Fibonacci numbers are a sequence where the number 1 is the first two terms. N is the number of the term and F(n) is the value of that term. The most appealing rectangle to the ancient Greeks was the one with the proportion of width/length equal to length/ length+width. You solve for x by cross multiplying, and using the quadratic formula. Approximate the answer to 3 decimal places and that number is called the Golden Ratio.