algebraic geometry
algebraic geometry, branch of geometry, based on analytic geometry, that is concerned with geometric objects (loci) defined by algebraic relations among their coordinates (see Cartesian coordinates). In plane geometry an algebraic curve is the locus of all points satisfying the polynomial equation f(x,y)=0; in three dimensions the polynomial equation f(x,y,z)=0 defines an algebraic surface. In general, points in nspace are defined by ordered sequences of numbers (x_{1},x_{2},x_{3}, … x_{n}), where each ntuple specifies a unique point and x_{1}, x_{2}, x_{3}, … x_{n} are members of a given field (e.g., the complex numbers). An algebraic hypersurface is the locus of all such points satisfying the polynomial equation f(x_{1},x_{2},x_{3}, … x_{n})=0, whose coefficients are also chosen from the given field. The intersection of two or more algebraic hypersurfaces defines an algebraic set, or variety, a concept of particular importance in algebraic geometry.
Cite this article
Pick a style below, and copy the text for your bibliography.

MLA

Chicago

APA
"algebraic geometry." The Columbia Encyclopedia, 6th ed.. . Encyclopedia.com. 25 May. 2017 <http://www.encyclopedia.com>.
"algebraic geometry." The Columbia Encyclopedia, 6th ed.. . Encyclopedia.com. (May 25, 2017). http://www.encyclopedia.com/reference/encyclopediasalmanacstranscriptsandmaps/algebraicgeometry
"algebraic geometry." The Columbia Encyclopedia, 6th ed.. . Retrieved May 25, 2017 from Encyclopedia.com: http://www.encyclopedia.com/reference/encyclopediasalmanacstranscriptsandmaps/algebraicgeometry
coordinate geometry
coordinate geometry (algebraic geometry) Branch of mathematics combining the methods of pure geometry with those of algebra. Any geometrical point can be given an algebraical value by relating it to coordinates, marked off from a frame of reference. Thus, if a point is marked on a square grid so that it is x_{1} squares along the x axis and y_{1} squares along the y axis, it has the coordinates (x_{1}, y_{1}). Polar coordinates can also be used. It was first introduced in the 17th century by René; Descartes. See also Cartesian coordinates
Cite this article
Pick a style below, and copy the text for your bibliography.

MLA

Chicago

APA
"coordinate geometry." World Encyclopedia. . Encyclopedia.com. 25 May. 2017 <http://www.encyclopedia.com>.
"coordinate geometry." World Encyclopedia. . Encyclopedia.com. (May 25, 2017). http://www.encyclopedia.com/environment/encyclopediasalmanacstranscriptsandmaps/coordinategeometry
"coordinate geometry." World Encyclopedia. . Retrieved May 25, 2017 from Encyclopedia.com: http://www.encyclopedia.com/environment/encyclopediasalmanacstranscriptsandmaps/coordinategeometry