{
  "id": "1012.0781",
  "version": "v3",
  "published": "2010-12-03T16:37:53.000Z",
  "updated": "2017-11-16T17:06:43.000Z",
  "title": "Correlation between Angle and Side",
  "authors": [
    "Steven R. Finch"
  ],
  "comment": "13 pages",
  "categories": [
    "math.PR",
    "math.CA"
  ],
  "abstract": "Let alpha be an arbitrary angle in a random spherical triangle Delta and a be the side opposite alpha. (The sphere has radius 1; vertices of Delta are independent and uniform.) If some other side is constrained to be pi/2, then E(alpha*a)=3.05.... If instead some other angle is fixed at pi/2, then E(alpha*a)=2.87.... In our study of the latter scenario, both Apery's constant and Catalan's constant emerge. We also review Miles' 1971 proof that E(alpha*a)=pi^2/2-2 when no constraints are in place.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-12-10T14:01:03.000Z",
      "comment": "12 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2017-11-16T17:06:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60D05",
      "51M04",
      "51M25",
      "62H10",
      "62E15",
      "97G60",
      "33C05",
      "33E05"
    ],
    "keywords": [
      "correlation",
      "random spherical triangle delta",
      "side opposite alpha",
      "catalans constant emerge",
      "arbitrary angle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1012.0781F"
    }
  }
}