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This is the golden ratio, or part of it at least. Commonly believed in art to be a very aesthetically pleasing proportion, it has a close relationship with the Fibonacci sequence.
From the fibonacci sequence, it can be calculated by taking the limit of the ratio of consecutive Fibonacci numbers (i.e. lim{n -> inf} [(F_n+1)/(F_n)])
Examples of the Fibonacci sequence can also be seen in a lot of different forms of nature.