Conway's Constant

Author

Eric W. Weisstein
April 16, 2004

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

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

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

Root

Polynomial[l_List,x_]:=Fold[x #1+#2&,0,l]

(poly=Polynomial[{1,0,-1,-2,-1,2,2,1,-1,-1,-1,-1,-1,2,5,3,-2,-10,-3,-2,6,6,1,9,-3,-7,-8,-8,10,6,8,-5,-12,7,-7,7,1,-3,10,1,-6,-2,-10,-3,2,9,-3,14,-8,0,-7,9,3,-4,-10,-7,12,7,2,-12,-4,-2,5,0,1,-7,7,-4,12,-6,3,-6},x]//Expand)//TraditionalForm

Plot

<<Graphics`Colors`

roots=Table[Root[poly,n],{n,71}];

ListPlot[Through[{Re,Im}[#]]&/@N[roots],PlotStyle->{PointSize[.02],RGBColor[0,0,1]},AspectRatio->Automatic,Epilog->{PointSize[.03],RGBColor[1,0,0],Point[Flatten[Through[{Re,Im}[Select[N[roots],Positive]]]]]}]

Constant

λ=Select[roots,Positive]

N[λ,110]

Continued Fraction

ContinuedFraction[λ,50]