Topic summary

Projective harmonic conjugates

Extracted from the Wikipedia article Projective harmonic conjugate.

Iterated projective harmonic conjugates and the golden ratio

Let $P 0, P 1, P 2$ be three different points on the real projective line. Consider the infinite sequence of points $P n$ , where $P n$ is the harmonic conjugate of $P n -3$ with respect to $P n -1, P n -2$ for $n > 2$ . This sequence is convergent.

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