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A constant, sometimes also called a "mathematical constant," is any well-defined genuine number i beg your pardon is substantially interesting in part way. In this work, the hatchet "constant" is usually reserved for genuine nonintegral numbers of interest, when "number" is provided to refer to interesting integers (e.g., Brun"s constant, yet beast number). However, in contexts together as direct combination, the ax "constant" is generally used to median "scalar" or "real number," and also need not exclude integer values.

You are watching: What is a constant in an equation

A function, equation, etc., is claimed to "be constant" (or be a consistent function) if it always assumes the same value elevation of how its parameters are varied.

Certain constants are recognized to many decimal digits and recur throughout many diverse areas of mathematics, frequently in unexpected and surprising places (e.g., pi, e, and to part extent, the Euler-Mascheroni consistent

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). Various other constants room more dedicated and may be recognized to just a couple of digits. S.Plouffe maintains a site around the computation and identification of numerical constants. Plouffe"s site also contains a page offering the largest variety 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 also obscure.

The mathematician Glaisher remarked, "No doubt the desire to attain the values of these amounts to a good many figures is additionally partly because of the reality that many of lock are amazing in themselves; because that

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,
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,
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,
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, and also many other numerical quantities occupy a curious, and also some of them practically a mysterious, ar in mathematics, so that there is a natural tendency to execute all that can be done towards their an exact determination" (Gourdon and also Sebah).

The following table perform some typical constants, their symbols, and approximate values.

constantkeolistravelservices.com LanguagesymbolOEISapprox. Value
Apéry"s constantZeta<3>
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A0021171.20206...
Catalan"s constantCatalan
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A0067520.915966...
Delian constant2^(1/3)
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" />
A0025801.25992...
eE
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A0011132.71828...
Euler-Mascheroni constantEulerGamma
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A0016200.577216...
Glaisher-Kinkelin constantGlaisher
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A0749621.28243...
golden ratioGoldenRatio
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A0016221.61803...
Khinchin"s constantKhinchin
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A0022102.68545...
natural logarithm the 2Log<2>
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A0021620.693147...
piPi
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A0007963.14159...
Pythagoras"s constantSqrt<2>
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A0021931.41421...
Soldner"s constant
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A0707691.45136...

Gourdon and Sebah and Lyster maintain internet pages comparing the fastest known algorithms for computer digits of usual constants.


SEE ALSO: Coefficient, consistent Function, consistent of Integration, continuous of Proportionality, constant Polynomial, Number, Piecewise constant Function, real Number, Scalar

RELATED keolistravelservices.com SITES: http://functions.keolistravelservices.com.com/Constants/


REFERENCES:

Bailey, D.H. And Crandall, R.E. "On the arbitrarily Character that FundamentalConstant Expansions." Exper. Math. 10, 175-190, 2001. Http://www.nersc.gov/~dhbailey/dhbpapers/baicran.pdf.

Borwein, J. And also Bailey, D. Math by Experiment: Plausible thinking in the 21st Century. Wellesley, MA: A K Peters, p.145, 2003.

Borwein, J. And Borwein, P. ADictionary of actual Numbers. London: Chapman & Hall, 1990.

Finch, S.R. MathematicalConstants. Cambridge, England: Cambridge university Press, 2003.

Gourdon, X. And Sebah, P. "Numbers, Constants and also Computation." http://numbers.computation.free.fr/Constants/constants.html.

Gourdon, X. And also Sebah, P. "User Constants (Compute log(2), zeta(3), CatalanConstant, Pi through Arctan recipe ... Through pifast." http://numbers.computation.free.fr/Constants/PiProgram/userconstants.html.

Gourdon, X. And also Sebah, P. "Constants and Records of Computation." http://numbers.computation.free.fr/Constants/Miscellaneous/Records.html.

Kondo, S. "PI civilization OF JA0HXV." http://ja0hxv.calico.jp/pai/estart.html.

Le Lionnais, F. Lesnombres remarquables. Paris: Hermann, 1983.

Lyster, S. "Stu"s Pi Page: The faster Pi programs on the Planet." http://home.istar.ca/~lyster/otherconstants.html.

Michon, G.P. "Final Answers: numerical Constants." http://home.att.net/~numericana/answer/constants.htm.

Munafo, R. "Notable nature of details Numbers." http://home.earthlink.net/~mrob/pub/math/numbers.html.

Niklasch, G. "Some Number-Theoretical Constants developing as products of Rational functions of

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over the Primes." http://www.gn-50uma.de/alula/essays/Moree/Moree.en.shtml.

Plouffe, S. "Plouffe"s Inverter." http://pi.lacim.uqam.ca/eng/.

Plouffe, S. "Plouffe"s Inverter: Table of current Records because that the Computationof Constants." http://pi.lacim.uqam.ca/eng/records_en.html.

Plouffe, S. "Miscellaneous mathematical Constants." http://www.worldwideschool.org/library/books/sci/math/MiscellaneousMathematicalConstants/toc.html.

Robinson, H.P. And Potter, E. MathematicalConstants. Report UCRL-20418. Berkeley, CA: college of California, 1971.

Trott, M. "Mathematical Constants." §2.2.4 in The Mathematica GuideBook because that Programming. New York: Springer-Verlag, pp.171-180, 2004. Http://www.mathematicaguidebooks.org/.

Wells, D.W. The Penguin thesaurus of Curious and Interesting Numbers. Harmondsworth, England: Penguin Books, 1986.


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