What is the difference between a rectangular coordinate system and a polar coordinate system?

1 Answer
Jim H
Mar 26, 2015

One of the most interesting differences is that every point in the plane has exactly one representation as a pair of coordinates in the rectangular (or any other parallelogram) coordinate system, but has infinitely many representations in polar coordinates.

Example:

The point whose rectangular coordinates are (1,1) corresponds to polar coordinates:
(sqrt2, pi/4) and also (sqrt2, (9 pi)/4) and (sqrt2, (-7 pi)/4) and (-sqrt2, ( 5 pi)/4) and infinitely many others.

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