Geodesic
Iterated Routh's Triangles
Journal for geometry and graphics, Tome 21 (2017) no. 2, pp. 153-168.

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 51M04, 51N10, 60D05, 15B51
Mots-clés : Routh's triangles, Ceva's theorem, random iterations, job allocation procedure 
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     title = {Iterated {Routh's} {Triangles}},
     journal = {Journal for geometry and graphics},
     pages = {153--168},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {2017},
     url = {http://geodesic.mathdoc.fr/item/JGG_2017_21_2_JGG_2017_21_2_a1/}
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E. Carroll; A. P. Ghosh; X. H. Nguyen; A. Roitershtein . Iterated Routh's Triangles. Journal for geometry and graphics, Tome 21 (2017) no. 2, pp. 153-168. http://geodesic.mathdoc.fr/item/JGG_2017_21_2_JGG_2017_21_2_a1/