7/23/2019 Intro to Parametric Equation

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Parametric equations express a set of related quantities as explicit functions of an independent

variable, known as a parameter. An equation, relating variables x and y in Cartesian coordinates,

can be expressed by parametric equations which describe a position on the curve.

In mathematics,parametric equationsof acurveexpress the coordinatesof the points of the curve

as functions of avariable,called a parameter.!"#"$or example,

are parametric equations for the unit circle,where tis the parameter. %ogether, these equations

are called a parametric representationof the curve.

A common example occurs in kinematics, where the tra&ectoryof a point is usually represented

by a parametric equation with time as the parameter.

%he notion ofparametric equationhas been generali'ed to surfaces, manifoldsand algebraic

varietiesof 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 oneand oneparameter

is used, for surfaces dimension twoand twoparameters, etc.).

%he parameter typically is designated tbecause often the parametric equations represent a

physical process in time. *owever, the parameter may represent some other physical quantity

such as a geometric variable, or may merely be selected arbitrarily for convenience. +oreover,

more than one set of parametric equations may specify the same curve. "

https://en.wikipedia.org/wiki/Mathematicshttps://en.wikipedia.org/wiki/Mathematicshttps://en.wikipedia.org/wiki/Curvehttps://en.wikipedia.org/wiki/Curvehttps://en.wikipedia.org/wiki/Curvehttps://en.wikipedia.org/wiki/Coordinateshttps://en.wikipedia.org/wiki/Variable_(mathematics)https://en.wikipedia.org/wiki/Variable_(mathematics)https://en.wikipedia.org/wiki/Variable_(mathematics)https://en.wikipedia.org/wiki/Parameterhttps://en.wikipedia.org/wiki/Parametric_equation#cite_note-1https://en.wikipedia.org/wiki/Parametric_equation#cite_note-2https://en.wikipedia.org/wiki/Unit_circlehttps://en.wikipedia.org/wiki/Unit_circlehttps://en.wikipedia.org/wiki/Kinematicshttps://en.wikipedia.org/wiki/Trajectoryhttps://en.wikipedia.org/wiki/Surfacehttps://en.wikipedia.org/wiki/Manifoldhttps://en.wikipedia.org/wiki/Algebraic_varietyhttps://en.wikipedia.org/wiki/Algebraic_varietyhttps://en.wikipedia.org/wiki/Algebraic_varietyhttps://en.wikipedia.org/wiki/Dimension_of_a_manifoldhttps://en.wikipedia.org/wiki/Parametric_equation#cite_note-3https://en.wikipedia.org/wiki/Curvehttps://en.wikipedia.org/wiki/Coordinateshttps://en.wikipedia.org/wiki/Variable_(mathematics)https://en.wikipedia.org/wiki/Parameterhttps://en.wikipedia.org/wiki/Parametric_equation#cite_note-1https://en.wikipedia.org/wiki/Parametric_equation#cite_note-2https://en.wikipedia.org/wiki/Unit_circlehttps://en.wikipedia.org/wiki/Kinematicshttps://en.wikipedia.org/wiki/Trajectoryhttps://en.wikipedia.org/wiki/Surfacehttps://en.wikipedia.org/wiki/Manifoldhttps://en.wikipedia.org/wiki/Algebraic_varietyhttps://en.wikipedia.org/wiki/Algebraic_varietyhttps://en.wikipedia.org/wiki/Dimension_of_a_manifoldhttps://en.wikipedia.org/wiki/Parametric_equation#cite_note-3https://en.wikipedia.org/wiki/Mathematics