A constant, sometimes also called a "mathematical constant," is any well-defined real number which is significantly interesting in
some way. In this work, the term "constant" is generally reserved for real nonintegral numbers of interest, while "number" is used to refer to interesting integers
(e.g., Brun's constant, but beast
number). However, in contexts such as linear
combination, the term "constant" is generally used to mean "scalar" or "real number,"
and need not exclude integer values.
A function, equation, etc., is said to "be constant" (or be a constant function) if it always assumes the same value independent of how its parameters
are varied.
Certain constants are known to many decimaldigits and recur throughout many diverse areas of mathematics, often in unexpected and surprising
places (e.g., pi, e, and
to some extent, the Euler-Mascheroni constant). Other constants are more specialized
and may be known to only a few digits. S. Plouffe
maintains a site about the computation and identification of numerical constants.
Plouffe's site also contains a page giving the largest number of digits
computed for the most common constants. S. Finch maintains a delightful, more
expository site containing detailed essays and references on constants both common
and obscure.
The mathematician Glaisher remarked, "No doubt the desire to obtain the values of these quantities to a great many figures is also partly due to the fact that most
of them are interesting in themselves; for , ,
, , and many other numerical quantities occupy a curious, and
some of them almost a mysterious, place in mathematics, so that there is a natural
tendency to do all that can be done towards their precise determination" (Gourdon
and Sebah).
The following table lists some common constants, their symbols, and approximate values.
). Other constants are more specialized
and may be known to only a few digits. S. Plouffe
maintains a site about the computation and identification of numerical constants.
Plouffe's site also contains a page giving the largest number of digits
computed for the most common constants. S. Finch maintains a delightful, more
expository site containing detailed essays and references on constants both common
and obscure.
, 
,
, 
, and many other numerical quantities occupy a curious, and
some of them almost a mysterious, place in mathematics, so that there is a natural
tendency to do all that can be done towards their precise determination" (Gourdon
and Sebah).
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over the Primes."