{
  "id": "2202.10822",
  "version": "v1",
  "published": "2022-02-22T11:25:37.000Z",
  "updated": "2022-02-22T11:25:37.000Z",
  "title": "Neighbors",
  "authors": [
    "Gábor Fejes Tóth",
    "Lázló Fejes Tóth",
    "Włodzimierz Kuperberg"
  ],
  "categories": [
    "math.MG",
    "math.CO"
  ],
  "abstract": "Two members of a packing are neighbors if they have a common boundary point. A multitude of problems arises in connection with neighbors in a packing. The oldest one concerns a dispute between Newton and Gregory about the maximum number of neighbors a member can have in a packing of congruent balls. Other problems ask for the average number of neighbors or the maximum number of mutually neighboring members in a packing. The present work gives a survey of these problems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-22T11:25:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "maximum number",
      "common boundary point",
      "average number",
      "problems arises",
      "congruent balls"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}