{
  "id": "1807.06284",
  "version": "v1",
  "published": "2018-07-17T08:57:30.000Z",
  "updated": "2018-07-17T08:57:30.000Z",
  "title": "Best rational approximations of an irrational number",
  "authors": [
    "Jean-Louis Sikorav"
  ],
  "comment": "6 tables",
  "categories": [
    "math.NT"
  ],
  "abstract": "The concept of nearest integer is used to derive theorems and algorithms for the best approximations of an irrational by rational numbers, which are improved with the pigeonhole principle and used to offer an informed presentation of the theory of continued fractions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-17T08:57:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "best rational approximations",
      "irrational number",
      "nearest integer",
      "best approximations",
      "rational numbers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}