| Version 9 |
Version 8 |
| \PMlinkescapeword{constant} |
\PMlinkescapeword{constant} |
| {\em Parameter} means often a quantity which is considered as constant in a certain situation but which may take different values in other situations; so the parameter is a ``variable constant''.\; But in giving a curve or a surface in {\em parametric form}, the parameters work as proper variables which determine the values of the coordinates of the points; then we can describe the parameters as ``auxiliary variables''. |
{\em Parameter} means often a quantity which is considered as constant in a certain situation but which may take different values in other situations; so the parameter is a ``variable constant''.\; But in giving a curve or a surface in {\em parametric form}, the parameters work as proper variables which determine the values of the coordinates of the points; then we can describe the parameters as ``auxiliary variables''. |
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| The parametric \PMlinkescapetext{presentation} |
The parametric \PMlinkescapetext{presentation} |
| \begin{align*} |
\begin{align*} |
| \begin{cases} |
\begin{cases} |
| x = a\cos{t}\\ |
x = a\cos{t}\\ |
| y = a\sin{t} |
y = a\sin{t} |
| \end{cases} |
\end{cases} |
| \end{align*} |
\end{align*} |
| of the origin-centered circle \PMlinkescapetext{contains} both above-mentioned sorts of parameters:\; $a$ (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. |
of the origin-centered circle \PMlinkescapetext{contains} both above-mentioned sorts of parameters:\; $a$ (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. |
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| In the analytic geometry, one speaks of the {\em parameter of parabola}:\, 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). |
In the analytic geometry, one speaks of the {\em parameter of parabola}:\, 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). |
