Journal for Geometry and Graphics 21 (2017), No. 2, 153--168
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.
emily-carroll@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 3-dimensional affine transformation and a curious interpretation of the iterative process as a 3-person 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
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