Fundamental Theorem of Space Curves
If two single-valued continuous functions 
(Curvature) and 
(Torsion) are given for 
, then there exists Exactly One Space Curve, determined exceptfor 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.
- Residue Class
- Residue (Complex Analysis)
- Residue (Congruence)
- Residue Index
- Residue Theorem (Complex Analysis)
- Residue Theorem (Group)
- Resolution
- Resolution Class
- Resolution Modulus
- Resolvable
- Resolving Tree
- Resonance Overlap
- Resonance Overlap Method
- R-Estimate
- Restricted Divisor Function
- Restricted Growth Function
- Restricted Growth String
- Resultant
- Retardance
- Reuleaux Polygon
- Reuleaux Triangle
- Reversal
- Reverse Greedy Algorithm
- Reverse-Then-Add Sequence
- Reversion of Series