Jensen Disk

Author

Eric W. Weisstein
October 30, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/ComplexAnalysis/JensenDisk.nb.

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

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

Figure

<<Graphics`Colors`

JensenDisks[p_,z_]:=Module[{},
Map[{Re[#],Im[#]}&,List@@
({#,Conjugate[#]}&/@(Last/@Reduce[p==0&&Im[z]>0,z])),{2}]
]

circle[x__]:=Circle[Mean[{x}],Norm[Subtract@@{x}]/2]
diameter[x__]:=Line[{x}]

With[{p=z^6+z^5+z^4+z^3+z^2+z+1},
d=JensenDisks[p,z];
Show[Graphics[{
{Hue[.5],Disk@@@circle@@@d},
{Blue,circle@@@d},
PointSize[.02],
{Red,
diameter@@@d,
Point[{Re[#],Im[#]}]&/@(List@@Last/@Roots[p==0,z])
}
},
AspectRatio->Automatic,Ticks->None,Axes->True,AxesFront->True,
PlotLabel->TraditionalForm[P[z]==p]
]]]