Variations on the Tait-Kneser theorem

Details Variations on the Tait-Kneser theorem Variations on the Tait-Kneser theorem

2006-02-14

arxiv.org/abs/math/0602317v2

Mathematics

Differential Geometry

14 pages, 6 figures, v2: references added

Scientific paper

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.

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