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I asked my students where we see the golden ratio and one of them
suggested astronomy. This was news to me so I assigned her to
research it and bring it back to class. Most of the URLs she came up
with were wacko stuff and numerology, but one web site looked a
little more interesting. Mario Livio has more credibility than the
other sites, but I'd still thought I'd ask this list about \phi
showing up in equations for Kerr black holes.
http://www.huffingtonpost.com/mario-livio/the-golden-ratio_b_1818907.html