Explore Curve on MathWorld

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.


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.


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.

Classroom Articles on Pre-Calculus (Up to High School Level)

  • Asymptote
  • Logarithm
  • Complex Conjugate
  • Natural Logarithm
  • Complex Number
  • Normal Vector
  • Complex Plane
  • Plane
  • Conic Section
  • Polar Coordinates
  • Cross Product
  • Range
  • Determinant
  • Rational Function
  • Domain
  • Reflection
  • Dot Product
  • Rotation
  • e
  • Rotation Matrix
  • Exponential Function
  • Scalar
  • Function
  • Spherical Coordinates
  • i
  • Tangent Line
  • Imaginary Number
  • Translation
  • Inverse Function
  • Vector
  • Locus