How is a curve defined in geometry?

Basics of Geometry Read more from
Chapter Geometry and Trigonometry

Acurve is a continuous collection of points drawn from one-dimensional space to n-dimensional space; it is also considered an object that can be created by moving a point. But note: Our usual use of the word “curve” does not mean a straight line, but in mathematics, a line or triangle is often referred to as a curve.

Different forms of geometry define curves in various ways. Analytic geometry uses plane curves—such as circles, ellipses, hyperbolas, and parabolas— which are usually considered as the graph of an equation or function. The properties of these curves are largely dependent on the degree of the equation in the case of algebraic curves (curves with algebraic equations) or on the particular function, as in the case of transcendental curves (curves whose equations are not algebraic). Even more complex are space curves, all of which require special techniques used only in differential geometry.


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