api: YAML JSON TOON Database
version: 1.0.0
format: toon
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[2]: You need a constant's value or its symbol and meaning.,You want to cite a constant with an explicit number of digits.
  caveats[2]: 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[3]: geometric-formulas,trigonometric-identities,statistics-basics
  entry_count: 17
  fields[4]{section,field,type,example}:
    data,name,string,Pi
    data,symbol,string,pi
    data,value,number|string,"3.1415926535"
    data,description,string,Ratio of a circle circumference to its diameter.
  category: Mathematics
  category_slug: mathematics
  tags: "math,constants,reference"
  view_count: 46
  created_at: 1793403093
  updated_at: 1793403093
data[17]{name,symbol,value,description}:
  Pi,pi,3.1415926535,Ratio of a circle circumference to its diameter.
  Euler's Number,e,2.7182818284,Base of the natural logarithm.
  Golden Ratio,phi,1.6180339887,Ratio where the sum of two quantities divided by the larger equals the larger divided by the smaller.
  Square Root of 2,sqrt(2),1.4142135623,Positive algebraic number whose square is 2.
  Square Root of 3,sqrt(3),1.7320508075,Positive algebraic number whose square is 3.
  Natural Logarithm of 2,ln(2),0.6931471805,Natural logarithm of 2.
  Imaginary Unit,i,sqrt(-1),Defined by the property that its square is -1.
  Tau,tau,6.2831853072,Ratio of a circle circumference to its radius; equal to 2 pi.
  Euler-Mascheroni Constant,gamma,0.5772156649,Limiting difference between the harmonic series and the natural logarithm.
  Square Root of 5,sqrt(5),2.2360679775,"Appears in the golden ratio, which equals (1 + sqrt(5)) / 2."
  Natural Logarithm of 10,ln(10),2.302585093,Converts between natural and base-10 logarithms.
  Catalan's Constant,G,0.9159655942,Alternating sum of the reciprocals of odd squares; appears in combinatorics and number theory.
  Apery's Constant,zeta(3),1.2020569032,Value of the Riemann zeta function at 3; Apery proved it is irrational.
  Silver Ratio,delta_S,2.4142135624,"Equal to 1 + sqrt(2); the continued fraction [2; 2, 2, 2, ...]."
  Plastic Number,rho,1.3247179572,"The real root of x^3 = x + 1, the smallest Pisot number."
  Khinchin's Constant,K,2.6854520011,Geometric mean of the continued-fraction coefficients of almost every real number.
  Feigenbaum Constant delta,delta,4.6692016091,Limiting ratio of successive period-doubling bifurcation intervals in many chaotic systems.