Inversion

Author

Eric W. Weisstein
July 22, 2003

This notebook downloaded from http://mathworld.wolfram.com/notebooks/PlaneGeometry/Inversion.nb.

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

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

Initialization

<<PlaneGeometry`

Chessboard

<<Chess`

Show[GraphicsArray[{
Graphics[
ChessBoard[8,BlackColor->Red],
AspectRatio->Automatic],
Graphics[
Invert[ChessBoard[8,BlackColor->Red],Circle[{0,0},.01],Divisions->100],AspectRatio->Automatic]
}]]

Circles

opts={PlotRange->All,AspectRatio->Automatic,DisplayFunction->Identity};

Show[GraphicsArray[Partition[
		{Show[InverseCircles[.8,{{2,0},1},5,.2],opts],Show[InverseCircles[1,{{2,0},1},5,.2],opts],
Show[InverseCircles[1,{{.6,0},1},5,.2],opts],
			Show[InverseCircles[1,{{1.42,0},1},5,.2],opts],
Show[InverseCircles[1,{{.6,0},2},5,.2],opts],
				Show[InverseCircles[1,{{0,0},2},5,.2],opts]},2]]]

Inversion

conf={Circle[{0,0},2],
Circle[{0,0},2.5],
Circle[{0,0},1.5],
Circle[{0,0},1/GoldenRatio],Line[Table[2{Cos[#],Sin[#]}&[2Pi i/5],{i,1,11,2}]],
Line/@Table[2.5{{Cos[#],Sin[#]},{Cos[#+Pi],Sin[#+Pi]}}&[2Pi i/5],{i,1,5}]};
conf2={Circle[{0,0},1],
Circle[{0,0},Cos[Pi/5.]],Line[Table[{Cos[#],Sin[#]}&[2Pi i/5],{i,0,5}]]
};

Show[GraphicsArray[{
{
Graphics[conf,AspectRatio->Automatic],
Graphics[Invert[{{6.,0},2.1},conf][[1]],AspectRatio->Automatic],
Graphics[Invert[{{4,1},1},conf][[1]],AspectRatio->Automatic,PlotRange->All]
},{
Graphics[conf2,AspectRatio->Automatic],
Graphics[Invert[{{.12,.2},2},conf2][[1]],AspectRatio->Automatic],
Graphics[Invert[{{3,.6},3},conf2][[1]],AspectRatio->Automatic]
}}]]