In differential geometry, the fundamental theorem of space curves states that every regular curve in three-dimensional space, with non-zero curvature, has its shape (and size or scale) completely determined by its curvature and torsion.[1] [2]
A curve can be described, and thereby defined, by a pair of scalar fields: curvature
\kappa
\tau
If a pair of curves are in different positions but have the same curvature and torsion, then they are congruent to each other.
. Differential Geometry of Curves and Surfaces. Manfredo do Carmo . 0-13-212589-7 . 1976.