Solution
= Solution
The <fundamental theorem of regular space curves> states that smooth functions $\kappa(s)>0$ and $\tau(s)$ determine a unit-speed regular curve in $\mathbb R^3$ with that <curvature of a space curve>[curvature] and <torsion of a space curve>[torsion], uniquely up to a <proper Euclidean motion of Euclidean three-space>. Existence follows by solving the <Frenet-Serret formulas> for an oriented orthonormal frame and then integrating its tangent vector.