May 2014
Intermediate to advanced
350 pages
9h 55m
English
Content preview from Computing
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74 ◾ Computing
sequence are 1. A French-born mathematician, Albert Girard (1595–1632)
[12, 13], was the rst person who formulated the inductive denition of
the Fibonacci sequence as:
F
0
= 0, F
1
= 1, F
n+2
= F
n+1
+ F
n
(n ≥ 0)
where F
n
is the nth Fibonacci number (n = 0, 1, 2, 3, …). He stated that the
ratios of two consecutive Fibonacci numbers tend to the golden ratio =
(1 +
5
)/2. is result was published in 1634, 2 years aer his death. e
tree representations for equations F
n+2
= F
n+1
+ F
n
and F
n+4
= 3F
n+1
+ 2F
n
are
shown in Figure9.2.
Many authors attribute the discovery of the following equation to
J. P. M. Binet (1786–1856) in 1843, ...
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