Those are the only coordinate systems that I've heard of. Clearly we can invent other coordinate systems that have the two properties
a) All points in Euclidean space are represented by the system (surjectivity).
b) A point in Euclidean space cannot be represented in two or more different ways by the system (injectivity).
To take an example of such a coordinate system, I thought of this: Say that for any point $p$ in Euclidean space with Cartesian coordinates $(x_1,y_1)$, we associate it with a square with a center in the origin whose side length is $s=2 \cdot |\max(x_1,y_1)|$. Then starting at the point with Cartesian coordinates $(s,0)$, we travel on the square in a counterclockwise way until we find $p$, then calculate the distance $d$ that we have traveled. Using this coordinate system, we can say that the coordinate is expressed as $(s/2,d)$. Hence, the points $(3,2)$ and $(-4,9)$ in Cartesian coordinates would have the coordinates $(3,2)$ and $(9,22)$ respectively using this system. Clearly this coordinate system satisfies the above properties (it just uses squares instead of the circles in the polar coordinate system), but I can't think of a situation where it would be useful. So back to my question, do there exist any coordinate systems besides the Cartesian and polar ones that are useful for some situations (for some problems maybe or applications)?