Fundamental Theorem of Space Curves

If two single-valued continuous functions kappa(s) (curvature) and tau(s) (torsion) are given for s>0, then there exists exactly one space curve, determined except for orientation and position in space (i.e., up to a Euclidean motion), where s is the arc length, kappa is the curvature, and tau is the torsion.

See also

Arc Length, Curvature, Euclidean Motion, Fundamental Theorem of Plane Curves, Torsion

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Gray, A. "The Fundamental Theorem of Space Curves." §7.7 in Modern Differential Geometry of Curves and Surfaces with Mathematica, 2nd ed. Boca Raton, FL: CRC Press, pp. 219-222, 1997.Struik, D. J. Lectures on Classical Differential Geometry. New York: Dover, p. 29, 1988.

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Fundamental Theorem of Space Curves

Cite this as:

Weisstein, Eric W. "Fundamental Theorem of Space Curves." From MathWorld--A Wolfram Web Resource.

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