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Fibonacci Numbers

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... Fibonacci, whose Liber Abaci published in 1202 introduced the sequence to ... The sequence is defined by the following recurrence relation: ... – PowerPoint PPT presentation

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Title: Fibonacci Numbers


1
Fibonacci Numbers
2
Fibonacci Numbers
  • In mathematics, the Fibonacci numbers are a
    sequence of numbers named after Leonardo of Pisa,
    known as Fibonacci, whose Liber Abaci published
    in 1202 introduced the sequence to Western
    European mathematics.
  • The sequence is defined by the following
    recurrence relation
  • That is, after two starting values, each number
    is the sum of the two preceding numbers. The
    first Fibonacci numbers also denoted as Fn, for
    n  0, 1, , are 0, 1, 1, 2, 3, 5, 8, 13, 21,
    34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584,
    4181, 6765, 10946, 17711, 28657, 46368, 75025,
    121393,
  • Each third number of the series is an even
    number.
  • The sequence named after Fibonacci was first
    described in Indian mathematics.
  • The sequence extended to negative index n
    satisfies Fn Fn-1 Fn-2 for all integers n,
    and F-n (-1)n1Fn
  • .., -8, 5, -3, 2, -1, 1, followed by the sequence
    above.

3
Fibonacci Rectangles
4
1
5
1
1
6
1
1
2
7
1
1
3
2
8
1
1
3
2
5
9
1
1
3
8
2
5
10
13
1
1
3
8
2
5
11
13
21
1
1
3
8
2
5
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