If two single-valued continuous functions (Curvature) and (Torsion) are given for , then there exists Exactly One Space Curve, determined except for orientation and position in space (i.e., up to a Euclidean Motion), where is the Arc Length, is the Curvature, and is the Torsion.

**References**

Gray, A. ``The Fundamental Theorem of Space Curves.'' §7.7 in
*Modern Differential Geometry of Curves and Surfaces.* Boca Raton, FL: CRC Press,
pp. 123 and 142-145, 1993.

Struik, D. J. *Lectures on Classical Differential Geometry.* New York: Dover, p. 29,
1988.

© 1996-9

1999-05-26