Serge Tabachnikov, Vladlen Timorin
Published 2006-02-14, updated 2006-02-23Version 2
The classical Tait-Kneser theorem states that the osculating circles of a smooth plane curve, free from curvature extrema, are pairwise disjoint. We prove a number of analogs of this theorem, e.g., for ovals of osculating cubics, osculating polynomials and trigonometric polynomials; in each case, we will obtain a non-differentiable foliation with smooth leaves.
Comments: 14 pages, 6 figures, v2: references added
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