Transcript The Fibonacci Sequence

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