{
  "id": "1409.6455",
  "version": "v1",
  "published": "2014-09-23T09:31:34.000Z",
  "updated": "2014-09-23T09:31:34.000Z",
  "title": "Writing pi as sum of arctangents with linear recurrent sequences, Golden mean and Lucas numbers",
  "authors": [
    "Marco Abrate",
    "Stefano Barbero",
    "Umberto Cerruti",
    "Nadir Murru"
  ],
  "journal": "International Journal of Number Theory, Vol. 10, No. 5, 1309-1319, 2014",
  "doi": "10.1142/S1793042114500286",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we study the representation of pi as sum of arcotangents. In particular, we obtain new identities by using linear recurrent sequences. Moreover, we provide a method in order to express pi as sum of arcotangents involving the Golden mean, the Lucas numbers, and more in general any quadratic irrationality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-23T09:31:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B37",
      "11B39"
    ],
    "keywords": [
      "linear recurrent sequences",
      "golden mean",
      "lucas numbers",
      "writing pi",
      "arctangents"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.6455A"
    }
  }
}