Difference between revisions of "Regular curve"
From Maths
m |
m (→See also) |
||
| Line 14: | Line 14: | ||
==See also== | ==See also== | ||
| − | * [[ | + | * [[Parameterised curve]] |
* [[Curve]] | * [[Curve]] | ||
{{Definition|Geometry of Curves and Surfaces|Differential Geometry}} | {{Definition|Geometry of Curves and Surfaces|Differential Geometry}} | ||
Revision as of 18:45, 25 March 2015
Contents
Definition
A curve [math]\gamma:\mathbb{R}\rightarrow\mathbb{R}^3[/math] usually (however [math]\gamma:A\subseteq\mathbb{R}\rightarrow\mathbb{R}^n[/math] more generally) is called regular if all points ([math]\in\text{Range}(\gamma)[/math]) are regular
Definition: Regular Point
A point [math]\gamma(t)[/math] is called regular of [math]\dot\gamma\ne 0[/math] otherwise it is a Singular point
Important point
The curve [math]\gamma(t)\mapsto(t,t^2)[/math] is regular however [math]\gamma'(t)\mapsto(t^3,t^6)[/math] is not - it is not technically a reparametrisation
Any reparametrisation of a regular curve is regular
TODO: reparametrisation theorem
