Journal for Geometry and Graphics 24 (2020), No. 2, 217--232
Copyright Heldermann Verlag 2020
The Circumcevian-Inversion Perspector of Two Triangles
Suren
Haryana, India
surenxyz0@gmail.com
Peter J. C. Moses
Engineering Division, Moparmatic Co., Worcestershire, United Kingdom
moparmatic@gmail.com
Clark Kimberling
Department of Mathematics, University of Evansville, Evansville, Indiana, U.S.A.
ck6@evansville.edu
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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