
Journal for Geometry and Graphics 21 (2017), No. 2, 153168 Copyright Heldermann Verlag 2017 Iterated Routh's Triangles Emily Carroll Dept. of Mathematics, Iowa State University, 420 Carver Hall, Ames, IA 50011, U.S.A. emilycarroll@outlook.com Arka P. Ghosh Dept. of Mathematics, Iowa State University, 420 Carver Hall, Ames, IA 50011, U.S.A. apghosh@iastate.edu Xuan Hien Nguyen Dept. of Mathematics, Iowa State University, 420 Carver Hall, Ames, IA 50011, U.S.A. xhnguyen@iastate.edu Alexander Roitershtein Dept. of Mathematics, Iowa State University, 420 Carver Hall, Ames, IA 50011, U.S.A. roiterst@iastate.edu We consider a series of iterated Routh's triangles. In a general deterministic case we find the limit point of the sequence. We discuss a representation of the limit as a fixed point of a 3dimensional affine transformation and a curious interpretation of the iterative process as a 3person job allocation procedure. For a random sequence of iterations, we show that the expected value of the limiting point is the centroid of the original triangle. Keywords: Routh's triangles, Ceva's theorem, random iterations, job allocation procedure. MSC: 51M04; 51N10, 60D05, 15B51 [ Fulltextpdf (353 KB)] for subscribers only. 