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As you saw in the previous problems, as n increases, the ratio of any Fibonacci number Fn to the previous Fibonacci number Fn - 1 approaches one particular number, approximately 1.618. This number, called the golden mean, is referred to by the Greek letter phi (ø).
To explore this concept, let's start with a square, size 1 • 1, which is the first Fibonacci number. Then put a square above it with a side equal to the next Fibonacci number (which is also 1). Then put a square next to them with a side equal to the next Fibonacci number (2):
You are now approximating what is known as a golden rectangle. A golden rectangle has the property that a square constructed on its longer side will make a new configuration that is also a golden rectangle -- one that is similar to the first in that its sides have the same ratio as the original rectangle.
If you continue this process, each rectangle you create will be closer to the golden rectangle, just as the ratio of consecutive Fibonacci numbers gets closer to the golden ratio. The ratio of the sides of a golden rectangle is ø, the golden mean.
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