algebraic geometry

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.x2 + math.y2 = math.r2). Objects so defined can then be analyzed for symmetries, intercepts, and other properties without having to refer to a graph.

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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.amath.x + math.b, and quadratic equations, in the form math.y = math.amath.x2 + math.bmath.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.

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