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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.

Peter J. C. Moses
Engineering Division, Moparmatic Co., Astwood Bank, nr. Redditch, Worcestershire, B96 6DT, England

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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