{
  "id": "1603.06307",
  "version": "v1",
  "published": "2016-03-21T01:53:58.000Z",
  "updated": "2016-03-21T01:53:58.000Z",
  "title": "The golden ratio, Fibonacci numbers and BBP-type formulas",
  "authors": [
    "Kunle Adegoke"
  ],
  "journal": "Fibonacci Quarterly 52 (2): 129-138, (2014)",
  "categories": [
    "math.NT"
  ],
  "abstract": "We derive interesting arctangent identities involving the golden ratio, Fibonacci numbers and Lucas numbers. Binary BBP-type formulas for the arctangents of certain odd powers of the golden ratio are also derived, for the first time in the literature. Finally we derive golden-ratio-base BBP-type formulas for some mathematical constants, including $\\pi$, $\\log 2$, $\\log\\phi$ and $\\sqrt 2\\,\\arctan\\sqrt 2$. The $\\phi-$nary BBP-type formulas derived here are considerably simpler than similar results contained in earlier literature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-21T01:53:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B39",
      "11Y60"
    ],
    "keywords": [
      "golden ratio",
      "fibonacci numbers",
      "binary bbp-type formulas",
      "derive golden-ratio-base bbp-type formulas",
      "similar results"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}