The cartesian coordinate system is the basic coordinate system people are familiar with. If you were to plot a basic X Y graph, where X and Y increase towards infinity, you are graphing in the cartesian coordinate system.
There are a few other popular coordinate systems for more advanced math, but they are rarely used by most people. (polar coordinate system is common for some calculus equations)
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The Cartesian Coordinate System was discovered by Rene Descartes.
The z axis in the vertical axis in the Cartesian Coordinate System.
I am not sure that anyone was named AFTER the Cartesian coordinate system. Malcolm X, possibly!
The Cartesian coordinate system can be used in 3 or more dimensions.
The word "Cartesian" is named after the creator of the system itself, Rene Descartes (1596-1650), whose Latin name was Renatus Cartesius.