For curves in space, the concepts of curvature and torsion are of fundamental importance.
We know that line segments are uniquely determined by their lengths, circles by their radii,
triangles by side-angle-side etc. In geometry, we look for geometric quantities which distinguish
one figure from another. The importance of curvature and torsion can easily be estimated
from the fact that it can be proved that a curve is uniquely determined (except for its position
in space) if its curvature and torsion are given as continuous functions of arc length â€˜sâ€™.