curve, in mathematics, a line no part of which is straight; more generally, it is considered to be any one-dimensional collection of points, thus including the straight line as a special kind of curve. In analytic geometry a plane curve is usually considered as the graph of an equation or function, and the properties of curves are seen to depend largely on the degree of the equation in the case of algebraic curves (i.e., curves with algebraic equations) or on the particular function in the case of transcendental curves (i.e., curves whose equations are not algebraic). For examples of plane curves, see circle; ellipse; hyperbola; parabola. A twisted or skew curve is one that does not lie all in one plane, e.g., the helix, a curve having the shape of a wire spring. A thorough treatment of space curves requires the techniques of differential geometry.

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