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Gossard Perspector


GossardPerspector

The Gossard perspector, also called the Zeeman-Gossard perspector, is the triangle center X_(402) at which a reference triangle and its Gossard triangle are perspective (Kimberling).

Suppose the Euler line of ABC intersects the sidelines BC, CA, and AB at distinct finite points D, E, and F, respectively, and that the three corner triangles AEF, BFD, and CDE have defined Euler lines. These three Euler lines form the sidelines of the Gossard triangle and have the directions of BC, CA, and AB, respectively. The Gossard triangle is the image of ABC under a 180 degrees rotation about the perspector, which lies on their common Euler line (Kellogg 1916, Kimberling).

The perspector is halfway from the triangle centroid of ABC to the point given by the arithmetic mean of the position vectors of D, E, and F (Kimberling). It is the Dao-Zeeman perspector of the Euler line.


See also

Dao-Zeeman Perspector, Euler Line, Perspective Triangles, Triangle Center

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References

Kellogg, O. D. "The Ninth Regular Meeting of the Southwestern Section." Bull. Amer. Math. Soc. 22, 215-219, 1916. https://doi.org/10.1090/S0002-9904-1916-02759-5.Kimberling, C. "X(402) = Zeeman-Gossard Perspector." Encyclopedia of Triangle Centers. https://faculty.evansville.edu/ck6/encyclopedia/ETC.html#X402.

Cite this as:

Weisstein, Eric W. "Gossard Perspector." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GossardPerspector.html

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