Fibonacci Sequence

# Fibonacci Sequence - This sequence can be written as...

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Jason Christian Fibonacci Writing January 27, 2007 Beauty in Numbers In 1202, the Liber abaci introduced the base ten number system, but not only did Fibonacci’s book create the number system still used over 800 years later, it also introduced a “golden” mathematical sequence. The Fibonacci numbers, named after their maker, can be found nearly everywhere. By looking in nature, examining ratios, and simply opening our eyes, we will find the Fibonacci numbers. Just as gravity exists as a law of nature, the Fibonacci numbers seem also to be one of Mother Nature’s laws. Through the process of solving a mathematical problem, Leonardo Pisano – more commonly known as Fibonacci – found the Fibonacci sequence. Fibonacci was solving a problem pertaining to the reproduction of rabbits in a year in which only a single pair initially exists and every month each pair bears a new pair starting on the second month.
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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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