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A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems.
[1] For example, the constant π may be defined as the ratio of the length of a circle's circumference to its diameter.
The following list includes a decimal expansion and set containing each number, ordered by year of discovery.
The column headings may be clicked to sort the table alphabetically, by decimal value, or by set.
Explanations of the symbols in the right hand column can be found by clicking on them.
Pythagoras constant[4] Theodorus' constant[6] Real root of
Real root of
Ratio of the perimeter of Bernoulli's lemniscate to its diameter.
Limiting difference between the harmonic series and the natural logarithm.
where W is the Lambert W function with the Riemann zeta function
is the lemniscate constant.
with the Dirichlet beta function
where γ is the Euler–Mascheroni constant and p is prime where sk is the kth term of Sylvester's sequence 2, 3, 7, 43, 1807, ...
in degrees Real root of
where the sum ranges over all primes p such that p + 2 is also a prime Real root of
Real number
2 π
is the nth term of the Thue–Morse sequence where Li(t) is the logarithmic integral, and ρ(t) is the Dickman function 0.1 2 3 4 5 6 7 8 9 10 11 12 13 14 ... 0.2 3 5 7 11 13 17 19 23 29 31 37 ... where
π
− 3 π
− π
where γ is the Euler–Mascheroni constant and ζ '(2) is the derivative of the Riemann zeta function evaluated at s = 2 Positive root of
where Fn is the nth Fibonacci number where E[λn,2] is the expected longest common subsequence of two random length-n binary strings where the sequence an is given by n-th period-doubling bifurcation of logistic map
or any other one-dimensional map with a single quadratic maximum
where pk is the kth prime number where tk is the kth term of the Thue–Morse sequence Foias constant is the unique real number such that if x1 = α then the sequence diverges to infinity.
The following list includes the continued fractions of some constants and is sorted by their representations.
Continued fractions with more than 20 known terms have been truncated, with an ellipsis to show that they continue.
Rational numbers have two continued fractions; the version in this list is the shorter one.
Decimal representations are rounded or padded to 10 places if the values are known.