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Natural parameter

From Encyclopedia of Mathematics
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on a rectifiable curve

A parameter for a curve with parametric representation such that the arc length on the curve between two points and is equal to . The parametrization of a curve by the natural parameter is known as its natural parametrization. The natural parametrization of a -times differentiable (analytic) curve with no singular points is also times differentiable (analytic).


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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
This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article