Editing Analytic geometry (section)

{{short description|Study of geometry using a coordinate system}}
{{About|coordinate geometry|the geometry of analytic varieties|Algebraic geometry#Analytic geometry}}
{{General geometry |branches}}
In [[mathematics]], '''analytic geometry''', also known as '''coordinate geometry''' or '''Cartesian geometry''', is the study of [[geometry]] using a [[coordinate system]]. This contrasts with [[synthetic geometry]].

Analytic geometry is used in [[physics]] and [[engineering]], and also in [[aviation]], [[Aerospace engineering|rocketry]], [[space science]], and [[spaceflight]]. It is the foundation of most modern fields of geometry, including [[Algebraic geometry|algebraic]], [[Differential geometry|differential]], [[Discrete geometry|discrete]] and [[computational geometry]].

Usually the Cartesian coordinate system is applied to manipulate equations for planes, straight lines, and circles, often in two and sometimes three dimensions. Geometrically, one studies the Euclidean plane (two dimensions) and Euclidean space. As taught in school books, analytic geometry can be explained more simply: it is concerned with defining and representing geometric shapes in a numerical way and extracting numerical information from shapes' numerical definitions and representations. 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]].