Second Napoleon Point

Author

Eric W. Weisstein
February 15, 2003

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

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

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

Initialization

<<PlaneGeometry`;

Center Function

CenterFunction[NapoleonPoint[2]]//TraditionalForm

Figure

t=Triangle[{{0.,0.},{.9,.7},{2.,-.3}}];
Show[
Graphics[{
{Thickness[.01],t},
{Red,nt=NapoleonTriangle[2][t],
EqualSideTicks[nt,4,.04,.06]
},
{DarkGreen,
LongestLine[{Sequence@@#,Coordinates[NapoleonPoint[2][t]]}]&/@Transpose[{Vertices[t],RotateLeft[Vertices[nt]]}]
},
{Blue,
Transpose[{e=ErectPolygons[t,-1],MapIndexed[EqualSideTicks[#1,#2[[1]],.04,.02]&,e]}]
},
PointLabels[Join[
Transpose[{Point/@Vertices[t],{"A","B","C"}}],
Append[#,Blue]&/@Transpose[{Point/@First/@Vertices/@e,{"E(Subscript[', AB])","E(Subscript[', BC])","E(Subscript[', AC])"}}],
Append[#,Red]&/@Transpose[{Point/@Vertices[nt],{"N(Subscript[', AB])","N(Subscript[', BC])","N(Subscript[', AC])"}}],
{{NapoleonPoint[2][t],"N'",DarkGreen}}
],{PointSize[.025],LabelOffset->.08}
]
}],AspectRatio->Automatic]