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Napoleon Points


FirstNapoleonPoint

The first Napoleon point N is the concurrence of lines drawn between vertices of a given triangle DeltaABC and the opposite vertices of the corresponding inner Napoleon triangle DeltaN_(AB)N_(AC)N_(BC). The triangle center function of the first Napoleon point is

 alpha=csc(A-1/6pi).
SecondNapoleonPoint

The second Napoleon point N^' is the concurrence of lines drawn between vertices of a given triangle DeltaABC and the opposite vertices of the corresponding outer Napoleon triangle DeltaN_(AB)^'N_(AC)^'N_(BC)^'. The triangle center function of the point is

 alpha=csc(A+1/6pi).

See also

Fermat Points, First Napoleon Point, Inner Napoleon Triangle, Inner Vecten Triangle, Napoleon's Theorem, Outer Napoleon Triangle, Outer Vecten Triangle, Second Napoleon Point

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References

Casey, J. A Treatise on the Analytical Geometry of the Point, Line, Circle, and Conic Sections, Containing an Account of Its Most Recent Extensions with Numerous Examples, 2nd rev. enl. ed. Dublin: Hodges, Figgis, & Co., pp. 442-444, 1893.Kimberling, C. "Central Points and Central Lines in the Plane of a Triangle." Math. Mag. 67, 163-187, 1994.Kimberling, C. "Napoleon Points." http://faculty.evansville.edu/ck6/tcenters/class/napoleon.html.Rigby, J. "Napoleon Revisited." J. Geometry 33, 129-146, 1988.

Referenced on Wolfram|Alpha

Napoleon Points

Cite this as:

Weisstein, Eric W. "Napoleon Points." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/NapoleonPoints.html

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