{
  "id": "1707.04830",
  "version": "v1",
  "published": "2017-07-16T06:26:48.000Z",
  "updated": "2017-07-16T06:26:48.000Z",
  "title": "A new bound on Banach-Mazur distance between planar convex bodies",
  "authors": [
    "Serhii Brodiuk",
    "Nazarii Palko",
    "Andriy Prymak"
  ],
  "categories": [
    "math.MG"
  ],
  "abstract": "We prove that the Banach-Mazur distance between any two planar convex bodies is at most $\\tfrac{19-\\sqrt{73}}4<2.614$, improving the previously known bound of $3$ obtained by Lassak. For the lower bound, it is known that the Banach-Mazur distance between a regular pentagon and a triangle is $1+\\frac{\\sqrt{5}}{2}\\approx 2.118$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-16T06:26:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "52A10",
      "52A27",
      "52A40"
    ],
    "keywords": [
      "planar convex bodies",
      "banach-mazur distance",
      "lower bound",
      "regular pentagon"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}