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This paper shows that the method of Galperin which had been widely acceptedin the literature since 1983 for constructing a non-dense and non-periodictrajectory in a triangle can never work. This is done by showing that allpossible examples that can be produced by Galperin's method of which there areinfinitely many all produce a periodic trajectory.

On non-periodic and non-dense billiard trajectories Part 1 and Part 2