First Napoleon Point

Author

Eric W. Weisstein
February 15, 2003

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

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

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

Initialization

<<PlaneGeometry`

Center Function

CenterFunction[NapoleonPoint[1]]//TraditionalForm

Figure

t=Triangle[{{0.,0.},{.9,.7},{2.,-.3}}];
Show[
Graphics[{
{Thickness[.01],t},
{Red,nt=NapoleonTriangle[1][t],
EqualSideTicks[nt,4,.04,.04]
},
{Blue,
Transpose[{e=ErectPolygons[t,1],MapIndexed[EqualSideTicks[#1,#2[[1]],.04,.02]&,e]}]
},
{DarkGreen,
LongestLine[{Sequence@@#,Coordinates[NapoleonPoint[1][t]]}]&/@Transpose[{Vertices[t],RotateLeft[Vertices[nt]]}]
},
PointLabels[Join[
Transpose[{Point/@Vertices[t],{"A","B","C"}}],
Append[#,Red]&/@Transpose[{Point/@Vertices[nt],{"(Subscript[N, AB])","(Subscript[N, BC])","(Subscript[N, AC])"}}],
Append[#,Blue]&/@Transpose[{Point/@(#[[2]]&/@Vertices/@e),{"(Subscript[E, AB])","(Subscript[E, BC])","(Subscript[E, AC])"}}],
{{NapoleonPoint[1][t],"N",DarkGreen}}
],{PointSize[.025],LabelOffset->.08}
]
}],AspectRatio->Automatic,PlotRange->All]