Does the continued fraction of the golden ratio (phi) have visual representations in inversive or projective geometry? I was looking at the circles of Apollonius represented as harmonic conjugates in a map of inversion in a circle, and it seems like there might be an interesting way to represent the continuing inversion, addition, inversion, addition etc of phi in this sort of conformal visualization? I know phi shows up in Farey circles, as the point reached on the tangent line, but I'm not sure if one could make that line the line at infinity or some such construction.
2026-02-23 02:39:26.1771814366
Representing the continued fraction of phi as inversion in a circle
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I found a subsequent paper from that posted by Gerry above, by Jerzy Kocik containing some illustrations:
https://arxiv.org/pdf/1910.05924.pdf