Two Dimensional Coordinate Systems are a method of describing a point in a plane using an ordered pair of numbers $(n_1,n_2)$ called coordinates such that $n_1$ = constant is a set of non-intersecting lines (or curves). Similarly, $n_2$ = constant produce a second set of non-intersecting lines (or curves). Therefore the ordered pair of numbers indicate a point located at the intersection of a pair of the lines (or curves), one from each set.

A special class of coordinate systems are those where each line of one set intersect at right angles to every line of the other set. Such a system is called an Orthogonal Coordinate System.

Here are some orthogonal coordinate systems in two dimensions

Cartesian Coordinate System
- Coordinate curves are both straight lines
- named after the inventor of the system René Descartes
Polar Coordinate System
- Coordinate curves are circles and straight lines
Parabolic Coordinate System
- Coordinate curves are both parabolas
Bipolar Coordinate System
- Coordinate curves are both circles
Elliptic Coordinate System
- Coordinate curves are ellipses and hyperbolae

By extension Coordinate Systems exist for three and more dimensions.


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