Curve
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 line is a special case of curve null curvature.
Contents
Description
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.
Meanings in various disciplines
Various disciplines within mathematics have given the term curve 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 above.
Closed curves
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.
Related meanings
Closely related meanings include the graph of a function (as in Phillips curve) and a two-dimensional graph.
See also
- Algebraic curve
- Bézier curve
- Coordinate curve
- Curvature
- Curve fitting
- Curve orientation
- Curve sketching
- Differential geometry of curves
- Gallery of curves
- Graph of a function
- Implicit curve
- Line (geometry)
- List of curves topics
- List of curves
- Mathematics
- Osculating circle
- Parametric equation
- Parametric surface
- Path (topology)
- Pearls of Sluze
- Phillips curve
- Position vector
- Vector-valued function
- Vertex (geometry)
External links
- Curve @ Wikipedia
