Common Mathematical Constants
Widely used mathematical constants and their approximate values.
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 it when
- You need a constant's value or its symbol and meaning.
- You want to cite a constant with an explicit number of digits.
Watch out for
- 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.
The data
17 rows
| 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. |
Fields
The shape of this dataset, read from the data itself: every column, its type and a real value. Agents can use this to plan a query without fetching the whole document.
| 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. |
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