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Cartesian and Polar Coordinates

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

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robphy
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Do you mean this?

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

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