Tells u about what is Fibonacci and how it is found in nature

2. The Fibonacci numbers are
0, 1, 1, 2, 3, 5, 8, 13, ... (add
the last two to get the next)
It is called the Fibonacci
series after Leonardo
Fibonacci.

3. The "shallow diagonals" of Pascal's
triangle
sum to Fibonacci numbers.

4. The Fibonacci numbers are
studied as part of number
theory and have applications
in the counting of
mathematical objects such as
sets, permutations and
sequences and to computer
science.

5. FIBONACCI SEQUENCE IS
ALSO SEEN IN RABIT
MULTIPLICATION

7. Every human has two hands, each one of
these has five fingers, each finger has
three parts which are separated by two
knuckles. All of these fit into the sequence.
Fibonacci Fingers?

9. •The Fibonacci numbers are Nature's
numbering system.
•They appear everywhere in Nature,
from the leaf arrangement in plants, to
the pattern of the florets of a flower,
pinecone, or the scales of a pineapple.
• The Fibonacci numbers are therefore
applicable to the growth of every living
thing, including a single cell, a grain of
wheat, a hive of bees.

10. If we take the ratio of two successive
numbers in Fibonacci's series, (1, 1, 2, 3,
5, 8, 13, ..) and we divide each by the
number before it, we will find the
following series of numbers:
1/1 = 1, 2/1 = 2, 3/2 = 1·5, 5/3 =
1·666..., 8/5 = 1·6, 13/8 = 1·625, 21/13 =
1·61538... The ratio is called the golden
ratio. It has a value of approximately
1·618034 and is denoted by the Greek
letter phi.

11. Flowers often have a Fibonacci number of petals,
daisies can have 34, 55 or even as many as 89
petals!

12. Sunflower
head
displaying
florets in
spirals of
34 and 55
around the
outside
The beautiful spirals of the sun flower
head reveal the astonishing double
connection with the Fibonacci series

13. One-petalled
Two-petalled flowers

14. Three petals
Five petals - there are
hundreds of species,
both wild and
cultivated, with five
petals.

15. Eight-petalled flowers are not
so common as five-petalled,
but there are quite a number
of well-known species with
eight petals.

16. Thirteen, ...
Twenty-one
34 petals

20. The florets within this cluster are
arranged spirally. Typically each floret
is oriented toward the next by
approximately the golden angle,
producing a pattern of interconnecting
spirals where the number of left
spirals and the number of right spirals
are successive Fibonacci numbers.

26. This poppy seed head has 13 ridges on top.
Fibonacci numbers can also be seen
in the arrangement of seeds on flower heads.

27. some plants
branch in such
a way that they
always have a
Fibonacci
number of
growing points.

28. many plants show
the Fibonacci
numbers in the
arrangements of
the leaves around
their stems.
FIBONACCI SEQUENCE IN PLANTS

29. Pine cones show the Fibonacci Spirals

31. The scales are
spirally
arranged in
fibonacci
number ratios.

33. Here is a curve which crosses the X-
axis at the Fibonacci numbers

34. FIBONACCI SEQUENCE IN VEGETABLES

40. The adjacent picture
shows a design
featuring the
pentagons and
hexagons used in the
Mosque. which were
developed out of the
connections between
the Fibonacci
series,and the Golden
Proportion.
The Fibonacci numbers play a significant
role in nature and in art and architecture.

41. The sequence has been used in the
design of a building,

45. The series can be extended and the numbers can be found directly by applying this
formula-Fn-2=Fn-Fn-1