Curve arc length parametrization definition I did some assignments related to curve arc length parametrization.
But what I can't seem to find online is a formal definition of it.
I've found procedures and ways to find a curve's equation by arc length parametrization, but I'm still missing a formal definition which I have to write in my assignment.
I saw many links related to the topic
http://homepage.smc.edu/kennedy_john/ArcLengthParametrization.pdf
but they all seem too long and don't provide a short, concise definition.
Could anyone help me writing a formal definition of curve arc length parametrization?

Suppose $\gamma:[a,b]\rightarrow {\Bbb R}$ is a smooth curve with $\gamma'(t) \not = 0$ for $t\in[a,b]$.  
Define $$s(t) = \int_a^t ||\gamma'(\xi)||\,d\xi$$ for $t\in[a,b]$.  This function $s$ has a  positive derivative, so it possesses a differentiable inverse.  You can use it to get a unit-speed reparametrization of your curve.
