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 n-space are defined by ordered sequences of numbers (x1,x2,x3, … xn), where each n-tuple specifies a unique point and x1, x2, x3, … xn 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(x1,x2,x3, … xn)=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.
"algebraic geometry." The Columbia Encyclopedia, 6th ed.. . Encyclopedia.com. (June 20, 2019). https://www.encyclopedia.com/reference/encyclopedias-almanacs-transcripts-and-maps/algebraic-geometry
"algebraic geometry." The Columbia Encyclopedia, 6th ed.. . Retrieved June 20, 2019 from Encyclopedia.com: https://www.encyclopedia.com/reference/encyclopedias-almanacs-transcripts-and-maps/algebraic-geometry
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 most-recent information available at these sites:
Modern Language Association
The Chicago Manual of Style
American Psychological Association
- 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." World Encyclopedia. . Encyclopedia.com. (June 20, 2019). https://www.encyclopedia.com/environment/encyclopedias-almanacs-transcripts-and-maps/coordinate-geometry
"coordinate geometry." World Encyclopedia. . Retrieved June 20, 2019 from Encyclopedia.com: https://www.encyclopedia.com/environment/encyclopedias-almanacs-transcripts-and-maps/coordinate-geometry