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.
ck6@evansville.edu
Peter J. C. Moses
Engineering Division, Moparmatic Co., Worcestershire, United Kingdom
moparmatic@gmail.com
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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