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Higher-Order Curvatures of Plane and Space Parametrized Curves

We start by introducing and studying two sequences of curvatures provided by the higher-order derivatives of the usual Frenet equation of a given plane curve C. These curvatures are expressed by a recurrence starting with the pair (0,−k) where k is the classical curvature function of C. Moreover, for the space curves, we succeed in introducing three recurrent sequences of curvatures starting with the triple (−k,0,τ). Some kinds of helices of a higher order are defined.