TOPICS

# 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.