let's say $\beta$:$I$->1$E^{3}$ is a arc length paramertic curve that lies on the unit sphere. Let's say that $k$ isn't zero. If $j$:$I$->$R$:$j(s)$=det[$\beta(s)$ $\beta'(s)$ $\beta''(s)$] = $\beta''(s)$$(\beta(s)$ x $\beta'(s)$) then $k(s)=\sqrt(1+j^{2}(s))$ and $\tau$=$j'(s)$/(1+$j^{2}(s)$)
I started with k=$||T'(s)||$=$||\beta''(s)||$=$||(\beta(s)$ x $\beta'(s))j(s)||$ But i'm stuck with the crossproduct. Can someone help me further?
