{
 "stars_by_formula": [
  [
   0,
   0
  ],
  [
   51,
   154
  ],
  [
   103,
   51
  ],
  [
   154,
   206
  ],
  [
   206,
   103
  ]
 ],
 "stars": [
  {
   "point": [
    206,
    103
   ],
   "name": "(2 + φ)/5",
   "norm": 103,
   "norm_word": "SOLOMON",
   "walk_cell": 65791,
   "by_exponent": 65791
  },
  {
   "point": [
    51,
    154
   ],
   "name": "−(2 + φ)/5",
   "norm": 103,
   "norm_word": "SOLOMON",
   "walk_cell": 32767,
   "by_exponent": 32767
  },
  {
   "point": [
    154,
    206
   ],
   "name": "1/√5",
   "norm": 154,
   "norm_word": "ROAD TO DAMASCUS",
   "walk_cell": 65919,
   "by_exponent": 65919
  },
  {
   "point": [
    103,
    51
   ],
   "name": "−1/√5",
   "norm": 154,
   "norm_word": "ROAD TO DAMASCUS",
   "walk_cell": 32895,
   "by_exponent": 32895
  }
 ],
 "inv5": 103,
 "norms": {
  "fifth": 103,
  "minus_fifth": 154,
  "middle": 193,
  "quarter": 193
 },
 "fibonacci": [
  {
   "a": 1,
   "b": 1,
   "norm": 1
  },
  {
   "a": 1,
   "b": 2,
   "norm": -1
  },
  {
   "a": 2,
   "b": 3,
   "norm": 1
  },
  {
   "a": 3,
   "b": 5,
   "norm": -1
  },
  {
   "a": 5,
   "b": 8,
   "norm": 1
  },
  {
   "a": 8,
   "b": 13,
   "norm": -1
  },
  {
   "a": 13,
   "b": 21,
   "norm": 1
  },
  {
   "a": 21,
   "b": 34,
   "norm": -1
  },
  {
   "a": 34,
   "b": 55,
   "norm": 1
  },
  {
   "a": 55,
   "b": 89,
   "norm": -1
  },
  {
   "a": 89,
   "b": 144,
   "norm": 1
  },
  {
   "a": 144,
   "b": 233,
   "norm": -1
  }
 ],
 "norm_counts": [
  258,
  1
 ],
 "mean_step": {
  "stars": 7.1,
  "halves": 82.6,
  "whole": 64.2,
  "halves_count": 15
 },
 "flower": {
  "arms": [
   18.2,
   108.4,
   196.7,
   282.4
  ],
  "turn": 16.4,
  "between": [
   90.3,
   88.3,
   85.7,
   95.7
  ],
  "error_arm": 2.5,
  "error_four": 1.2,
  "angles": {
   "about the middle": 18.43,
   "star to star": 26.57,
   "the star's own arms": 31.72
  },
  "off": {
   "about the middle": [
    0.2,
    0.0,
    1.7,
    6.0
   ],
   "star to star": [
    8.4,
    8.2,
    9.9,
    14.2
   ],
   "the star's own arms": [
    13.5,
    13.3,
    15.0,
    19.3
   ]
  },
  "square_off": {
   "about the middle": 2.0,
   "star to star": 10.2,
   "the star's own arms": 15.3
  },
  "stars_from_middle": [
   18.43,
   108.43,
   198.43,
   288.43
  ]
 },
 "rifts": {
  "lean": {
   "f9": 24.6,
   "f36": 85,
   "f37": 37.8,
   "f38": 27,
   "f82": 25,
   "f89": 87.6,
   "f99": 19.0,
   "f116": 1.5
  },
  "beside": {
   "f9": [
    26.57
   ],
   "f38": [
    26.57
   ],
   "f82": [
    26.57
   ],
   "f99": [
    18.43
   ]
  },
  "picture_angles": {
   "from_the_middle": 18.43,
   "star_to_star": 26.57,
   "the_stars_arms": 31.72
  }
 },
 "edges": {
  "share_within_30": 0.826,
  "area_within_30": 0.214,
  "sheet_count": 6646
 },
 "sheet": {
  "fibre_edges": 2069,
  "row_edges": 2192,
  "both_edges": 1083
 },
 "holes_210": {
  "step": 1.7143,
  "list": [
   {
    "hole": "f28 pointed",
    "ratio": 0.421,
    "error": 0.024,
    "altitude": 24.9,
    "altitude_error": 1.5,
    "tilt": 65.13,
    "steps": 37.99,
    "steps_error": 0.9
   },
   {
    "hole": "f34",
    "ratio": 0.491,
    "error": 0.022,
    "altitude": 29.4,
    "altitude_error": 1.4,
    "tilt": 60.62,
    "steps": 35.36,
    "steps_error": 0.8
   },
   {
    "hole": "f116",
    "ratio": 0.542,
    "error": 0.047,
    "altitude": 32.8,
    "altitude_error": 3.2,
    "tilt": 57.18,
    "steps": 33.36,
    "steps_error": 1.9
   },
   {
    "hole": "f41",
    "ratio": 0.633,
    "error": 0.041,
    "altitude": 39.3,
    "altitude_error": 3.1,
    "tilt": 50.69,
    "steps": 29.57,
    "steps_error": 1.8
   },
   {
    "hole": "f15",
    "ratio": 0.647,
    "error": 0.039,
    "altitude": 40.3,
    "altitude_error": 2.9,
    "tilt": 49.7,
    "steps": 28.99,
    "steps_error": 1.7
   },
   {
    "hole": "f46",
    "ratio": 0.719,
    "error": 0.051,
    "altitude": 46.0,
    "altitude_error": 4.2,
    "tilt": 43.99,
    "steps": 25.66,
    "steps_error": 2.5
   },
   {
    "hole": "f37 on the seam",
    "ratio": 0.724,
    "error": 0.106,
    "altitude": 46.4,
    "altitude_error": 8.8,
    "tilt": 43.65,
    "steps": 25.46,
    "steps_error": 5.1
   },
   {
    "hole": "f28 upper of the pair",
    "ratio": 0.735,
    "error": 0.043,
    "altitude": 47.3,
    "altitude_error": 3.6,
    "tilt": 42.66,
    "steps": 24.89,
    "steps_error": 2.1
   },
   {
    "hole": "f28 lower of the pair",
    "ratio": 0.768,
    "error": 0.019,
    "altitude": 50.2,
    "altitude_error": 1.7,
    "tilt": 39.83,
    "steps": 23.23,
    "steps_error": 1.0
   },
   {
    "hole": "f11",
    "ratio": 0.77,
    "error": 0.044,
    "altitude": 50.4,
    "altitude_error": 4.0,
    "tilt": 39.62,
    "steps": 23.11,
    "steps_error": 2.3
   },
   {
    "hole": "f72",
    "ratio": 0.826,
    "error": 0.028,
    "altitude": 55.7,
    "altitude_error": 2.9,
    "tilt": 34.3,
    "steps": 20.01,
    "steps_error": 1.7
   },
   {
    "hole": "f82",
    "ratio": 0.887,
    "error": 0.085,
    "altitude": 62.5,
    "altitude_error": 10.6,
    "tilt": 27.52,
    "steps": 16.06,
    "steps_error": 6.2
   },
   {
    "hole": "f107",
    "ratio": 0.891,
    "error": 0.048,
    "altitude": 63.0,
    "altitude_error": 6.1,
    "tilt": 26.96,
    "steps": 15.73,
    "steps_error": 3.5
   }
  ]
 },
 "diffraction": {
  "wavelength_nm": 480,
  "px_per_mm": 16.4,
  "scale": "the leaf's height, 225 mm, taken as 3,700 px",
  "list": [
   {
    "hole": "f15r",
    "long_mm": 9.2,
    "short_mm": 6.0,
    "ring_arcsec": 20.2,
    "ring_mm_at_1m": 0.098,
    "sun_image_mm_at_1m": 15.3
   },
   {
    "hole": "f72v1",
    "long_mm": 13.9,
    "short_mm": 11.5,
    "ring_arcsec": 10.5,
    "ring_mm_at_1m": 0.051,
    "sun_image_mm_at_1m": 20.8
   },
   {
    "hole": "f82r",
    "long_mm": 4.8,
    "short_mm": 4.2,
    "ring_arcsec": 28.6,
    "ring_mm_at_1m": 0.139,
    "sun_image_mm_at_1m": 13.5
   },
   {
    "hole": "f116v",
    "long_mm": 7.4,
    "short_mm": 4.0,
    "ring_arcsec": 30.2,
    "ring_mm_at_1m": 0.146,
    "sun_image_mm_at_1m": 13.3
   }
  ]
 },
 "openings": {
  "rule": "each opening's place as fractions of its page, laid on the picture; distance to the nearest of the five stars, the picture's side 1, the picture wrapping round",
  "mean": 0.1687,
  "list": [
   {
    "leaf": "f52",
    "opening": "ragged, no clean rim",
    "place": "0.650, 0.771",
    "nearest_star": "154 + 206φ",
    "distance": 0.058
   },
   {
    "leaf": "f99",
    "opening": "a sewn rift standing open, bent like a comma",
    "place": "0.350, 0.230",
    "nearest_star": "103 + 51φ",
    "distance": 0.059
   },
   {
    "leaf": "f28",
    "opening": "two holes close together, a rag of skin between",
    "place": "0.210, 0.677",
    "nearest_star": "51 + 154φ",
    "distance": 0.078
   },
   {
    "leaf": "f46",
    "opening": "round hole",
    "place": "0.518, 0.760",
    "nearest_star": "154 + 206φ",
    "distance": 0.091
   },
   {
    "leaf": "f9",
    "opening": "sewn rift, open",
    "place": "0.878, 0.323",
    "nearest_star": "206 + 103φ",
    "distance": 0.11
   },
   {
    "leaf": "f14",
    "opening": "a bite at the edge",
    "place": "0.794, 0.286",
    "nearest_star": "206 + 103φ",
    "distance": 0.114
   },
   {
    "leaf": "f37",
    "opening": "sewn tear",
    "place": "0.693, 0.724",
    "nearest_star": "154 + 206φ",
    "distance": 0.12
   },
   {
    "leaf": "f36",
    "opening": "a scar with a lifted flap, a small hole in it",
    "place": "0.700, 0.725",
    "nearest_star": "154 + 206φ",
    "distance": 0.125
   },
   {
    "leaf": "f37",
    "opening": "round hole on the seam",
    "place": "0.712, 0.721",
    "nearest_star": "154 + 206φ",
    "distance": 0.137
   },
   {
    "leaf": "f38",
    "opening": "sewn rift, part open",
    "place": "0.259, 0.475",
    "nearest_star": "51 + 154φ",
    "distance": 0.138
   },
   {
    "leaf": "f89",
    "opening": "sewn slit",
    "place": "0.138, 0.467",
    "nearest_star": "51 + 154φ",
    "distance": 0.146
   },
   {
    "leaf": "f28",
    "opening": "pointed oval hole",
    "place": "0.647, 0.467",
    "nearest_star": "206 + 103φ",
    "distance": 0.167
   },
   {
    "leaf": "f36",
    "opening": "sewn rift",
    "place": "0.488, 0.932",
    "nearest_star": "154 + 206φ",
    "distance": 0.173
   },
   {
    "leaf": "f107",
    "opening": "round hole",
    "place": "0.764, 0.572",
    "nearest_star": "206 + 103φ",
    "distance": 0.176
   },
   {
    "leaf": "f82",
    "opening": "round hole",
    "place": "0.630, 0.324",
    "nearest_star": "206 + 103φ",
    "distance": 0.186
   },
   {
    "leaf": "f116",
    "opening": "sewn seam, a slit open on it",
    "place": "0.864, 0.130",
    "nearest_star": "0, the corner",
    "distance": 0.189
   },
   {
    "leaf": "f82",
    "opening": "sewn rift",
    "place": "0.248, 0.790",
    "nearest_star": "51 + 154φ",
    "distance": 0.196
   },
   {
    "leaf": "f116",
    "opening": "oval hole",
    "place": "0.824, 0.121",
    "nearest_star": "0, the corner",
    "distance": 0.213
   },
   {
    "leaf": "f34",
    "opening": "oval hole",
    "place": "0.332, 0.779",
    "nearest_star": "51 + 154φ",
    "distance": 0.223
   },
   {
    "leaf": "f41",
    "opening": "oval hole",
    "place": "0.772, 0.135",
    "nearest_star": "0, the corner",
    "distance": 0.265
   },
   {
    "leaf": "f36",
    "opening": "a torn place with rags of skin, no oval rim",
    "place": "0.506, 0.550",
    "nearest_star": "154 + 206φ",
    "distance": 0.267
   },
   {
    "leaf": "f11",
    "opening": "oval hole",
    "place": "0.536, 0.442",
    "nearest_star": "206 + 103φ",
    "distance": 0.268
   },
   {
    "leaf": "f72",
    "opening": "oval hole",
    "place": "0.517, 0.447",
    "nearest_star": "103 + 51φ",
    "distance": 0.274
   },
   {
    "leaf": "f15",
    "opening": "oval hole",
    "place": "0.453, 0.488",
    "nearest_star": "51 + 154φ",
    "distance": 0.277
   }
  ]
 },
 "why": {
  "first_differences": [
   [
    2,
    1
   ],
   [
    1,
    -2
   ]
  ],
  "square_of_the_matrix": 5,
  "stars": "k x (2, 1)/5, k = 0..4: 0 and the units 1, phi, -1, -phi over sqrt5; in the field of five phi = 3, 3^2 = -1",
  "angles": {
   "arctan(1/phi)": 31.7175,
   "arctan 2": 63.4349,
   "arctan 1/2": 26.5651,
   "arctan 1/3": 18.4349
  },
  "prague": {
   "latitude": 50.0875,
   "obliquity_1420": 23.5146,
   "midsummer_noon": 63.4271,
   "shadow_over_post": 0.50017,
   "from_the_zenith": 26.5729,
   "less_than_45": 18.4271,
   "ceiling_is_arctan_2_at": 50.0797,
   "longest_day_10_phi_hours_at": 50.0951,
   "midway": 50.0874
  },
  "north_star_1420": {
   "from_the_pole": 3.86,
   "lowest": 46.23,
   "highest": 53.95
  }
 },
 "sky_at_the_angles": [
  {
   "angle": 18.4349,
   "what": "arctan 1/3, the square's turn",
   "sun": [
    "5 Jan, Capricorn 23",
    "19 Nov, Sagittarius 6"
   ],
   "stars": [
    {
     "name": "9Bet Lep",
     "v": 2.84,
     "dec": -21.37773,
     "height": 18.53477,
     "side": "south",
     "off": 0.09982
    },
    {
     "name": "41Pi  Sgr",
     "v": 2.89,
     "dec": -21.75628,
     "height": 18.15622,
     "side": "south",
     "off": -0.27873
    },
    {
     "name": "Diphda",
     "v": 2.04,
     "dec": -21.18891,
     "height": 18.72359,
     "side": "south",
     "off": 0.28864
    },
    {
     "name": "Dschubba",
     "v": 2.32,
     "dec": -20.8087,
     "height": 19.1038,
     "side": "south",
     "off": 0.66885
    }
   ]
  },
  {
   "angle": 26.5651,
   "what": "arctan 1/2, star to star",
   "sun": [
    "5 Feb, Aquarius 25",
    "19 Oct, Scorpio 5"
   ],
   "stars": [
    {
     "name": "7Del Crv",
     "v": 2.95,
     "dec": -13.29428,
     "height": 26.61822,
     "side": "south",
     "off": 0.05317
    },
    {
     "name": "Zubenelgenubi",
     "v": 2.75,
     "dec": -13.52356,
     "height": 26.38894,
     "side": "south",
     "off": -0.17612
    },
    {
     "name": "4Gam Crv",
     "v": 2.59,
     "dec": -14.31387,
     "height": 25.59863,
     "side": "south",
     "off": -0.96642
    },
    {
     "name": "35Eta Oph",
     "v": 2.43,
     "dec": -14.80557,
     "height": 25.10693,
     "side": "south",
     "off": -1.45812
    }
   ]
  },
  {
   "angle": 31.7175,
   "what": "arctan(1/phi), the star's arm",
   "sun": [
    "19 Feb, Pisces 9",
    "5 Oct, Libra 21"
   ],
   "stars": [
    {
     "name": "Spica",
     "v": 0.98,
     "dec": -8.08271,
     "height": 31.82979,
     "side": "south",
     "off": 0.11232
    },
    {
     "name": "22Bet Aqr",
     "v": 2.91,
     "dec": -8.00963,
     "height": 31.90287,
     "side": "south",
     "off": 0.18539
    },
    {
     "name": "Rigel",
     "v": 0.12,
     "dec": -9.02863,
     "height": 30.88387,
     "side": "south",
     "off": -0.83361
    },
    {
     "name": "13Zet Oph",
     "v": 2.56,
     "dec": -9.21918,
     "height": 30.69332,
     "side": "south",
     "off": -1.02416
    }
   ]
  },
  {
   "angle": 45.0,
   "what": "45, the half",
   "sun": [
    "24 Mar, Aries 13",
    "1 Sep, Virgo 17"
   ],
   "stars": [
    {
     "name": "60Bet Oph",
     "v": 2.77,
     "dec": 5.00032,
     "height": 44.91282,
     "side": "south",
     "off": -0.08718
    },
    {
     "name": "Bellatrix",
     "v": 1.64,
     "dec": 5.64573,
     "height": 45.55823,
     "side": "south",
     "off": 0.55823
    },
    {
     "name": "Procyon",
     "v": 0.38,
     "dec": 6.55285,
     "height": 46.46535,
     "side": "south",
     "off": 1.46535
    },
    {
     "name": "Betelgeuse",
     "v": 0.5,
     "dec": 7.11864,
     "height": 47.03114,
     "side": "south",
     "off": 2.03114
    }
   ]
  },
  {
   "angle": 50.1524,
   "what": "arm + turn",
   "sun": [
    "7 Apr, Aries 26",
    "18 Aug, Virgo 4"
   ],
   "stars": [
    {
     "name": "50Gam Aql",
     "v": 2.72,
     "dec": 9.34572,
     "height": 49.25822,
     "side": "south",
     "off": -0.89421
    },
    {
     "name": "3Bet CMi",
     "v": 2.9,
     "dec": 9.27862,
     "height": 49.19112,
     "side": "south",
     "off": -0.9613
    },
    {
     "name": "88Gam Peg",
     "v": 2.83,
     "dec": 11.95559,
     "height": 51.86809,
     "side": "south",
     "off": 1.71566
    },
    {
     "name": "Unukalhai",
     "v": 2.65,
     "dec": 8.39,
     "height": 48.3025,
     "side": "south",
     "off": -1.84992
    }
   ]
  },
  {
   "angle": 58.2825,
   "what": "arctan(phi), the star's other arm",
   "sun": [
    "4 May, Taurus 22",
    "22 Jul, Leo 8"
   ],
   "stars": [
    {
     "name": "6Bet Ari",
     "v": 2.64,
     "dec": 17.87543,
     "height": 57.78793,
     "side": "south",
     "off": -0.49459
    },
    {
     "name": "Denebola",
     "v": 2.14,
     "dec": 17.77932,
     "height": 57.69182,
     "side": "south",
     "off": -0.59071
    },
    {
     "name": "Alhena",
     "v": 1.93,
     "dec": 16.69405,
     "height": 56.60655,
     "side": "south",
     "off": -1.67597
    },
    {
     "name": "123Zet Tau",
     "v": 3.0,
     "dec": 20.58702,
     "height": 60.49952,
     "side": "south",
     "off": 2.21699
    }
   ]
  },
  {
   "angle": 63.4349,
   "what": "arctan 2",
   "sun": [
    "12 Jun, Gemini 30, the Sun's highest noon of the year, 63.4262"
   ],
   "stars": [
    {
     "name": "68Del Leo",
     "v": 2.56,
     "dec": 23.63653,
     "height": 63.54903,
     "side": "south",
     "off": 0.11408
    },
    {
     "name": "Kochab",
     "v": 2.08,
     "dec": 76.51574,
     "height": 63.57176,
     "side": "north",
     "off": 0.13681
    },
    {
     "name": "27Bet Her",
     "v": 2.77,
     "dec": 22.88296,
     "height": 62.79546,
     "side": "south",
     "off": -0.63949
    },
    {
     "name": "Algieba",
     "v": 2.61,
     "dec": 22.66464,
     "height": 62.57714,
     "side": "south",
     "off": -0.85781
    }
   ]
  }
 ]
}