torsion formula for a parametric space curve I managed to prove 
$$ k(t) = \frac{ | a^{\prime} \times a^{\prime \prime} | }{ | a^{\prime} | ^3 } $$
for a regular parametric curve $a : I \to R^3 $ where $k(t)$ stands for its curvature but I am stucked in proving 
$$ \tau (t) = \frac{( a^{\prime} \times a^{\prime \prime} ) \cdot a^{\prime \prime \prime }}{ |a^{\prime} \times a^{\prime \prime} | ^2 } $$
Can I ask anybody to give me any hint or reference?
Thanks in advance.

reparametrize $\alpha (t)$ with $\beta (s(t))$ where $s=s(t)$ is its arc length. Direct computation gives 
$$\alpha (t) = \beta (s(t)) $$
$$ \dot{ \alpha } (t) = \hat{T} (s(t)) \dot{ s(t) } $$
$$ \ddot{\alpha}(t) = k( s(t) ) \hat{N} (s(t)) \dot{s}(t) ^2 + \hat{T} (s(t)) \ddot{s} (t) $$
$$\dddot{\alpha} (t) = (\dddot{s}(t) - k^2 (s(t)) \dot{s} (t)^3 ) \hat{T} ( s(t)) + (3 k (s(t)) \dot{s} (t) \ddot{s}(t) + k^{\prime} (s(t)) \dot{s} (t) ^3 ) \hat{N} ( s(t) ) - k( s(t)) \tau (s(t)) \dot{s} (t) ^3 \hat{B} (s(t)) $$
The rest is simple calculation.
