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