Do you mean this? Distinct rectangular coordinates map to distinct points. However, distinct polar coordinates don't always map to distinct points. For example, and map to the same point.
http://www.physicsforums.com/showthread.php?t=48654
Polar coordinate system - Wikipedia, the free encyclopedia
In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a fixed point and an angle from a fixed direction. ...
en.wikipedia.org/wiki/Polar_coordinate_system
Uniqueness of polar coordinates. Adding any number of full turns (360°) to the ... The two polar coordinates r and θ can be converted to the Cartesian ...
wapedia.mobi/en/Polar_coordinates wapedia.mobi/en/Polar_coordinates
Both the Cartesian and the polar coordinate marginal measures of phase space .... Marginal measures and the uniqueness question In view of the importance of ...
linkinghub.elsevier.com/retrieve/pii/S0034487702800441
structure is extended by the transformation relating Cartesian and polar coordinates. Hence, the differentiable charts at A are determined by the projective ...
www.iop.org/EJ/article/0264-9381/8/8/014/cq910814.pdf
by a new, instructive method and the uniqueness of the operator form is proven. ... transformation (Cartesian into spherical polar coordinates) of the ...
www.springerlink.com/index/P1V5534296661G7J.pdf
Vectors and Tensor Operations in Polar Coordinates ... D.2.2 Converting between cylindrical polar and rectangular cartesian coordinates ... 5.1.4 Uniqueness & existence...
solidmechanics.org/text/AppendixD/AppendixD.htm
Even though in nature one never observes an infinite string, such a string is a concept with properties which are ... This means that the infinite string is a natural way by which to grasp the properties and behavior of any system which exhibits these attributes. ... Problem: Construct the Green's function for the system...
www.math.ohio-state.edu/~gerlach/math/BVtypset/node108.... www.math.ohio-state.edu/~gerlach/math/BVtypset/node108.html
Note: Many equations which are simple in Cartesian coordinates are very complicated in polar coordinates, and vice versa. To solve any particular problem, one system may be much more tractable than the other. The ability to convert from one to the other quite readily allows us to try both, then use only the easier one.
mathforum.org/dr.math/faq/formulas/faq.polar.html mathforum.org/dr.math/faq/formulas/faq.polar.html
has Cartesian coordinates ... Coordinate axes and Cartesian coordinates ... Polar representations...
www.maths.usyd.edu.au/u/MOW/vectors/vectors-6/v-6-2.htm... www.maths.usyd.edu.au/u/MOW/vectors/vectors-6/v-6-2.html