Minkowski-Bower Constant

Author

Eric W. Weisstein
January 6, 2023

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Constants/Minkowski-BowerConstant.nb.

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

©2023 Wolfram Research, Inc. except for portions noted otherwise

Value

val=0.420372339423223075640993006646221873949189866600611871291654664686553370885979080355743905603928336;

Plot[
{MinkowskiQuestionMark[x],x},
{x,0,1},
AxesLabel->{x,None},
PlotLegends->"Expressions",
LabelStyle->FontFamily->"Times",
Epilog->{
AbsolutePointSize[7],Point[{1,1}val],
Dashed,Line[val{{1,0},{1,1},{0,1}}],
Text[Style[f,FontFamily->"Times"],{1,1}val,{0,-2}]
}
]

Plot[{MinkowskiQuestionMark[x],x},{x,0,3}]

FindInstance

FindInstance[MinkowskiQuestionMark[x]==x&&42<100x<43,x]

Root[{MinkowskiQuestionMark[#]-#&,0.4203723394232`}]

FixedPoint

FixedPoint[MinkowskiQuestionMark,0.420372339423223075640993006646221873949189866,SameTest->(Abs[#1-#2]<1*^-10&)]//Timing

FixedPoint[MinkowskiQuestionMark,0.420372339423223075640993006646221873949189866,SameTest->(Abs[#1-#2]<1*^-50&)]//Timing

FindRoot

r200=x/.FindRoot[MinkowskiQuestionMark[x]-x,{x,.42,.421},WorkingPrecision->200,MaxIterations->500]

s1=RealDigits[r200,10,120][[1]]

r250=x/.FindRoot[MinkowskiQuestionMark[x]-x,{x,.42,.421},WorkingPrecision->250,MaxIterations->500]

s2=RealDigits[r250,10,120][[1]]

s1-s2

r300=x/.FindRoot[MinkowskiQuestionMark[x]-x,{x,.42,.421},WorkingPrecision->300,MaxIterations->500]

s3=RealDigits[r300,10,120][[1]]

s2-s3

RealDigits[x/. FindRoot[MinkowskiQuestionMark[x]-x,{x,.42,.421},WorkingPrecision->200,MaxIterations->500],10,99][[1]]==RealDigits[val,10,99][[1]]