Harold Reiter and Arthur Holshouser, Using complex weighted centroids to create homothetic polygons,
Forum Geometricorum, 12 (2012) 247--254.

Abstract.   After first defining weighted centroids that use complex arithmetic, we then make a simple observation which proves Theorem 1. We next define complex homothety. We then show how to apply this theory to triangles (or polygons) to create endless numbers of homothetic triangles (or polygon). The first part of the paper is fairly standard. However, in the final part of the paper, we give two examples which illustrate that examples can easily be given in which the simple basic underpinning is so disguised that it is not at all obvious. Also, the entire paper is greatly enhanced by the use of complex arithmetic.

[ps file] [pdf]