Variations on the Tait-Kneser theorem
Differential Geometry
2007-05-23 v2 Algebraic Geometry
Abstract
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.
Cite
@article{arxiv.math/0602317,
title = {Variations on the Tait-Kneser theorem},
author = {Serge Tabachnikov and Vladlen Timorin},
journal= {arXiv preprint arXiv:math/0602317},
year = {2007}
}
Comments
14 pages, 6 figures, v2: references added