
Journal for Geometry and Graphics 14 (2010), No. 1, 001014 Copyright Heldermann Verlag 2010 DilationInduced Perspectivities among Triangles Clark Kimberling Dept. of Mathematics, University of Evansville, 1800 Lincoln Avenue, Evansville, IN 47722, U.S.A. ck6@evansville.edu Peter J. C. Moses Moparmatic Co., 1154 Evesham Road, Astwood Bank  Redditch, Worcesteshire B96 6DT, England mows@mopar.freeserve.co.uk In the plane of a triangle ABC, let DEF be a triangle and U a point. Except for special cases, there are at most two nontrivial Udilations of DEF that are perspective to ABC. Of particular interest are configurations in which DEF is perspective to ABC, as when DEF is a cevian or anticevian triangle. Midcevian and midisotomic triangles are introduced. Many loci associated with perspectivities among these triangles are Z cubics. Keywords: Perspective triangles, cevian triangles, anticevian triangles, midcevian triangles, midisotomic triangles. MSC: 51M04 [ Fulltextpdf (258 KB)] for subscribers only. 