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Steiner's Ellipse

Let $\alpha':\beta':\gamma'$ be the Isotomic Conjugate Point of a point with Trilinear Coordinates $\alpha:\beta:\gamma$. The isotomic conjugate of the Line at Infinity having trilinear equation

\begin{displaymath}
a\alpha+b\beta+c\gamma=0
\end{displaymath}

is

\begin{displaymath}
{\beta'\gamma'\over a}+{\gamma'\alpha'\over b}+{\alpha'\beta'\over c}=0,
\end{displaymath}

known as Steiner's ellipse (Vandeghen 1965).

See also Isotomic Conjugate Point, Line at Infinity


References

Vandeghen, A. ``Some Remarks on the Isogonal and Cevian Transforms. Alignments of Remarkable Points of a Triangle.'' Amer. Math. Monthly 72, 1091-1094, 1965.




© 1996-9 Eric W. Weisstein
1999-05-26