View source for Regular curve



==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|reparametrisation]] 

==Any reparametrisation of a regular curve is regular==
{{Todo|reparametrisation theorem}}

==See also==
* [[Parameterisation]]
* [[Curve]]

{{Definition|Geometry of Curves and Surfaces|Differential Geometry}}