The Fibonacci Sequence

The Fibonacci Sequence

By Steven Cornell Was created by Leonardo Pisano Bogollo. It shows the growth of an idealized rabbit population.

They mate after one month After a month a new pair of rabbits are born The third month, the first pair creates another pair (so there are 3 pairs now). The fourth month the first 2 create new

pairs (so 5 exist now). Etc. In the sequence, the next number is found by adding up the preceding two numbers in the sequence or with the

equation: Xn = Xn-1 + Xn-2 Find the fourth term of the sequence: Xn = Xn-1 + Xn-2

Xn = 1 + 0 = 1 Xn = 1 + 1 = 2 Xn = 2 + 1 = 3 Xn = 3 + 2 = 5 SO, the fourth term is 5.

First take the numbers of the series and form them into boxes with the sides equal to the numbers, then place them in an outward spiral: When an arc is drawn through the boxes from one corner to the opposing one it forms a spiral

known as the Golden Spiral which can be seen in a nautilus shell. When a ratio of the numbers in the Fibonacci series is made, it is seen that they approach the number that is approximately 1.618034 (which is also known as the golden number).

1/1 = 1, 2/1 = 2, 3/2 = 1.5, 5/3 = 1.6666, 8/5 = 1.6, 13/8 = 1.625, 21/13 = 1.6153846, etc.

Its used very often in nature and can be seen in the arrangement of leaves on a stem, the branching of trees, the flowering of artichokes, etc.

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