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Golden Ratio
Leonardo Fibonacci was an Italian mathematician with a
penchant for decimalization and rabbits! Having introduced the
numbers 0 to 9 to Europe (like some medieval Big Bird from
Sesame Street), he turned his attention to a different series
of numbers:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55......
The Fibonacci sequence is generated by adding the
previous two numbers in the list together to form the next and
so on and so on...
Divide any number in the Fibonacci
sequence by the one before it, for example 55/34, or 21/13,
and the answer is always close to 1.61803. This is known as
the Golden Ratio, and hence Fibonacci's Sequence is also
called the Golden Sequence. Unlikely though it might seem,
this series of numbers is the common factor linking rabbits,
cauliflowers and snails.
Fibonacci used his sequence
of numbers to investigate the population growth of his
favourite furry lop-eared friend, the rabbit. He based his
model on a maximum-security bunny heaven where rabbits cannot
escape or die, and the problem he devised goes like this...
Suppose a newly born pair of rabbits (one male and one
female) are put in a field. These rabbits take a month to
become sexually mature, after which time they produce a new
pair of baby rabbits or 'kits' (again, one male and one
female). How many pairs will there be in subsequent years?
Think about it and if your answer is "enough for a
very large pie", think some more. |
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As models of population growth go, it may not be the best,
as it does not allow for rabbits to have more than two kits,
to have kits of the same sex, or to take time off at Easter to
deliver goodies. However, as a special series of numbers, the
Fibonacci sequence has a hidden beauty all of it's own. Count
the number of florets spiralling out from the centre of a
cauliflower. Look closely and you will find two spirals
running in opposite directions, and the number of florets in
each are two consecutive Fibonacci numbers.
Like
cauliflowers and rabbits, snails too are touched by nature's
golden ratio. Draw a rectangle in the proportions of the
golden ratio, then draw consecutively smaller 'golden
rectangles' within it and join diagonal corners with an arc.
The result is a perfect snail shell.
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Fibonacci's Midas touch may have given mathematicians the
blueprint for Mother Nature
herself. |
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