Iterated harmonic divisions and the golden ratio,
Forum Geometricorum, 16 (2016) 429--430.
Abstract. On the projective real line we consider sequences of points in which every four consecutive points form two harmonic point pairs. Surprisingly, the asymptotic behavior of one type of these sequences is characterized by the golden ratio. Another type of these sequences is projectively equivalent to a dense set on the unit circle generated by an irrational rotation by nearly 137.5 degrees.
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