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Stammler Triangle


StammlerTriangle

The Stammler triangle is the triangle formed by the centers of the Stammler circles. It is an equilateral triangle. It circumscribes the circumcircle and homothetic to the first Morley triangle (Stammler 1997). The points of contact of this triangle and the circumcircle form the circumtangential triangle.

It has trilinear vertex matrix

 [cosA-2cos((B-C)/3) cosB+2cos((B+2C)/3) cosC+2cos((2B+C)/3); cosA+2cos((A+2C)/3) cosB-2cos((C-A)/3) cosC+2cos((2A+C)/3); cosA+2cos((A+2B)/3) cosB+2cos((2A+B)/3) cosC-2cos((A-B)/3)].

The circumcircle of the Stammler triangle is the Stammler circle.

All triangle centers of the Stammler triangle correspond to the circumcenter of the reference triangle.


See also

Proportionally-Cutting Circle, Stammler Circle, Stammler Circles, Stammler Hyperbola

Portions of this entry contributed by Floor van Lamoen

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References

Ehrmann, J.-P. and van Lamoen, F. M. "The Stammler Circles." Forum Geom. 2, 151-161, 2002. http://forumgeom.fau.edu/FG2002volume2/FG200219index.html.Stammler, L. "Cutting Circles and the Morley Theorem." Beitr. Alg. Geom. 38, 91-93, 1997. http://www.emis.de/journals/BAG/vol.38/no.1/7.html.

Referenced on Wolfram|Alpha

Stammler Triangle

Cite this as:

van Lamoen, Floor and Weisstein, Eric W. "Stammler Triangle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/StammlerTriangle.html

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