Introduction
I choose to explore Fibonacci’s number to learn more about the symmetry in nature. I was
curious about the reason that plants and animal grow certain ways. Also, I was hoping to explore
the reasoning of the shapes in plants and the seed shape in plants. I had always seen the poster in
my math class room showing some of the objects in nature that deal with Fibonacci’s number. I
wanted to learn more about the number to fulfill my curiosity for the subject and learn more
about nature.
Fibonacci’s Number
The
Fibonacci numbers
or
Fibonacci sequence
are the numbers in the
following integer
sequence
By definition, the first two numbers in the Fibonacci sequence are either 1 and 1, or 0 and 1,
depending on the chosen starting point of the sequence, and each subsequent number is the
sum of the previous two.
The sequence, in which
each number is the sum of the two preceding numbers
is known
as the
Fibonacci series
The
Fibonacci sequence,
generated by the rule f1 = f2 = 1 , fn+1 = fn + fn-1
In
mathematical terms, the sequence
F
n
of Fibonacci numbers is defined by the recurrence
relation
with seed values
or
1 |
P a g e

List of Fibonacci’s Number
The first 21 Fibonacci numbers
F
n
for
n
= 0, 1, 2, ..., 20 are:
F
0
F
1
F
2
F
3
F
4
F
5
F
6
F
7
F
8
F
9
F
10
F
11
F
12
F
13
F
14
F
15
F
16
F
17
F
18
F
19
F
20
0
1
1
2
3
5
8
13
21
34
55
89
144
233
377
610
987
1597
258
4
4181
676
5
The sequence can also be extended to negative index
n
using the re-arranged recurrence
relation
which yields the sequence of "negafibonacci" numbers
[18]
satisfying
Thus the bidirectional sequence is
F
−8
F
−7
F
−6
F
−5
F
−4
F
−3
F
−2
F
−1
F
0
F
1
F
2
F
3
F
4
F
5
F
6
F
7
F
8
−21
13
−8
5
−3
2
−1
1
0
1
1
2
3
5
8
13
21
2 |
P a g e

Fibonacci’s Number in Nature
Fibonacci sequences appear in biological settings, in two
consecutive Fibonacci numbers, such as branching in trees,
arrangement of leaves on a stem, the fruitlets of a pineapple,
the
flowering of artichoke, an uncurling fern and the arrangement of
a pine cone, and the family tree of honeybees.
The Fibonacci numbers are Nature's numbering system
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, and even all of mankind.

#### You've reached the end of your free preview.

Want to read all 10 pages?

- Winter '16
- Gray
- Plants, Fibonacci number