Natural parameter
From Encyclopedia of Mathematics
The printable version is no longer supported and may have rendering errors. Please update your browser bookmarks and please use the default browser print function instead.
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=32588
Natural parameter. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Natural_parameter&oldid=32588
This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article