"The universe consists entirely of waves of motion which spring from stillness and return to stillness".
Walter Russell
Individuality is the trade mark of any artist , engineer or architect each desire a uniqueness to there creation , a quality that separate from any other . Man naturally has this individuality his fingerprint. there are 6.5 billion people on the face of the earth and no two fingerprint are the same everything we touch and may contact with it is branded with a small expressed image reviling to all who see it , who was there .
Around 1200 AD the man name Leonardo Pisano Bigollo was a young man in his twenties, a member of an important trading family of Pisa. In his travels throughout the Middle East, he was captivated by the mathematical ideas .he returned to Pisa he published these ideas in a book on mathematics called Liber Abaci, which became a landmark in Europe. Leonardo, who has since come to be known as Fibonacci, became the most celebrated mathematician of the Middle Ages. His book was a discourse on mathematical methods in commerce, but is now remembered mainly for two contributions, one obviously important at the time and one seemingly insignificant. He discovered the sequence
1,1,2,3,5,8,13,21,34,55,89,144,233,377,610......
Each number are getting by adding last two digits together.
0+1=1
1+1=2
2+1=3
In terms of application FIBONACCI NUMBER appears in nature surprisingly often or the number of SPIRAL on a sun flower or a pineapple tends to be a Fibonacci numbers as Well . In fact there are many application of Fibonacci numbers but what I found most inspirational about them of beautiful number patterns they display .
FIBONACCI NUMBER appears on a sun flower
Let me tell you one of the magic of Fibonacci numbers
If you do the square of Fibonacci numbers you will get the numbers like that.
1, 1, 2, 3, 5, 8 , 13, 21, 34, 55 ,.............
Square of these numbers
1,1, 4, 9, 25, 64, 169, 441, 1156, 3025 ,......
If will add 1+1=2
1+4 =5
4+9= 13
9+25=34
And yes the patterns continues . ...
In fact here is another one suppose you wanna squares the numbers and adding up of fist few Fibonacci numbers let's see what we get..
1+1+4=6= 2×3 Look those
Numbers these are
1+1+4+9=15=3×5 Not Fibonacci
numbers but
1+1+4+9+25=40=5×8 Numbers
Present inside .
1+1+4+9+25+64=104=8×13
So the patterns continues amazing ....
These numbers are amazing now let's see something special application of these numbers .
1^2 +1^2 +2^2 +3^2 +5^2 +8^2= 8×13
This why ..
I will show you the picture
I will put square one by one and add them to form a rectangle and soo on
I put 1by 1 square and I will put another 1by 1 square
Together they form 1by 2 rectangle then I will put 2 by 2 square next to the 3 by 3 square and then add 5 by 5 square and then 8 by 8 square
Creating a one giant rectangle OK.
Now question is that what is the are of this rectangle.
That will be
1^2+1^2+2^2 +3^3 +5^2 +8^2 = 8×13
Amazingly we get the are of rectangle.
We will form a rectangle so on
And if divide these numbers .
8×13 13÷8= 1.625
13×21. 21÷13=1.615
21×34. 34÷21=1.619
And soo on and these ratios are closer and closer to Golden ratio
1:1.618033
The number which fascinating the everyone
FIBONACCI NUMBER present everywhere in the universe
The most famous and beautiful examples of the occurrence of the Fibonacci sequence in nature are found in a variety of trees and flowers, generally asociated with some kind of spiral structure. For instance, leaves on the stem of a flower or a branch of a tree often grow in a helical pattern, spiraling aroung the branch as new leaves form further out. Picture this: You have a branch in your hand. Focus your attention on a given leaf and start counting around and outwards. Count the leaves, and also count the number of turns around the branch, until you return to a position matching the original leaf but further along the branch. Both numbers will be Fibonacci numbers.
For example, for a pear tree there will be 8 leaves and 3 turns. Here are some more examples:
Branches of the Fibonacci Family
Tree Leaves Turns
Elm 2 1
Cherry. 3 2
Beech 3 1
Poplar 5 2
Weeping willow 8 3
Pear 8 3
Almond 13. 8
You can take a walk in a park and find this pattern on plants and bushes quite easily.
Many flowers offer a beautiful confirmation of the Fibonacci mystique. A daisy has a central core consisting of tiny florets arranged in opposing spirals. There are usually 21 going to the left and 34 to the right. A mountain aster may have 13 spirals to the left and 21 to the right. Sunflowers are the most spectacular example, typically having 55 spirals .
Soo Fibonacci numbers is everywhere in the nature
A golden rectangle can be made by the perfect square .
If you find the mid point of that square and from this point from the compass take opposite diagonal point and make an Arch you will get GOLDEN RECTANGLE
From this rectangle you will have golden ratio.
.
So here it will proceed further .
our body is design on the basis of golden ratio
Each of these part have a relation 1:1.1618
Every where
by dp
Amazing facts are more in the next part
To be continued......
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