# Curve

In mathematics, a **curve** (also called a **curved line** in older texts) is, generally speaking, an object similar to a line but which is not required to be straight. This entails that a line is a special case of curve, namely a curve with null curvature. Often curves in two-dimensional (plane curves) or three-dimensional (space curves) Euclidean space are of interest.

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—i.e., a path from any of its points to the same point.

Closely related meanings are "graph of a function" (as in "Phillips curve") and "two-dimensional graph".

In non-mathematical language, the term is often used metaphorically, as in "learning curve".

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