MathDB
Miklos Schweitzer 1968_10

Source:

October 8, 2008
geometryperimeteradvanced fieldsadvanced fields unsolved

Problem Statement

Let h h be a triangle of perimeter 1 1, and let H H be a triangle of perimeter λ \lambda homothetic to h h. Let h1,h2,... h_1,h_2,... be translates of h h such that , for all i i, hi h_i is different from h_{i\plus{}2} and touches H H and h_{i\plus{}1} (that is, intersects without overlapping). For which values of λ \lambda can these triangles be chosen so that the sequence h1,h2,... h_1,h_2,... is periodic? If λ≥1 \lambda \geq 1 is such a value, then determine the number of different triangles in a periodic chain h1,h2,... h_1,h_2,... and also the number of times such a chain goes around the triangle H H. L. Fejes-Toth
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