# the curvature of the curves

• March 5th 2014, 12:37 PM
Kaatie
the curvature of the curves
Hello, I need to compute the curvature of this arclength-parametrized curve:

$a(s)=( \sqrt{1+s^2}, ln(s+ \sqrt{1+s^2}))$

Could you give mi a hint?
• March 5th 2014, 02:25 PM
romsek
Re: the curvature of the curves
$\vec{T}=\dfrac{\partial}{\partial s}a(s)$

$\hat{T}=\dfrac{\vec{T}}{\left\| \vec{T} \right \|}$

$\large \kappa =\left\| \dfrac{d \hat{T}}{ds}\right \|$