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In the case of a single parameter, parametric equations are commonly used to express the trajectory of a moving point, in which case, the parameter is often, but not necessarily, time, and the point describes a curve, called a parametric curve. In the case of two parameters, the point describes a surface, called a parametric surface.
Parametric equation, a representation of a curve through equations, as functions of a variable; Parametric statistics, a branch of statistics that assumes data has come from a type of probability distribution; Parametric derivative, a type of derivative in calculus
Such a parametric equation completely determines the curve, without the need of any interpretation of t as time, and is thus called a parametric equation of the curve (this is sometimes abbreviated by saying that one has a parametric curve). One similarly gets the parametric equation of a surface by considering functions of two parameters t and u.
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A parametric surface is a surface in the Euclidean space which is defined by a parametric equation with two parameters :. Parametric representation is a very general way to specify a surface, as well as implicit representation .
A Lissajous figure, made by releasing sand from a container at the end of a Blackburn pendulum. A Lissajous curve / ˈ l ɪ s ə ʒ uː /, also known as Lissajous figure or Bowditch curve / ˈ b aʊ d ɪ tʃ /, is the graph of a system of 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. [8] [9] 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.