{
  "id": "math/0602317",
  "version": "v2",
  "published": "2006-02-14T22:35:20.000Z",
  "updated": "2006-02-23T21:19:26.000Z",
  "title": "Variations on the Tait-Kneser theorem",
  "authors": [
    "Serge Tabachnikov",
    "Vladlen Timorin"
  ],
  "comment": "14 pages, 6 figures, v2: references added",
  "categories": [
    "math.DG",
    "math.AG"
  ],
  "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.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-02-23T21:19:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53A20",
      "51N15"
    ],
    "keywords": [
      "variations",
      "classical tait-kneser theorem states",
      "smooth plane curve",
      "smooth leaves",
      "curvature extrema"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......2317T"
    }
  }
}