Abstract
Starting with a triangle ABC and a real number s, we let AAs, BBs, CCs be the cevians that divide the sides BC, CA, AB, respectively, in the ratio s : 1 − s, and we let \({\mathcal{H}_s(ABC)}\) be the triangle whose side lengths are equal to those of AAs, BBs, CCs. We investigate the sequence of (the shapes of) triangles \({\mathcal{H}_s^n(ABC)}\) , n = 1, 2, ... by introducing a new shape function that suits this sequence. We also use this shape function to prove a theorem of C. F. Parry concerning automedian triangles.
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