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
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
Explore with Wolfram|Alpha
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
Subject classifications
![[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)].](/images/equations/StammlerTriangle/NumberedEquation1.svg)
