section_path: Geometry/Parametric equations
section_name: Parametric equations
paragraph_text: Parametric equations
  
  A parametric equation for a curve expresses the coordinates of the points of the curve as functions of a variable, called a parameter. For example,
  
  are parametric equations for the unit circle, where t is the parameter. Together, these equations are called a parametric representation of the curve.
  
  The notion of parametric equation has been generalized to surfaces, manifolds and algebraic varieties of higher dimension, with the number of parameters being equal to the dimension of the manifold or variety, and the number of equations being equal to the dimension of the space in which the manifold or variety is considered (for curves the dimension is one and one parameter is used, for surfaces dimension two and two parameters, etc.).