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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