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10

Part of 1968 Miklós Schweitzer

Problems(1)

Miklos Schweitzer 1968_10

Source:

10/8/2008
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
geometryperimeteradvanced fieldsadvanced fields unsolved