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