En la matemática (inicialmente estudiado en la geometría elemental y, en forma más rigurosa, en la geometría diferencial), la curva (o línea curva) es una línea continua de una dimensión, que varía de dirección paulatinamente. Ejemplos sencillos de curvas cerradas simples son la elipse o la circunferencia o el óvalo, el cicloide; ejemplos de curvas abiertas, la parábola, la hipérbola y la catenaria y una infinidad de curvas estudiadas en la geometría analítica plana. La recta asume el caso límite de una circunferencia de radio de curvatura infinito y de curvatura 0; además, una recta es la imagen homeomorfa de un intervalo abierto. Todas las curvas tienen dimensión topológica igual a 1. La noción curva, conjuntamente con la de superficie, es uno de los objetos primordiales de la geometría diferencial, ciertamente con profusa aplicación de las herramientas del cálculo diferencial.

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In mathematics, a curve (also called a curved line in older texts) is, generally speaking, an object similar to a line but that need not be straight. Thus, a curve is a generalization of a line, in that curvature is not necessarily zero. Various disciplines within mathematics have given the term different meanings depending on the area of study, so the precise meaning depends on context. However, many of these meanings are special instances of the definition which follows. A curve is a topological space which is locally homeomorphic to a line. In everyday language, this means that a curve is a set of points which, near each of its points, looks like a line, up to a deformation. A simple example of a curve is the parabola, shown to the right. A large number of other curves have been studied in multiple mathematical fields. A closed curve is a curve that forms a path whose starting point is also its ending point—that is, a path from any of its points to the same point. Closely related meanings include the graph of a function (as in Phillips curve) and a two-dimensional graph.

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