Parametric equation - Revision history

Karl Jones: /* External links */

2016-04-08T11:05:21Z

‎External links

Karl Jones: /* External links */

2016-04-08T11:05:03Z

‎External links

Karl Jones at 01:22, 1 March 2016

2016-03-01T01:22:06Z

Karl Jones: Created page with "In mathematics, '''parametric equations''' of a curve express the coordinates of the points of the curve as functions of a variable, called a parameter. == Descriptio..."

2016-03-01T01:21:28Z

Created page with "In mathematics, '''parametric equations''' of a curve express the coordinates of the points of the curve as functions of a variable, called a parameter. == Descriptio..."

New page

In [[mathematics]], '''parametric equations''' of a [[curve]] express the coordinates of the points of the curve as functions of a variable, called a parameter.

== Description ==

For example,

<pre>
\begin{align}
x &= \cos t \\
y &= \sin t
\end{align}
</pre>

are parametric equations for the unit circle, where t is the parameter. Together, these equations are called a [[parametric representation]] of the curve.

A common example occurs in [[kinematics]], where the trajectory of a point is usually represented by a parametric equation with time as the parameter.

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.).

The parameter typically is designated t because often the parametric equations represent a physical process in [[time]]. However, the parameter may represent some other physical quantity such as a [[geometric variable]], or may merely be selected arbitrarily for convenience.

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

== See also ==

* [[Curve]]
* [[Kinematics]]
* [[Mathematics]]

== External links ==

* [https://en.wikipedia.org/wiki/Parametric_equation Parametric equation] @ Wikipedia

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 * [https://en.wikipedia.org/wiki/Parametric_equation Parametric equation] @ Wikipedia
 [[Category:Design]]
 [[Category:Mathematics]]

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	* [https://en.wikipedia.org/wiki/Parametric_equation Parametric equation] @ Wikipedia		* [https://en.wikipedia.org/wiki/Parametric_equation Parametric equation] @ Wikipedia
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-In [[mathematics]], '''parametric equations''' of a [[curve]] express the coordinates of the points of the curve as functions of a variable, called a parameter.
+In [[mathematics]], '''parametric equations''' of a [[curve]] express the coordinates of the points of the curve as functions of a variable, called a [[parameter]].
 == Description ==
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 * [[Kinematics]]
 * [[Mathematics]]
 == External links ==
 * [https://en.wikipedia.org/wiki/Parametric_equation Parametric equation] @ Wikipedia