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Journal for Geometry and Graphics 24 (2020), No. 2, 217--232
Copyright Heldermann Verlag 2020

The Circumcevian-Inversion Perspector of Two Triangles

Haryana, India

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

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

Beginning with a point P in the plane of a triangle ABC, reflections and circumcircle-inversions are used to define a triangle X'Y'Z' that is perspective to ABC. The perspector, denoted by Cip(P), defines a transform, Cip, that is applied to selected curves; e.g., Cip maps the Euler line to itself in a manner well represented by Shinagawa coefficients, and in general Cip maps lines to conics. Barycentric coordinates are used to determine properties of Cip and related points and mappings. Four new equilateral triangles are presented.

Keywords: Barycentric coordinates, circumcircle, circumcevian, inversion, perspective, Shinagawa coefficients.

MSC: 51N20; 51N15

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