Stammler Hyperbola


The Stammler hyperbola of a triangle is the Feuerbach hyperbola of its tangential triangle, and its center is the focus of the Kiepert parabola, which is Kimberling center X_(110).

It has trilinear equation


The Stammler hyperbola passes through Kimberling centers X_i for i=1 (incenter I), 3 (circumcenter O), 6 (symmedian point K), 155, 159, 195, 399 (Parry reflection point), 610, 1498, 1740, 2574, 2575, 2916, 2917, 2918, 2929, 2930, 2931, 2935, and 2948. It also passes through the excenters J_A, J_B, and J_C, as well as through the centers of the Stammler circles.

The polar triangle of the Stammler hyperbola is the reference triangle.

The anticevian triangle of a point on the hyperbola has vertices on the hyperbola. The vertices of the antipedal triangles for Kimberling centers X_i with i=1, 3, 64, 2574, and 2575 also lie on the Stammler hyperbola (P. Moses, pers. comm., Jan. 24, 2005).

See also

Feuerbach Hyperbola, Stammler Circles, Stammler Triangle

Explore with Wolfram|Alpha

Cite this as:

Weisstein, Eric W. "Stammler Hyperbola." From MathWorld--A Wolfram Web Resource.

Subject classifications