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Study of geometric objects expressed as equations and represented by graphs in a given coordinate system. In contrast to Euclidean geometry, algebraic geometry represents geometric objects using algebraic equations (e.g., a circle of radius *math.r* is defined by *math.x*^{2} + *math.y*^{2} = *math.r*^{2}). Objects so defined can then be analyzed for symmetries, intercepts, and other properties without having to refer to a graph.

Learn more about algebraic geometry with a free trial on Britannica.com.

Encyclopedia Britannica, 2008. Encyclopedia Britannica Online.

Mathematical statement of equality between algebraic expressions. An expression is algebraic if it involves a finite combination of numbers and variables and algebraic operations (addition, subtraction, multiplication, division, raising to a power, and extracting a root). Two important types of such equations are linear equations, in the form *math.y* = *math.a**math.x* + *math.b*, and quadratic equations, in the form *math.y* = *math.a**math.x*^{2} + *math.b**math.x* + *math.c*. A solution is a numerical value that makes the equation a true statement when substituted for a variable. In some cases it may be found using a formula; in others the equation may be rewritten in simpler form. Algebraic equations are particularly useful for modeling real-life phenomena.

Learn more about algebraic equation with a free trial on Britannica.com.

Encyclopedia Britannica, 2008. Encyclopedia Britannica Online.

Algebraic may refer to:

- Algebraic chess notation — a method used to record and describe the play of chess games.
- Algebraic data types.
- Algebraic group — a term from algebraic geometry.
- Algebraic numbers (those which are roots of certain polynomials).
- Or in general, it could refer to any subject studied within the Algebra branch of mathematics.
- Algebraic in reference to calculators refers to the order of entering operations (contrast reverse Polish notation).

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Last updated on Monday February 19, 2007 at 05:50:23 PST (GMT -0800)

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This article is licensed under the GNU Free Documentation License.

Last updated on Monday February 19, 2007 at 05:50:23 PST (GMT -0800)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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