• Feb 28th 2011, 12:00 AM
lllll
let $\kappa$ denote the curvature of a closed spacecurve $\alpha$. Find $\oint_{\alpha} \frac{1}{\kappa} \ d\kappa$
Looking at this, I would imagine that this would either be $0$ since $\alpha$ is closed or $T$, the tangent Vector, but I'm not to sure on how to achieve the desired result.
$\oint_{\alpha} \frac{\|\alpha'\|^3}{\|\alpha' \times \alpha''\|} \cdot \|\alpha'\| \ dt$
$\oint_{\alpha} \frac{1}{\kappa} \ d\kappa = \oint_{\alpha} d \ln | \kappa | = 0$