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. 23 Jan. 2019 <https://www.encyclopedia.com>.
"algebraic geometry." The Columbia Encyclopedia, 6th ed.. . Encyclopedia.com. (January 23, 2019). https://www.encyclopedia.com/reference/encyclopediasalmanacstranscriptsandmaps/algebraicgeometry
"algebraic geometry." The Columbia Encyclopedia, 6th ed.. . Retrieved January 23, 2019 from Encyclopedia.com: https://www.encyclopedia.com/reference/encyclopediasalmanacstranscriptsandmaps/algebraicgeometry
Citation styles
Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).
Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.
Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the mostrecent information available at these sites:
Modern Language Association
The Chicago Manual of Style
http://www.chicagomanualofstyle.org/tools_citationguide.html
American Psychological Association
Notes:
 Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
 In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.
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. 23 Jan. 2019 <https://www.encyclopedia.com>.
"coordinate geometry." World Encyclopedia. . Encyclopedia.com. (January 23, 2019). https://www.encyclopedia.com/environment/encyclopediasalmanacstranscriptsandmaps/coordinategeometry
"coordinate geometry." World Encyclopedia. . Retrieved January 23, 2019 from Encyclopedia.com: https://www.encyclopedia.com/environment/encyclopediasalmanacstranscriptsandmaps/coordinategeometry
Citation styles
Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).
Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.
Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the mostrecent information available at these sites:
Modern Language Association
The Chicago Manual of Style
http://www.chicagomanualofstyle.org/tools_citationguide.html
American Psychological Association
Notes:
 Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
 In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.