Editing Equation (section)

===Cartesian equations===
[[File:Cartesian-coordinate-system-with-circle.svg|thumb|right|Cartesian coordinate system with a circle of radius 2 centered at the origin marked in red. The equation of a circle is {{nowrap|1=(''x'' − ''a'')<sup>2</sup> + (''y'' − ''b'')<sup>2</sup> = ''r''<sup>2</sup>}} where ''a'' and ''b'' are the coordinates of the center {{nowrap|(''a'', ''b'')}} and ''r'' is the radius.]]In [[Cartesian geometry]], equations are used to describe [[geometric figures]]. As the equations that are considered, such as [[implicit equation]]s or [[parametric equation]]s, have infinitely many solutions, the objective is now different: instead of giving the solutions explicitly or counting them, which is impossible, one uses equations for studying properties of figures. This is the starting idea of [[algebraic geometry]], an important area of mathematics.

One can use the same principle to specify the position of any point in three-[[dimension]]al [[space (mathematics)|space]] by the use of three Cartesian coordinates, which are the signed distances to three mutually perpendicular planes (or, equivalently, by its perpendicular projection onto three mutually perpendicular lines).

The invention of Cartesian coordinates in the 17th century by [[René Descartes]] revolutionized mathematics by providing the first systematic link between [[Euclidean geometry]] and [[algebra]]. Using the Cartesian coordinate system, geometric shapes (such as [[curve]]s) can be described by Cartesian equations: algebraic equations involving the coordinates of the points lying on the shape. For example, a circle of radius 2 in a plane, centered on a particular point called the origin, may be described as the set of all points whose coordinates ''x'' and ''y'' satisfy the equation {{nowrap|1=''x''<sup>2</sup> + ''y''<sup>2</sup> = 4}}.