The Fibonacci sequence may simply express the most efficient packing of the seeds (or scales) in the space available. As each row of seeds in a sunflower or each row of scales in a pine cone grows radially away from the center, it tries to grow the maximum number of seeds (or scales) in the smallest space. That is, these phenomena may be an expression of nature's efficiency. The same conditions may also apply to the propagation of seeds or petals in flowers. We observe that many of the natural things follow the Fibonacci sequence. Given his time frame and growth cycle, Fibonacci's sequence represented the most efficient rate of breeding that the rabbits could have if other conditions were ideal. Fibonacci sequence of numbers and the associated 'Golden Ratio' are manifested in nature and in certain works of art. Why are Fibonacci numbers in plant growth so common? One clue appears in Fibonacci's original ideas about the rate of increase in rabbit populations. To find the next number in this sequence (Fn), you can add 120 (that’s the n-2) to the 195 (the n-1) to get 315 (the Fn). For example, let’s look at a Fibonacci sequence starting with 75, 120, 195. The number of rows of the scales in the spirals that radiate upwards in opposite directions from the base in a pine cone are almost always the lower numbers in the Fibonacci sequence-3, 5, and 8. For any Fibonacci sequence, Fn will always be equal to (n-1) + (n-2). The corkscrew spirals of seeds that radiate outward from the center of a sunflower are most often 34 and 55 rows of seeds in opposite directions, or 55 and 89 rows of seeds in opposite directions, or even 89 and 144 rows of seeds in opposite directions. To see how it works in nature, go outside and find an intact pine cone (or any other cone). Similarly, the configurations of seeds in a giant sunflower and the configuration of rigid, spiny scales in pine cones also conform with the Fibonacci series. So the sequence, early on, is 1, 2, 3, 5, 8, 13, 21 and so on. All of these numbers observed in the flower petals-3, 5, 8, 13, 21, 34, 55, 89-appear in the Fibonacci series. Plants have made use of spirals in order to ensure that its leaves have the maximum exposure to light or to ensure maximum seed arrangement. There are exceptions and variations in these patterns, but they are comparatively few. Fibonacci numbers are also abundant in nature just try counting the spiral arms in a sunflower and you can see this for yourself. This series is formed from the starting numbers 1, 1, and then adding together the last 2 numbers to get the next one. The sequence 5, 8, 13, 21, 34, and 55 are members of the Fibonacci series. The numbers occur in these pairs more often than not. Some flowers have 3 petals others have 5 petals still others have 8 petals and others have 13, 21, 34, 55, or 89 petals. There can be 5 and 8, 8 and 13, 21 and 34, 34 and 55, and sometimes more. For example, although there are thousands of kinds of flowers, there are relatively few consistent sets of numbers of petals on flowers.
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