During one step every internal polygon rotates to the next position along its outer polygon, merging two green sides. How many full turns are made by the innermost triangle before the entire configuration returns to its initial state?
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Solution
The triangle makes 588 turns.
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One reply on “Flower of gears”
Bob Ruyle points out elsewhere that if we disregard whether the n-gons have turned from their original position when they return to their original “space”, then, in fact, the configuration returns after only 10 turns. The triangle turns (1/3-1/10)=7/30 of a turn per step, so would turn only 7/3 of one complete turn, instead of the 588 turns required to bring all the sides back to their starting positions.