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Journal for Geometry and Graphics 14 (2010), No. 1, 001--014
Copyright Heldermann Verlag 2010

Dilation-Induced Perspectivities among Triangles

Clark Kimberling
Dept. of Mathematics, University of Evansville, 1800 Lincoln Avenue, Evansville, IN 47722, U.S.A.

Peter J. C. Moses
Moparmatic Co., 1154 Evesham Road, Astwood Bank - Redditch, Worcesteshire B96 6DT, England

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 U-dilations 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 mid-isotomic triangles are introduced. Many loci associated with perspectivities among these triangles are Z cubics.

Keywords: Perspective triangles, cevian triangles, anticevian triangles, midcevian triangles, mid-isotomic triangles.

MSC: 51M04

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