Power Point

Author

Eric W. Weisstein
January 25, 2011

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

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

©2010 Wolfram Research, Inc. except for portions noted otherwise

Initialization

Examples

Select[CenterFunction/@Centers,FreeQ[#,b|c|A|B|C]&]

centers=Position[CenterFunction/@Centers,_?(FreeQ[#,b|c|A|B|C]&),{1},Heads->False]//Flatten

Centers[[centers]]

{CenterName[#],CenterFunction[#]}&/@Centers[[centers]]//ColumnForm

powercenters={BrocardPoint[3],X[75],Centroid,Incenter,SymmedianPoint,X[31],X[32]};

Figure

V5

t=Triangle[{{0,0},{.3,.5},{1,0}}];
Show[Graphics[{
t,
PointLabels[Transpose[{Point/@Vertices[t],{"A","B","C"}}],{LabelOffset->.03}],
PointLabels[Transpose[{Through[powercenters[t]],{"Ω''","I'","G","I","K","2","3"}}],
{Red,LabelOffset->.03}],
Red,
Line[TrilinearToCartesian[t,#]&/@Table[SideLengths[t]^n,{n,-20,20,.2}]]
},
AspectRatio->Automatic,PlotRange->All]]

V6

t=Triangle[{{0,0},{1,0},{.3,.5}}];
Graphics[{
t,
PointLabels[Transpose[{{"A","B","C"},VertexPoints[t]}],LabelOffset->.03],
Red,PointLabels[Transpose[{{"Ω''","I'","G","I","K","2","3"},Through[powercenters[t]]}],LabelOffset->.03],
Line[TrilinearToCartesian[t,#]&/@Table[SideLengths[Evaluate[t]]^n,{n,-20,20,.2}]]
}/.PointSize[_]:>PointSize[.02]]

"PowerPoint"->,