{
  "api": "math-constants",
  "title": "Math Constants",
  "description": "Notable mathematical constants with symbols, values and descriptions.",
  "emoji": "➗",
  "license": "GPL-2.0-or-later",
  "count": 20,
  "self": "https://gratisapi.com/api/math-constants/index",
  "endpoints": {
    "list": "https://gratisapi.com/api/math-constants/index",
    "item": "https://gratisapi.com/api/math-constants/{id}"
  },
  "fields": [
    "description",
    "id",
    "name",
    "symbol",
    "value"
  ],
  "results": [
    {
      "id": "pi",
      "name": "Pi",
      "symbol": "pi",
      "value": 3.141592653589793,
      "description": "Ratio of a circle's circumference to its diameter.",
      "url": "https://gratisapi.com/api/math-constants/pi"
    },
    {
      "id": "e",
      "name": "Euler's number",
      "symbol": "e",
      "value": 2.718281828459045,
      "description": "Base of the natural logarithm.",
      "url": "https://gratisapi.com/api/math-constants/e"
    },
    {
      "id": "golden-ratio",
      "name": "Golden ratio",
      "symbol": "phi",
      "value": 1.618033988749895,
      "description": "Ratio where (a+b)/a equals a/b.",
      "url": "https://gratisapi.com/api/math-constants/golden-ratio"
    },
    {
      "id": "square-root-2",
      "name": "Square root of 2",
      "symbol": "sqrt(2)",
      "value": 1.4142135623730951,
      "description": "Pythagoras' constant, diagonal of a unit square.",
      "url": "https://gratisapi.com/api/math-constants/square-root-2"
    },
    {
      "id": "square-root-3",
      "name": "Square root of 3",
      "symbol": "sqrt(3)",
      "value": 1.7320508075688772,
      "description": "Theodorus' constant.",
      "url": "https://gratisapi.com/api/math-constants/square-root-3"
    },
    {
      "id": "square-root-5",
      "name": "Square root of 5",
      "symbol": "sqrt(5)",
      "value": 2.23606797749979,
      "description": "Appears in the golden ratio formula.",
      "url": "https://gratisapi.com/api/math-constants/square-root-5"
    },
    {
      "id": "euler-mascheroni",
      "name": "Euler-Mascheroni constant",
      "symbol": "gamma",
      "value": 0.5772156649015329,
      "description": "Limit of harmonic series minus natural logarithm.",
      "url": "https://gratisapi.com/api/math-constants/euler-mascheroni"
    },
    {
      "id": "natural-log-2",
      "name": "Natural logarithm of 2",
      "symbol": "ln(2)",
      "value": 0.6931471805599453,
      "description": "Natural logarithm of two.",
      "url": "https://gratisapi.com/api/math-constants/natural-log-2"
    },
    {
      "id": "natural-log-10",
      "name": "Natural logarithm of 10",
      "symbol": "ln(10)",
      "value": 2.302585092994046,
      "description": "Natural logarithm of ten.",
      "url": "https://gratisapi.com/api/math-constants/natural-log-10"
    },
    {
      "id": "apery-constant",
      "name": "Apery's constant",
      "symbol": "zeta(3)",
      "value": 1.2020569031595942,
      "description": "Value of the Riemann zeta function at 3.",
      "url": "https://gratisapi.com/api/math-constants/apery-constant"
    },
    {
      "id": "catalan-constant",
      "name": "Catalan's constant",
      "symbol": "G",
      "value": 0.915965594177219,
      "description": "Sum of alternating reciprocals of odd squares.",
      "url": "https://gratisapi.com/api/math-constants/catalan-constant"
    },
    {
      "id": "feigenbaum-delta",
      "name": "Feigenbaum constant delta",
      "symbol": "delta",
      "value": 4.66920160910299,
      "description": "Ratio of bifurcation intervals in chaotic maps.",
      "url": "https://gratisapi.com/api/math-constants/feigenbaum-delta"
    },
    {
      "id": "feigenbaum-alpha",
      "name": "Feigenbaum constant alpha",
      "symbol": "alpha",
      "value": 2.502907875095892,
      "description": "Reduction scaling in period-doubling bifurcations.",
      "url": "https://gratisapi.com/api/math-constants/feigenbaum-alpha"
    },
    {
      "id": "twin-prime-constant",
      "name": "Twin prime constant",
      "symbol": "C_2",
      "value": 0.6601618158468696,
      "description": "Density constant for twin primes.",
      "url": "https://gratisapi.com/api/math-constants/twin-prime-constant"
    },
    {
      "id": "khinchin-constant",
      "name": "Khinchin's constant",
      "symbol": "K_0",
      "value": 2.685452001065306,
      "description": "Geometric mean of continued fraction terms.",
      "url": "https://gratisapi.com/api/math-constants/khinchin-constant"
    },
    {
      "id": "plastic-number",
      "name": "Plastic number",
      "symbol": "rho",
      "value": 1.324717957244746,
      "description": "Real root of x^3 = x + 1.",
      "url": "https://gratisapi.com/api/math-constants/plastic-number"
    },
    {
      "id": "silver-ratio",
      "name": "Silver ratio",
      "symbol": "delta_S",
      "value": 2.414213562373095,
      "description": "1 + square root of 2.",
      "url": "https://gratisapi.com/api/math-constants/silver-ratio"
    },
    {
      "id": "golden-angle",
      "name": "Golden angle",
      "symbol": "g",
      "value": 2.399963229728653,
      "description": "The golden ratio angle in radians.",
      "url": "https://gratisapi.com/api/math-constants/golden-angle"
    },
    {
      "id": "tau",
      "name": "Tau",
      "symbol": "tau",
      "value": 6.283185307179586,
      "description": "Ratio of a circle's circumference to its radius, 2*pi.",
      "url": "https://gratisapi.com/api/math-constants/tau"
    },
    {
      "id": "glaisher-kinkelin",
      "name": "Glaisher-Kinkelin constant",
      "symbol": "A",
      "value": 1.2824271291006226,
      "description": "Appears in asymptotics of the hyperfactorial.",
      "url": "https://gratisapi.com/api/math-constants/glaisher-kinkelin"
    }
  ]
}