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.

• Coates-Wiles Theorem
• Coaxal Circles
• Coaxaloid System
• Coaxal System
• Cobordant Manifold
• Cobordism
• Cobordism Group
• Cobordism Ring
• Cochleoid
• Cochleoid Inverse Curve
• Cochloid
• Cochran's Theorem
• Cocked Hat Curve
• Cocktail Party Graph
• Coconut
• Codazzi Equations
• Code
• Codimension
• Coding Theory
• Coefficient
• Coefficient Field
• Coercive Functional
• Cofactor
• Cohen-Kung Theorem
• Cohomology