Geodesic
Permutation Ellipses
Journal for geometry and graphics, Tome 24 (2020) no. 2, pp. 233-247
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We use homogeneous coordinates in the plane of a triangle to define a family of ellipses having the centroid of the triangle as center. The family, which includes the Steiner circumscribed and inscribed ellipses, is closed under many operations, including permutation of coordinates, complements and anticomplements, duality, and inversion.
Classification : 51N20, 51N15
Mots-clés : barycentric coordinates, Steiner circumellipse, Steiner inellipse, complement and anticomplement, dual conic, inversion in ellipse, Frégier ellipse 
@article{JGG_2020_24_2_JGG_2020_24_2_a7,
     author = {C. Kimberling and P. J. C. Moses},
     title = {Permutation {Ellipses}},
     journal = {Journal for geometry and graphics},
     pages = {233--247},
     year = {2020},
     volume = {24},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JGG_2020_24_2_JGG_2020_24_2_a7/}
}
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C. Kimberling; P. J. C. Moses. Permutation Ellipses. Journal for geometry and graphics, Tome 24 (2020) no. 2, pp. 233-247. http://geodesic.mathdoc.fr/item/JGG_2020_24_2_JGG_2020_24_2_a7/