The silver ratio is the quantity defined by the continued
fraction
(Wall 1948, p. 24). It follows that
|
(3)
|
so
|
(4)
|
(OEIS A014176).
The sequence ,
of power fractional parts, where is the fractional part,
is equidistributed for almost all
real numbers ,
with the silver ratio being one exception.
The more general expressions
|
(5)
|
are sometimes known in general as silver means (Knott). The first few values are summarized in the table below.
See also
Equidistributed Sequence,
Golden Ratio,
Golden
Ratio Conjugate,
Power Fractional Parts
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References
Knott, R. "The Silver Means." http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/cfINTRO.html#silver.Sloane, N. J. A. Sequences A001622/M4046,
A014176, A098316,
A098317, and A098318
in "The On-Line Encyclopedia of Integer Sequences."Wall, H. S.
Analytic
Theory of Continued Fractions. New York: Chelsea, 1948.Referenced
on Wolfram|Alpha
Silver Ratio
Cite this as:
Weisstein, Eric W. "Silver Ratio." From
MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SilverRatio.html
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