analytic geometry

Analytic geometryMathworldPlanetmath is the of geometryMathworldPlanetmathPlanetmath that uses mathematical analysis and calculations for investigating geometric problems. Many such problems can be put into the form of equations, and, by analyzing these equations, one may obtain solutions which can be interpreted geometrically.

The fundamental idea behind analytic geometry is that the position of any point on a plane can be given by an ordered pair of real numbers and any point in space by an ordered triple of real numbers; for this purpose, one has to have a coordinate systemMathworldPlanetmath which determines the values of the numbers which serve as the coordinatesMathworldPlanetmathPlanetmath of the points. One of the coordinate system often used in mathematics and physics is the Cartesian system which employs three orthogonalMathworldPlanetmathPlanetmath axes. The correspondence of the points on a plane and the ordered pairs (and similarly the points in space and the ordered triples) is a bijection. A locus condition for a line or a curve on the plane as well as for a line, a curve, or a surface in space may then be expressed as an equation or a system of equations.

For example, if we want to study the line which passes through the points corresponding to the ordered pairs (  (5, 0)  and  (0, 8),  one can infer that all points  (x,y)  of this line satisfy the equation


The Cartesian coordinate system was introduced and applied by the French mathematician and philosopher René Descartes in 1637 in his work Géométrie. Thus, Descartes is considered to be the founder of analytic geometry.

Title analytic geometry
Canonical name AnalyticGeometry
Date of creation 2013-03-22 17:36:23
Last modified on 2013-03-22 17:36:23
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 13
Author pahio (2872)
Entry type Topic
Classification msc 51N20
Classification msc 01A45
Related topic CartesianCoordinates
Related topic EuclideanGeometryOfThePlane
Related topic EuclideanGeometryOfTheSpace
Related topic LineInThePlane
Related topic LineInSpace
Related topic EquationOfPlane
Related topic EllipsePlanetmathPlanetmath
Related topic Hyperbola
Related topic Parabola
Related topic QuadraticSurfaces
Related topic CissoidOfDiocles
Related topic GeneratricesOfOneSheetedHyperboloid
Related topic ConicSection