# Curve

A curve is a continuous map from a one-dimensional space to an *n*-dimensional space. Loosely speaking, the word "curve" is often used to mean the function graph of a two- or three-dimensional curve.

Curve is a high school-level concept that would be first encountered in a pre-calculus course.

### Examples

Circle: | A circle is the set of points in a plane that are equidistant from a given center point. |

Ellipse: | A conic section with eccentricity less than one. It resembles a squashed circle. |

Hyperbola: | A hyperbola is a conic section with eccentricity greater than one and consists of two separate branches. |

Parabola: | A parabola is a conic section with eccentricity equal to one. Parabolas appear as the graphs of quadratic equations and the trajectories of projectiles. |

Plane Curve: | A plane curve is a curve that lies in a single plane. A plane curve may be closed or open. |

### Prerequisites

Function Graph: | A function graph is a set of points showing the values taken by a function. This type of plot is called simply a "graph" in common parlance, but is distinct from a collection of points and lines (also called a network) that mathematicians refer to when they speak of a "graph." |

Parametric Equations: | Parametric equations are a set of equations that together express a set of quantities as explicit functions of a number of independent variables, which are known as parameters. |