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CHAPTER – SEQUENCE AND SERIES
    FIBONACCI SEQUENCE



                         BY
                   C.RAM MUKILAN
                       XI A 1
                 KENDRIYA VIDYALAYA
                 NARIMEDU, MADURAI
When there is a staircase with three steps how many ways can
  you reach the top?




Case a                    Case b                     Case c
 There is a staircase, number of ways one can reach
   Zero step        –1
   First step       -1
   Second step      –2
   Third step       –3
   Fourth step      - 5


        When we observe……..

                 1 1 2 3 5 8 13 ………..
The number pattern is known as the Fibonacci sequence.




 1 1 2 3 5 8 13 21 34 55
FIBONACCI SPIRAL


             Box   Side


             1      1

             2      1

             3      2

             4      3

             5      5

             6      8

             7     13

             8     21
Fibonacci
On many plants, the number of petals is a Fibonacci
number:

Buttercups have 5 petals; lilies and iris have 3 petals;
some delphiniums have 8; corn marigolds have 13
petals; some asters have 21 whereas daisies can be found
with 34, 55 or even 89 petals.

13 petals: ragwort, corn marigold, cineraria, some daisies
21 petals: aster, black-eyed Susan, chicory
34 petals: plantain, pyrethrum
55, 89 petals: michaelmas daisies, the asteraceae family.

Some species are very precise about the number of
petals they have - e.g. buttercups, but others have petals
that are very near those above, with the average being a
Fibonacci number.
 A Fibonacci word is a specific sequence of binary digits. The Fibonacci
  word is formed by repeated concatenation in the same way that
  the Fibonacci numbers are formed by repeated addition.
    Fibonacci based
   constructions are currently
   used to model physical
   systems with aperiodic order
   such as quasicrystals. Crystal
   growth techniques have
   been used to grow Fibonacci
   layered crystals and study
   their light scattering
   properties
W5

B3     B2




8 white
13 w & b
Fibonacci
Fibonacci
 www.wikipedia.org
 www.youtube.com
 www.worldmystreries.com
 www.google.co.in
Fibonacci

Contenu connexe

Fibonacci

  • 1. CHAPTER – SEQUENCE AND SERIES FIBONACCI SEQUENCE BY C.RAM MUKILAN XI A 1 KENDRIYA VIDYALAYA NARIMEDU, MADURAI
  • 2. When there is a staircase with three steps how many ways can you reach the top? Case a Case b Case c
  • 3.  There is a staircase, number of ways one can reach  Zero step –1  First step -1  Second step –2  Third step –3  Fourth step - 5 When we observe…….. 1 1 2 3 5 8 13 ………..
  • 4. The number pattern is known as the Fibonacci sequence. 1 1 2 3 5 8 13 21 34 55
  • 5. FIBONACCI SPIRAL Box Side 1 1 2 1 3 2 4 3 5 5 6 8 7 13 8 21
  • 7. On many plants, the number of petals is a Fibonacci number: Buttercups have 5 petals; lilies and iris have 3 petals; some delphiniums have 8; corn marigolds have 13 petals; some asters have 21 whereas daisies can be found with 34, 55 or even 89 petals. 13 petals: ragwort, corn marigold, cineraria, some daisies 21 petals: aster, black-eyed Susan, chicory 34 petals: plantain, pyrethrum 55, 89 petals: michaelmas daisies, the asteraceae family. Some species are very precise about the number of petals they have - e.g. buttercups, but others have petals that are very near those above, with the average being a Fibonacci number.
  • 8.  A Fibonacci word is a specific sequence of binary digits. The Fibonacci word is formed by repeated concatenation in the same way that the Fibonacci numbers are formed by repeated addition. Fibonacci based constructions are currently used to model physical systems with aperiodic order such as quasicrystals. Crystal growth techniques have been used to grow Fibonacci layered crystals and study their light scattering properties
  • 9. W5 B3 B2 8 white 13 w & b
  • 12.  www.wikipedia.org  www.youtube.com  www.worldmystreries.com  www.google.co.in