Introduction
 Italian mathematician Leonardo
Pisano Fibonacci is known for the
Fibonacci number sequence.

Fibonacci
Numbers
Golden
Ratio
1+1
2
1+1
2
-----
1+2
3
1+2
3/2
1.5
2+3
5
2+3
5/3
1.666
3+5
8
3+5
8/5
1.6
5+8
13
5+8
13/8
1.625
8 + 13
21
8 + 13
21/13
1.615
13 + 21
34
13 + 21
34/21
1.619
21 + 34
55
21 + 34
55/34
1.618
34 + 55
89
34 + 55
89/55
1.618
55 + 89
144
55 + 89 144/89
1.618

In Real World …
 In nature
 The number of petals on a flower tend to be a Fibonacci
number.

In Real World …
 Leaves are also found in groups of Fibonacci numbers.
 Branching plants always branch off into groups of
Fibonacci numbers.

In Real World …
 In music
 The intervals between keys on a piano are Fibonacci
numbers.

In Real World …
 In human body
 The lengths of bones in a hand
are Fibonacci numbers.

Golden Ratio In Website Design
 Golden Ratio = Divine Proportion
 Discovered in ancient architectural design and is still
used today in architecture and design.
 If we want to design website for 800x600 resolution
monitor than I’ll make my width 760px.
 760 divided by 1.62 is 469.14 or 469
 Subtract the main column width from the whole width.
This will give you the second column width. 760 - 469 =
291.

In Real World …
 Face Of Monalisa
 People have shown that all
things of great beauty have a
ratio in their dimensions of a
number around 1.618

Think & Give Answer
 Suppose a newly-born pair of rabbits, one male, one female,
are put in a field.
 Rabbits are able to mate at the age of one month. So at the
end of its second month a female can produce another pair of
rabbits.
 Suppose that our rabbits never die. And the female always
produces one new pair (one male, one female) every month
from the second month on.
 How many pairs will there be in one year?