# Finding an explicit curve when torsion and curvature are equivalent

I know solving the Frenet-Serret equations for a given curvature and torsion is possible, but only analytically possible under special cases like plane curves. Is there something I can exploit to calculate a unit-speed curve where, for instance, $\kappa(s)=\tau(s)=\sqrt{2}/(1+s^2)$?

• See pages 32-33, 44-45 in Millman and Parker, Elements of Differential Geometry, Lancret's theorem. Mar 27, 2011 at 5:03