Geodesic
Mappings from the Plane of a Triangle to a Circumconic
Journal for geometry and graphics, Tome 24 (2020) no. 1, pp. 35-47.

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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.
Classification : 51N20, 51N15
Mots-clés : Triangle geometry, triangle center, circumconic, barycentric coordinates, circumcircle, perspective, area 
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     author = {C. Kimberling and P. J. C. Moses },
     title = {Mappings from the {Plane} of a {Triangle} to a {Circumconic}},
     journal = {Journal for geometry and graphics},
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C. Kimberling; P. J. C. Moses . Mappings from the Plane of a Triangle to a Circumconic. Journal for geometry and graphics, Tome 24 (2020) no. 1, pp. 35-47. http://geodesic.mathdoc.fr/item/JGG_2020_24_1_JGG_2020_24_1_a3/