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

### Other articles related to "curve, curves":

**Curve**

... Algebraic

**curves**are the

**curves**considered in algebraic geometry ... A plane algebraic

**curve**is the locus of the points of coordinates x, y such that f(x, y) = 0, where f is a polynomial in two variables defined over some field F ... If C is a

**curve**defined by a polynomial f with coefficients in F, the

**curve**is said defined over F ...

**Curve**Diffie–Hellman

... Elliptic

**curve**Diffie–Hellman (ECDH) is an anonymous key agreement protocol that allows two parties, each having an elliptic

**curve**public-private key pair, to establish a shared ... It is a variant of the Diffie–Hellman protocol using elliptic

**curve**cryptography ...

... A

**curve**in a two dimensional space is best represented by the parametric equations like x(c) and y(c) ... The family of

**curves**can be represented in the form where c is the parameter ... The envelope of a family of

**curves**g(x,y,c) = 0 is a

**curve**such that at each point on the

**curve**there is some member of the family that touches that particular point ...

**Curve**Lake First Nation 35, Ontario

...

**Curve**Lake is the name of two Ojibwe Indian reserves 14 km north of Peterborough, Ontario ... They serve as the landbase for the

**Curve**Lake First Nation ... Officially they are known as

**Curve**Lake First Nation No ...

**Curve**

... A parallel of a

**curve**is the envelope of a family of congruent circles centered on the

**curve**... It can also be defined as a

**curve**whose points are at a fixed normal distance of a given

**curve**... It is sometimes called the offset

**curve**but the term "offset" often refers also to translation ...

### 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)

“Nothing ever prepares a couple for having a baby, especially the first one. And even baby number two or three, the surprises and challenges, the cosmic *curve* balls, keep on coming. We can’t believe how much children change everything—the time we rise and the time we go to bed; the way we fight and the way we get along. Even when, and if, we make love.”

—Susan Lapinski (20th century)

“The years-heired feature that can

In *curve* and voice and eye

Despise the human span

Of durance—that is I;

The eternal thing in man,

That heeds no call to die.”

—Thomas Hardy (1840–1928)