სადაც <math>\mathbf{i}</math>, <math>\mathbf{j}</math>, და <math>\mathbf{k}</math> არიან [[ერთეულოვანი ვექტორი|ერთეულოვანი ვექტორები]] შესაბამისად <math>x</math>, <math>y</math>, და <math>z</math> ღერძების გასწვრივ.
==Applications==
Each axis may have different [[units of measurement]] associated with it (such as kilograms, seconds, pounds, etc.). Although four- and higher-dimensional spaces are difficult to visualize, the algebra of Cartesian coordinates can be extended relatively easily to four or more variables, so that certain calculations involving many variables can be done. (This sort of algebraic extension is what is used to define the geometry of higher-dimensional spaces.) Conversely, it is often helpful to use the geometry of Cartesian coordinates in two or three dimensions to visualize algebraic relationships between two or three of many non-spatial variables.
The graph of a function or relation is the set of all points satisfying that function or relation. For a function of one variable, ''f'', the set of all points (''x'',''y'') where ''y'' = ''f''(''x'') is the graph of the function ''f''. For a function of two variables, ''g'', the set of all points (''x'',''y'',''z'') where ''z'' = ''g''(''x'',''y'') is the graph of the function ''g''. A sketch of the graph of such a function or relation would consist of all the salient parts of the function or relation which would include its relative extrema, its concavity and points of inflection, any points of discontinuity and its end behavior. All of these terms are more fully defined in calculus. Such graphs are useful in calculus to understand the nature and behavior of a function or relation.
