The silver constant is the algebraic number given
by
(OEIS A116425), where 
denotes the 
th polynomial root in the
ordering used in this work. Here, 
is the largest real root
of the cubic equation.
Defining the nested radical expression
![x=RadicalBox[{7, +, 7, RadicalBox[{7, +, ...}, 3]}, 3],](/images/equations/SilverConstant/NumberedEquation1.svg) |
(4)
|
the silver constant is given by
 |
(5)
|
(T. Piezas, pers. comm., Feb. 16, 2006).
The silver constant is the seventh Beraha constant (Finch 2003, pp. 417-418). The value 
lies on a 3-map cycle of
the logistic map 
.
See also
Beraha Constants,
Logistic Map,
Nested Radical,
Plastic
Constant,
Silver Ratio,
Trigonometry
Angles--Pi/7
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References
Finch, S. R. Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 417-418,
2003.Le Lionnais, F. Les
nombres remarquables. Paris, France: Hermann, pp. 51 and 143, 1983.Saaty,
T. L. and Kainen, P. C. The
Four-Color Problem: Assaults and Conquest. New York: Dover, p. 162,
1986.Sloane, N. J. A. Sequence A116425
in "The On-Line Encyclopedia of Integer Sequences."Referenced
on Wolfram|Alpha
Silver Constant
Cite this as:
Weisstein, Eric W. "Silver Constant."
From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SilverConstant.html
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