This week it was a little more interesting for me because I love the Golden Ratio and Fibonacci. The reason why I like them both so much is because it is observed in many of the little things around us that we take for granted, especially in the beauty of nature in particular where examples are arrangements of patterns, leaves, markings, proportions and so on. (Narain, 2003; Meisner, 1997)
I don't know if I misunderstood, but in the lecture the explanation sounded like "The Fibonacci sequence is the Golden Ratio." This isn't true though.
The Fibonacci sequence and the golden ratio are indeed related but they're not the same thing. They do have some subtle differences.
In the Fibonacci sequence the ratio between each pair of numbers in the sequence is NOT constant. However, as you go further along the sequence the ratio approaches the Golden Ratio. (Gerry, 2010)
Apparently you can test out the differences visually with fractals as well. In a fractal if you use Golden Ratio you can zoom in to the fractal forever and see exactly the same thing prior to magnification. (Baird, 2008) Personally I think that's really beautiful because it's infinity and am quite obsessed with the idea of infinity.
Anyway, in comparison if you use the Fibonacci sequence to do the fractal when you zoom in you see self-similar shapes. Self-similar, NOT the exact same image. Then when you zoom in further the self-similarity halts and eventually stops the pattern since the sequence approaches the Golden Ratio but never quite reaches the ratio. (Baird, 2008)
Therefore, they are related but not the exact same thing.
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References:
Baird, E. (2008). Fun with Fractals. Retrieved September 26, 2011 from http://www.relativitybook.com/CoolStuff/erkfractals.html
Gerry. (2010). Golden Ratio and the Fibonacci sequence? I need some help!? Retrieved September 26, 2011 from http://answers.yahoo.com/question/index?qid=20100814074419AAFIkJI
Meisner, G. (1997). Nature - More Examples of Phi, the Golden Ratio and Fibonacci numbers. Retrieved September 26, 2011 from http://www.goldennumber.net/nature2.htm
Narain, D.L. (2003). The Golden Ratio in Nature. Retrieved September 26, 2011 from http://cuip.uchicago.edu/~dlnarain/golden/activity7.htm
