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.
Other articles related to "curve, curves":
... 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 ...
... 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 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 ...
... 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 (18091892)
“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 cant believe how much children change everythingthe 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 durancethat is I;
The eternal thing in man,
That heeds no call to die.”
—Thomas Hardy (18401928)