets All
Forgive me if I'm using the wrong terms but I'm trying to sync up two number ranges together.
Example: I have two x axis (ranges)  I would like to equate with each other 
(xaxis 1) 0-2pi or (0-6.28) 
(xaxis 2) 1-44100

So pi (3.14) is close to half way on (xaxis 1) 
so (axis 2) would be the same as 44100/2=22050 on (xaxis 2)  Is there some way I can figure out the other numbers no matter which axis I choose?
Thanks
 A: If you have a value $x$ between 0 and $2\pi$, this implies that the segment $[0,x]$ represents $\frac{x}{2\pi}$ of the whole interval $[0,2\pi]$ (as a fraction). Therefore, you want the corresponding point $y\in [1,44100]$ to cover the same fraction. This means that you want $y$ to satisfy
$$\frac{y-1}{44100-1}=\frac{x}{2\pi}.$$
The solution is 
$$y=\frac{44099x}{2\pi}+1.$$
A: If I understand correctly what you mean is let $x\in [0,2\pi]$ (this means the interval of all numbers between $0$ and $2\pi$ containing 0 and $2\pi$.
then you want a $y\in [1,44100]$ such that y is approximately at the same part of the interval right? so for if example if $x=0$ then $y=1$?
in other words you want $\frac{x}{2\pi}=\frac{y-1}{44100-1}$
this type of conversion is similar to celcius-farenheit conversion in that it doesn't send point $0$ to $0$.
To be explicit we have the conversion $f(y)=\frac{y-1}{(44100-1)2\pi}$
now if you want to take it from $x$ to $y$ you can do it in reverse or try to find the inverse function of this function.
A: Sure. Consider the first numbers $x$ values and the second numbers $y$ values. What you want is to relate the two with a function $y=f(x)$. You want to match the endpoints so that $f(0)=1$ and $f(2\pi)=44100$. As you observed you also will have $f(\pi)=22049.5$. Although you don't state so explicitly, I get the feeling you want the function to have the form $f(x)=mx+b$, the kind of function whose graph is a straight line. So you need to figure out $m$ and $b$. To do this just use the information from the end points. We have 
$$44100=m2\pi+b$$
and
$$1=m0+b.$$
Solve this system for $m$ and $b$ and you will have your relation $y=mx+b$.
Also, in your question, $\pi$ is not "close to" halfway between $0$ and $2\pi$; it is exactly halfway. Remember $3.14$ is only an approximation to $\pi$.
