
Journal for Geometry and Graphics 12 (2008), No. 1, 023034 Copyright Heldermann Verlag 2008 Yff Conics Clark Kimberling Dept. of Mathematics, University of Evansville, 1800 Lincoln Avenue, Evansville, IN 47722, U.S.A. ck6@evansville.edu [Abstractpdf] Suppose that $a,b,c$ are algebraic indeterminates and $U=u:v:w$ is a point given in homogeneous trilinear coordinates. The Yff conic of $U$ is defined as the locus of a point $X=x:y:z$ satisfying the equation $f(x,y,z) = f(u,v,w)$, where $f(u,v,w)=(vw+wu+uv)/(u^2+v^2+w^2)$. The symbolic substitution $(a,b,c) \to (bc,ca,ab)$ maps the Yff conic of the symmedian point to that of the centroid. This mapping and others are used to find a large number of special points on many Yff conics. Keywords: Ellipse, hyperbola, parabola, symbolic substitution, triangle center, trilinear coordinates, trilinear product, Yff conic. MSC: 51M05 [ Fulltextpdf (173 KB)] for subscribers only. 