# 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

$\{\begin{array}{cc}x=a\mathrm{cos}t\hfill & \\ y=a\mathrm{sin}t\hfill & \end{array}$ |

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^{} $[0,\mathrm{\hspace{0.17em}2}\pi ]$) 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 |