Why does it always take n numbers to characterize a point in n-dimensional space (or does it)? I don't know if this is obvious and a dumb question or not, but, here we go. To characterize a point in 2-d space we can use standard $x,y$ coordinates or we can use polar coordinates. There are probably other ways to do it other than those two as well. It's very interesting to me that those somehow both require exactly two numbers—either an $x$ and a $y$ or an $r$ and a $\theta$. It seems like a magical coincidence to me that these two completely different ways to describe a point require the same number of numbers. 
Then moving into 3-d space, there's the same thing. We can use $(x,y,z)$ or $(\rho,\phi ,z)$ (cylindrical coordinates) or $(r,\theta ,\phi)$ (spherical coordinates). These coordinate systems seem to be to function in vastly different ways, and yet they all take three numbers. It's a conspiracy.
So I mean on the one hand, it's intuitive that it should take three numbers to describe three dimensional space. On the other hand, I can't figure out why this should be true. So question a) why is this the case and question b) can we imagine a world where there were points in n dimensions and two coordinate systems that took different numbers of numbers to characterize points?
P.S. I don't really know what to tag this as.

It only takes one number. Just braid the digits up in some fashion. For example if we are working in base 10:
$$[1.1 \,\,\, 2.2 \, \,\,3.3]^T \to 123.123$$
The number will likely have to be bigger so we need more to store it, but it's clearly just one number. 
To recover just do a loop where you do a round robin:


*

*Check modulo 10.

*Append current bin.

*Drop last digit.

*Repeat for next bin.


( Inspired by Conways base 13 funtion. )
