Silver Ratio

Author

Eric W. Weisstein
September 2, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Constants/SilverRatio.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/SilverRatio.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Value

FromContinuedFraction[{{2}}]

2+ContinuedFractionK[2,{n,∞}]

N[%]

General Silver means

FromContinuedFraction[{{n}}]

Table[FromContinuedFraction[{{n}}],{n,5}]

Table[(1/2)(n+(Sqrt[(n^2)+4])),{n,5}]//Simplify

N[%,11]

Most/@First/@RealDigits/@%

Equidistributed

<<Statistics`DataManipulation`

Block[{$MaxExtraPrecision=5000,c=1+Sqrt[2]},
BarChart[BinCounts[
Table[FractionalPart[c^ n]//N,{n,5000}],{0,1,.05}],
PlotRange->All,BarSpacing->0,PlotLabel->TraditionalForm[#]]&[c]
]//Timing