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parametre
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(Definition)
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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 presentation
of the origin-centered circle contains both above-mentioned sorts 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).
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"parametre" is owned by pahio.
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Cross-references: directrix, distance, equation, focus, axis, perpendicular, chord, latus rectum, parabola, analytic geometry, interval, real, radius, circle, points, coordinates, variables, surface, curve
There are 211 references to this entry.
This is version 13 of parametre, born on 2007-05-21, modified 2009-08-07.
Object id is 9417, canonical name is Parameter.
Accessed 8522 times total.
Classification:
| AMS MSC: | 00A05 (General :: General and miscellaneous specific topics :: General mathematics) |
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Pending Errata and Addenda
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