Difference between revisions of "Natural parameter"
From Encyclopedia of Mathematics
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| − | A parameter | + | A parameter $s$ for a curve $\gamma$ with parametric representation $\mathbf r=\mathbf r(s)$ such that the arc length on the curve between two points $\mathbf r(s_1)$ and $\mathbf r(s_2)$ is equal to $|s_1-s_2|$. The parametrization of a curve by the natural parameter is known as its natural parametrization. The natural parametrization of a $k$-times differentiable (analytic) curve with no singular points is also $k$ times differentiable (analytic). |
Latest revision as of 16:54, 30 July 2014
on a rectifiable curve
A parameter $s$ for a curve $\gamma$ with parametric representation $\mathbf r=\mathbf r(s)$ such that the arc length on the curve between two points $\mathbf r(s_1)$ and $\mathbf r(s_2)$ is equal to $|s_1-s_2|$. The parametrization of a curve by the natural parameter is known as its natural parametrization. The natural parametrization of a $k$-times differentiable (analytic) curve with no singular points is also $k$ times differentiable (analytic).
Comments
See also (the references to) Natural equation.
How to Cite This Entry:
Natural parameter. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Natural_parameter&oldid=13269
Natural parameter. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Natural_parameter&oldid=13269
This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article