numerical-values.json

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[
  {
    "params": {
      "region": "equilateral-triangle",
      "n": 3
    },
    "number": "1",
    "comment": "Three independent uniform area points are noncollinear with probability $1$."
  },
  {
    "params": {
      "region": "equilateral-triangle",
      "n": 4
    },
    "number": "2/3",
    "comment": "This is Sylvester's four-point probability."
  },
  {
    "params": {
      "region": "equilateral-triangle",
      "n": 5
    },
    "number": "11/36"
  },
  {
    "params": {
      "region": "equilateral-triangle",
      "n": 6
    },
    "number": "91/900"
  },
  {
    "params": {
      "region": "equilateral-triangle",
      "n": 7
    },
    "number": "17/675"
  },
  {
    "params": {
      "region": "equilateral-triangle",
      "n": 8
    },
    "number": "323/66150"
  },
  {
    "params": {
      "region": "unit-square",
      "n": 3
    },
    "number": "1",
    "comment": "Three independent uniform area points are noncollinear with probability $1$."
  },
  {
    "params": {
      "region": "unit-square",
      "n": 4
    },
    "number": "25/36",
    "comment": "This is Sylvester's four-point probability."
  },
  {
    "params": {
      "region": "unit-square",
      "n": 5
    },
    "number": "49/144"
  },
  {
    "params": {
      "region": "unit-square",
      "n": 6
    },
    "number": "49/400"
  },
  {
    "params": {
      "region": "unit-square",
      "n": 7
    },
    "number": "121/3600"
  },
  {
    "params": {
      "region": "unit-square",
      "n": 8
    },
    "number": "20449/2822400"
  },
  {
    "params": {
      "region": "unit-disk",
      "n": 3
    },
    "number": "1",
    "comment": "Three independent uniform area points are noncollinear with probability $1$."
  },
  {
    "params": {
      "region": "unit-disk",
      "n": 4
    },
    "number": "0.7044798810431814999553515656382943865289535738726142325336403236419950638601466298589729510502696403",
    "comment": "This is Sylvester's four-point probability, $1-35/(12\\pi^2)$ CITE{Marckert}."
  },
  {
    "params": {
      "region": "unit-disk",
      "n": 5
    },
    "number": "0.3561883122726454106170159108548556277952202859367667208768592765057749605524623007641910719309445735",
    "comment": "The exact value is $1-305/(48\\pi^2)$ CITE{Marckert}."
  },
  {
    "params": {
      "region": "unit-disk",
      "n": 6
    },
    "number": "0.1343093863571099388567519390562815222062074839436436122362857629960799547838824432027786620320200015",
    "comment": "The exact value is $1-(146400\\pi^2-473473)/(11520\\pi^4)$ CITE{Marckert}."
  },
  {
    "params": {
      "region": "unit-disk",
      "n": 7
    },
    "number": "0.03909056230070790319009578457274220307412526130314250142005362829091538567473484718778033253057964058",
    "comment": "The exact value is $1-(512400\\pi^2-2900611)/(23040\\pi^4)$ CITE{Marckert}."
  },
  {
    "params": {
      "region": "unit-disk",
      "n": 8
    },
    "number": "0.009034262164855343163545962523547630210849646555099686962509365970595457222086937730075448400680513119",
    "comment": "The exact value is $1-(62664108221+1721664000\\pi^4-18670881600\\pi^2)/(48384000\\pi^6)$ CITE{Marckert}."
  }
]