
Journal for Geometry and Graphics 24 (2020), No. 2, 217232 Copyright Heldermann Verlag 2020 The CircumcevianInversion 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 circumcircleinversions 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 [ Fulltextpdf (416 KB)] 