Cartesian and Polar Coordinates

[Poweranimals]

What are the differences in the "uniqueness" of the representations in Cartesian coordinates and in polar coordinates?

[robphy]

Do you mean this?

Distinct rectangular coordinates map to distinct points.
However, distinct polar coordinates don't always map to distinct points.
For example, (r = 0, \theta=0) and (r = 0, \theta=\pi/3) map to the same point.