The golden ratio, 1:0.61803399…, is everywhere in nature. People have exploited this ratio in visual arts such as paintings, architecture, sculpture, websites, and photography for thousands of years. Well, websites and photography are a little more recent. Anyway, this number is closely related to the Fibonacci sequence \( F = \{ 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, \ldots \} \) in that \( \lim_{n \to \infty} \frac{F_n}{F_{n+1}} \approx 0.61803399\ldots \). Even more interesting is that the reciprocal \( \frac{1}{0.61803399\ldots} = 1.61803399\ldots \).

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