Journal for Geometry and Graphics 24 (2020), No. 1, 035--047
Copyright Heldermann Verlag 2020
Mappings from the Plane of a Triangle to a Circumconic
Clark Kimberling
Department of Mathematics, University of Evansville, 1800 Lincoln Avenue, Evansville, IN 47722, U.S.A.
ck6@evansville.edu
Peter J. C. Moses
Engineering Division, Moparmatic Co., Astwood Bank, nr. Redditch, Worcestershire, B96 6DT, England
moparmatic@gmail.com
Barycentric coordinates are used to define mappings M from the plane of a reference triangle ABC to a circumconic. Accordingly, the M-image of a triangle is a triangle inscribed in the conic. Certain triangles T defined in this manner have relatively simple barycentrics and appear to be new to the literature. Cases are examined in which T is perspective to ABC, or to a family of cevian, or anticevian, or cocevian triangles. Of particular interest are criteria for perspectivity that involve cubic curves.
Keywords: Triangle geometry, triangle center, circumconic, barycentric coordinates, circumcircle, perspective, area.
MSC: 51N20; 51N15.
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