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Napoleon Triangles

\begin{figure}\begin{center}\BoxedEPSF{NapoleonTriangleInner.epsf scaled 750}\end{center}\end{figure}

The inner Napoleon triangle is the Triangle $\Delta N_{AB}N_{AC}N_{BC}$ formed by the centers of internally erected Equilateral Triangles $\Delta ABE_{AB}$, $\Delta ACE_{AC}$, and $\Delta BCE_{BC}$ on the sides of a given Triangle $\Delta ABC$. It is an Equilateral Triangle.


\begin{figure}\begin{center}\BoxedEPSF{NapoleonTriangleOuter.epsf scaled 750}\end{center}\end{figure}

The outer Napoleon triangle is the Triangle $\Delta N_{AB}'N_{AC}'N_{BC}'$ formed by the centers of externally erected Equilateral Triangles $\Delta ABE_{AB}'$, $\Delta ACE_{AC}'$, and $\Delta BCE_{BC}'$ on the sides of a given Triangle $\Delta ABC$. It is also an Equilateral Triangle.

See also Equilateral Triangle, Napoleon Points, Napoleon's Theorem


References

Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. Washington, DC: Math. Assoc. Amer., pp. 60-65, 1967.




© 1996-9 Eric W. Weisstein
1999-05-25