I first became interested in the golden ratio when I was a PhD student at Dalhousie. I started tutoring a local sculptor who wanted to learn more math to help with his amazing wood carvings. He told me about the golden ratio- I had honestly never encountered it until then (this was before the da Vinci Code made it really famous). At first I was a little skeptical, and didn't want it to distract from my own work on fractal trees. But then I realized that my favourite trees happened to scale according to the golden ratio- they seemed to line up and just generally look nicer than most other trees. Then I became a little obsessed with learning more- so connections with the pentagon, Fibonacci, etc.
Here is a blog about the golden ratio and fractal trees, written by a guy who only had his BSc at the time of writing it. I met him at a conference on math and art, it was really cool because he had actually read a paper of mine (I tend to assume that nobody else is interested in what I am doing).
http://blog.wolfram.com/2014/05/22/adventures-into-the-mathematical-forest-of-fractal-trees/
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