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 every day 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.

The term *curve* has several meanings in non-mathematical language as well. For example, it can be almost synonymous with mathematical function (as in *learning curve*), or graph of a function (as in *Phillips curve*).

An arc or segment of a curve is a part of a curve that is bounded by two distinct end points and contains every point on the curve between its end points. Depending on how the arc is defined, either of the two end points may or may not be part of it. When the arc is straight, it is typically called a line segment.

Read more about Curve: History, Topology, Conventions and Terminology, Lengths of Curves, Differential Geometry, Algebraic Curve

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### Famous quotes containing the word curve:

“And out again I *curve* and flow

To join the brimming river,

For men may come and men may go,

But I go on forever.”

—Alfred Tennyson (1809–1892)

“In philosophical inquiry, the human spirit, imitating the movement of the stars, must follow a *curve* which brings it back to its point of departure. To conclude is to close a circle.”

—Charles Baudelaire (1821–1867)

“I have been photographing our toilet, that glossy enameled receptacle of extraordinary beauty.... Here was every sensuous *curve* of the “human figure divine” but minus the imperfections. Never did the Greeks reach a more significant consummation to their culture, and it somehow reminded me, in the glory of its chaste convulsions and in its swelling, sweeping, forward movement of finely progressing contours, of the Victory of Samothrace.”

—Edward Weston (1886–1958)