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Unformatted text preview: This sequence can be written as follows: f 1 = 1, f 2 = 1, and f n = f n -1 + f n 2 , for integer n > 2 Thus, the sequence follows with the numbers: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, While the mere existence of the numbers is not very impressive, the appearance of the numbers can peak ones interest. For example, if f (x) is the Fibonacci Sequence and A(x) = ( f n ) / ( f n-1 ) then the 618034 . 1 ) ( = x A Lim x , also known as the Golden Ratio. The Golden Ratio is used in many ways for aesthetic purposes. For example, when webpage designers design a webpage, they use the Golden Ratio to place the graphics and text on the page to look most appealing. Likewise, screensavers use geometric shapes with ratios of 1.618034 to create pleasing images....
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- Spring '08