# parametre

Parametre means often a quantity which is considered as constant in a certain situation but which may take different values in other situations; so the parametre is a “variable constant”.  But in giving a curve or a surface in parametric form, the parametres work as proper variables which determine the values of the coordinates of the points; then we can describe the parametres as “auxiliary variables”.

The parametric

 $\displaystyle\begin{cases}x=a\cos{t}\\ y=a\sin{t}\end{cases}$

of the origin-centered circle of parametres:  $a$ (the radius) is a variable constant which is held constant all the time when one considers one circle;  $t$ is an auxiliary variable which has to get all real values (e.g. from the interval$[0,\,2\pi]$)  for obtaining all points of the perimetre.

In the analytic geometry, one speaks of the parametre of parabola (a.k.a. latus rectum):  it means the chord of the parabola which is perpendicular to the axis and goes through the focus; it is the quantity $2p$ in the standard equation   $x^{2}=2py$  of the parabola ($p$ is the distance of the focus and the directrix).

 Title parametre Canonical name Parametre Date of creation 2013-03-22 17:06:59 Last modified on 2013-03-22 17:06:59 Owner pahio (2872) Last modified by pahio (2872) Numerical id 17 Author pahio (2872) Entry type Definition Classification msc 00A05 Synonym parameter Related topic Indeterminate Related topic DerivativeForParametricForm Related topic Curve Related topic PerimeterOfAstroid Related topic CissoidOfDiocles Related topic Variable Related topic SurfaceNormal Defines auxiliary variable Defines parametric form Defines parametric presentation Defines parameter of parabola