Fibonacci Numbers

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Fibonacci Numbers
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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.

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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