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Fundamental Theorem of Plane Curves

Two unit-speed plane curves which have the same Curvature differ only by a Euclidean Motion.

See also Fundamental Theorem of Space Curves


Gray, A. Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, pp. 103 and 110-111, 1993.

© 1996-9 Eric W. Weisstein