Editing Cartesian coordinate system (section)

===Quadrants and octants===
{{Main|Octant (solid geometry)|Quadrant (plane geometry)}}
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[[File:Cartesian coordinates 2D.svg|thumb|The four quadrants of a Cartesian coordinate system]]

The axes of a two-dimensional Cartesian system divide the plane into four infinite regions, called ''quadrants'',<ref name=":0" /> each bounded by two half-axes. These are often numbered from 1st to 4th and denoted by [[Roman numeral]]s: I (where the coordinates both have positive signs), II (where the abscissa is negative − and the ordinate is positive +), III (where both the abscissa and the ordinate are −), and IV (abscissa +, ordinate −). When the axes are drawn according to the mathematical custom, the numbering goes [[clockwise|counter-clockwise]] starting from the upper right ("north-east") quadrant.

Similarly, a three-dimensional Cartesian system defines a division of space into eight regions or '''octants''',<ref name=":0" /> according to the signs of the coordinates of the points. The convention used for naming a specific octant is to list its signs; for example, {{nowrap|(+ + +)}} or {{nowrap|(− + −)}}. The generalization of the quadrant and octant to an arbitrary number of dimensions is the '''[[orthant]]''', and a similar naming system applies.