View source for Analytic geometry

In [[mathematics]], '''analytic geometry''', also known as '''coordinate geometry''', or '''Cartesian geometry''', is the study of [[geometry]] using a [[coordinate system]].

== Description ==

Analytic geometry is widely used in [[physics]] and [[engineering]], and is the foundation of most modern fields of [[geometry]], including algebraic, differential, discrete and computational geometry.

Usually the Cartesian coordinate system is applied to manipulate equations for planes, straight lines, and squares, often in two and sometimes in three dimensions.

Geometrically, one studies the Euclidean plane (two dimensions) and Euclidean space (three dimensions).

As taught in school books, analytic geometry can be explained more simply: it is concerned with defining and representing geometrical shapes in a numerical way and extracting numerical information from shapes' numerical definitions and representations.

The numerical output, however, might also be a vector or a shape. That the algebra of the real numbers can be employed to yield results about the linear continuum of geometry relies on the Cantor–Dedekind axiom.

== Synthetic geometry ==

Analytic geometry contrasts with [[synthetic geometry]].

== See also ==

* [[Engineering]]
* [[Geometry]]
* [[Mathematics]]
* [[Physics]]
* [[René Descartes]]
* [[Synthetic geometry]]

== External links ==

* [https://en.wikipedia.org/wiki/Analytic_geometry Analytic geometry] @ Wikipedia

[[Category:Mathematics]]