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Natural parameter

From Encyclopedia of Mathematics - Reading time: 1 min

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[edit]

See also (the references to) Natural equation.


How to Cite This Entry: Natural parameter (Encyclopedia of Mathematics) | Licensed under CC BY-SA 3.0. Source: https://encyclopediaofmath.org/wiki/Natural_parameter
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