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Journal for Geometry and Graphics 24 (2020), No. 2, 233--247
Copyright Heldermann Verlag 2020

Permutation Ellipses

Clark Kimberling
Department of Mathematics, University of Evansville, Evansville, Indiana, U.S.A.

Peter J. C. Moses
Engineering Division, Moparmatic Co., Worcestershire, United Kingdom

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.

Keywords: barycentric coordinates, Steiner circumellipse, Steiner inellipse, complement and anticomplement, dual conic, inversion in ellipse, Frégier ellipse.

MSC: 51N20; 51N15

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