fibonacci-numbers

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. Shifting the register down the Fibonacci number results into the conversion from kilometers to miles (Hazewinkel, 2002) (Knott, Using the Fibonacci numbers to represent whole numbers, 2009). A close observation of our nature revels that Fibonacci numbers are often found in two consecutive Fibonacci numbers in biological setting (Douady & Couder, 1995), branching in trees, and arrangement of leaves on a stem, and the fruitlets of a pineapple (Jones & Wilson, 2006) for example. The flowering of artichoke and arrangements of a pine cone is yet another example (Brousseau, 1969). The Fibonacci numbers have also been observed in the family tree of honeybees (Thimbleby). H. Vogel in 1979 proposed a model for the pattern of florets found in the head of a sunflower (Vogel, 1979) as below: 2 , √ ∅ Here, is the index number of the floret while is a constant scaling factor. Figure 3 Sunflower head displaying florets in spirals of 34 and 55 around the outside Therefore, florets lie on Fermat's spiral. The divergence angle is approximately 137.51 ° which is known as the golden angle because this angle divides a circle in the golden ratio. The reason sunflower florets pack so efficiently is since this ratio is an irrational number; no floret has a neighbor at exactly the same angle from the center. The rational approximations to the golden ratio are of form : 1. For this reason, the nearest possible neighbor of floret number are those at for some index which is dependent of , the distance from the center. Fibonacci numbers Page 8
It is often observed that sunflowers and similar natural arrangements have 55 spirals in one direction while 89 in the other (Prusinkiewicz & Lindenmayer, 1991). Once again I would like to stress that this paper shall only be considered as the introduction to the Fibonacci numbers and there is still much more to Fibonacci numbers not covered in this paper. Fibonacci numbers Page 9
Page 1 and 2: NATIONAL UNIVERSITY Fibonacci Numbe
Page 3 and 4: In order to study Fibonacci numbers
Page 5 and 6: atio of two successive terms (Plato
Page 7: There are many other properties and
Page 11 and 12: Knott, R. (2005, August 19). The Fi

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