api: YAML JSON TOON Database
version: 1.0.0
format: yaml
dataset:
  id: 2751
  slug: common-mathematical-constants
  title: Common Mathematical Constants
  description: Widely used mathematical constants and their approximate values.
  summary: "The mathematical constants that recur across fields, each with its symbol, a decimal value to ten places and what it measures: pi, e, the golden ratio, square roots, the imaginary unit, and further constants such as tau, the Euler-Mascheroni constant, Catalan's constant, Apery's constant and the Feigenbaum constant."
  use_when:
    - You need a constant's value or its symbol and meaning.
    - You want to cite a constant with an explicit number of digits.
  caveats:
    - Values are rounded to ten decimal places and are approximations; most constants are irrational.
    - For some constants (the Euler-Mascheroni constant, Catalan's constant) it is not known whether they are irrational.
  related:
    - geometric-formulas
    - trigonometric-identities
    - statistics-basics
  entry_count: 17
  fields:
    - section: data
      field: name
      type: string
      example: Pi
    - section: data
      field: symbol
      type: string
      example: pi
    - section: data
      field: value
      type: number|string
      example: "3.1415926535"
    - section: data
      field: description
      type: string
      example: Ratio of a circle circumference to its diameter.
  category: Mathematics
  category_slug: mathematics
  tags: math,constants,reference
  view_count: 45
  created_at: 1793403093
  updated_at: 1793403093
data:
  - name: Pi
    symbol: pi
    value: 3.1415926535
    description: Ratio of a circle circumference to its diameter.
  - name: Euler's Number
    symbol: e
    value: 2.7182818284
    description: Base of the natural logarithm.
  - name: Golden Ratio
    symbol: phi
    value: 1.6180339887
    description: Ratio where the sum of two quantities divided by the larger equals the larger divided by the smaller.
  - name: Square Root of 2
    symbol: sqrt(2)
    value: 1.4142135623
    description: Positive algebraic number whose square is 2.
  - name: Square Root of 3
    symbol: sqrt(3)
    value: 1.7320508075
    description: Positive algebraic number whose square is 3.
  - name: Natural Logarithm of 2
    symbol: ln(2)
    value: 0.6931471805
    description: Natural logarithm of 2.
  - name: Imaginary Unit
    symbol: i
    value: sqrt(-1)
    description: Defined by the property that its square is -1.
  - name: Tau
    symbol: tau
    value: 6.2831853072
    description: Ratio of a circle circumference to its radius; equal to 2 pi.
  - name: Euler-Mascheroni Constant
    symbol: gamma
    value: 0.5772156649
    description: Limiting difference between the harmonic series and the natural logarithm.
  - name: Square Root of 5
    symbol: sqrt(5)
    value: 2.2360679775
    description: Appears in the golden ratio, which equals (1 + sqrt(5)) / 2.
  - name: Natural Logarithm of 10
    symbol: ln(10)
    value: 2.302585093
    description: Converts between natural and base-10 logarithms.
  - name: Catalan's Constant
    symbol: G
    value: 0.9159655942
    description: Alternating sum of the reciprocals of odd squares; appears in combinatorics and number theory.
  - name: Apery's Constant
    symbol: zeta(3)
    value: 1.2020569032
    description: Value of the Riemann zeta function at 3; Apery proved it is irrational.
  - name: Silver Ratio
    symbol: delta_S
    value: 2.4142135624
    description: Equal to 1 + sqrt(2); the continued fraction [2; 2, 2, 2, ...].
  - name: Plastic Number
    symbol: rho
    value: 1.3247179572
    description: The real root of x^3 = x + 1, the smallest Pisot number.
  - name: Khinchin's Constant
    symbol: K
    value: 2.6854520011
    description: Geometric mean of the continued-fraction coefficients of almost every real number.
  - name: Feigenbaum Constant delta
    symbol: delta
    value: 4.6692016091
    description: Limiting ratio of successive period-doubling bifurcation intervals in many chaotic systems.