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First Napoleon Point


FirstNapoleonPoint

The first Napoleon point N, also called the outer Napoleon point, 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_(BC)N_(AC). It has triangle center function

 alpha_(17)=csc(A+1/6pi)

and is Kimberling center X_(17) (Kimberling 1998, p. 69).


See also

First Fermat Point, Napoleon Points, Outer Napoleon Triangle, Second Napoleon Point

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References

Kimberling, C. "Triangle Centers and Central Triangles." Congr. Numer. 129, 1-295, 1998.Kimberling, C. "Napoleon Points." http://faculty.evansville.edu/ck6/tcenters/class/napoleon.html.Kimberling, C. "Encyclopedia of Triangle Centers: X(17)=1st Napoleon Point." http://faculty.evansville.edu/ck6/encyclopedia/ETC.html#X17.

Referenced on Wolfram|Alpha

First Napoleon Point

Cite this as:

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

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