The fibonacci sequence and golden ratio/ In art, nature , animals and humans all explained but is this a mere Coincidence??
Who was Fibonacci
The "greatest European mathematician of the middle ages", his full name was Leonardo of Pisa, or Leonardo Pisano in Italian since he was born in Pisa,Italy. Born in 1175 and commonly assumed to die in 1240. Fibonacci says his book Liber Abaci that he had studied the "nine Indian figures" and their arithmetic as used in various countries around the Mediterranean and wrote about them to make their use more commonly understood in his native Italy. So he probably merely included the "rabbit problem"(see below) from one of his contacts and did not invent either the problem or the series of numbers which now bear his name.
Pisa was an important commercial town in its day and had links with many Mediterranean ports. Leonardo's father, Guglielmo Bonacci, was a kind of customs officer in the present-day Algerian town of Béjaïa, formerly known as Bugia or Bougie, where wax candles were exported to France. They are still called "bougies" in French and Dutch.
By the way, don't confuse Leonardo of Pisa with Leonardo da Vinci! Vinci was just a few miles from Pisa on the way to Florence, but Leonardo da Vinci was born in Vinci in 1452, about 200 years after the death of Leonardo of Pisa.
What is the fibonacci sequence?
The Fibonacci sequence is a series of numbers where a number is found by adding up the two numbers before it. Starting with 0 and 1, the sequence goes 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 , 89 , 144 , 233 and so forth. This numbering pattern reveals itself in various ways throughout all of nature, as we shall see further in this topic.
There is a special relationship between the Golden Ratio(phi) and Fibonacci Numbers. When the smaller number of this pattern is divided into the larger number next to it, the ratio will be approximately 1.618(phi) if the larger one near to it divides the smaller number, the ratio is very close to 0.618 (=1/ phi).
When we take any two successive (one after the other) Fibonacci Numbers, their ratio is very close to the Golden Ratio. The higher u go in numbers, the closer the numbers get to the golden ratio (phi)
beauty of these numbers or ratio
Why did Greek sculptors, and others in ancient Greece and Egypt often use this ratio in designing many of their works of art? It produces what is called a Golden Rectangle. If the short side of the rectangle is 1, the long side will be 1.618. This rectangular shape was close to the pattern used in the designing of the Parthenon of Greece and for many of their numerous pictures, vases, doorways, windowns, statues, etc., and even for certain features of the Great Pyramid of Egypt. The United Nations building is a golden rectangle. Many of the things you use are patterned after the golden rectangle(credit cards, playing cards, postcards, light switch plates, writing pads)
Artists such as Leonardo da Vinci, Van Gogh, Vermeer, Sargent, Monet, Whistler, Renoir, and others employed the golden proportion in many of their works. Why the golden proportion? Art forms can be either of static or dynamic symmetry. In static symmetry the lines have definite measurements whereas in dynamic symmetry it is the proportioning of the areas that is given emphasis. It implies "growth, power, movement. It gives animation and life to an artist's work . Rather than the effect of stillness and quiet". This is the appeal of the golden proportion.
Another area of great interest is the occurrence of Fibonacci numbers in the spiral arrangement of leaves around a plant's stem (called phyllotaxis). This spiral pattern is observed by viewing the stem from directly above, and noting the arc of the stem form one leaf base to the next, and the fraction of the stem circumference which is inscribed. In each case the numbers are Fibonacci numbers. Now is this just coïncidence because this pattern assures that each leaf will receive its maximum exposure to sunlight and air without shading or crowding the other leaves.
Fibonacci's Rabbits
Fibonacci first noted the sequence when pondering a mathematical problem about rabbit breeding. Beginning with a male and female rabbit, how many pairs of rabbits could be born in a year? The problem assumes the following conditions:
- Begin with one male rabbit and female rabbit that have just been born.
- Rabbits reach sexual maturity after one month.
- The gestation period of a rabbit is one month.
- After reaching sexual maturity, female rabbits give birth every month.
- A female rabbit gives birth to one male rabbit and one female rabbit.
- Rabbits do not die.
After one month, the first pair is not yet at sexual maturity and can't mate. At two months, the rabbits have mated but not yet given birth, resulting in only one pair of rabbits. After three months, the first pair will give birth to another pair, resulting in two pairs. At the fourth month mark, the original pair gives birth again, and the second pair mates but does not yet give birth, leaving the total at three pair. This continues until a year has passed, in which there will be 233 pairs of rabbits.
DNA
DNA plays a crucial role in all living organisms because it is the key molecule responsible for storage and self-replication of genetic information. DNA can form a wide range of double helical structures and the most common form is B-DNA (Crick and Watson) The 'pitch' (one full 360 ° rotation of the helix) is just 34 angstroms, whilst the diameter of the B-DNA helix is variously given as 20 link or 21 angstroms. So the geometry of the most common DNA molecule might be seen to reflect the divine proportion: 34/21 = 1.6190.
X-ray crystallography has been used to examine the structure of the DNA molecule. A detailed geometric analysis (axial view) reveals five sets of concentric double pentagons. Each double pentagon can be seen as a pair of pentagons offset from each other by 36°, creating a decagon. A decagon pattern is clearly seen in the axial view of ideal B-DNA. So axial analysis of DNA reveals 10 concentric pentagons. Others have constructed a helix from 10 regular pentagons orientated about a decagon.
Why is the pentagon so important to DNA? Consider the double pentagon (decagon). If the base of the pentagon is 1, then the span (diagonal) of the pentagon is Φ. And we know that Φ has the unique self-replication property. Some claim that DNA uses this fundamental self-replication property.
Animals and golden ratio
There are many examples of the Golden Section or Divine Proportion in nature. Below are just a few:
The eye, fins and tail all fall at golden sections of the length of a dolphin’s body. The dimensions of the dorsal fin are golden sections (yellow and green). The thickness of the dolphin’s tail section corresponds to same golden section of the line from head to tail.
The eye-like markings of this moth fall at golden sections of the lines that mark its width and length.
The spiral growth of sea shells provide a simple, but beautiful, example.
Every key body feature of the angel fish falls at golden sections of its width and length. The nose, tail section, and centers of the fins of the angel fish fall at first (blue) golden sections. The second golden section (yellow) defines the indents on the dorsal and tail finds as well as the top of the body. The green section defines the marking around the eye and the magenta section defines the eye.
The eyes, beak, wing and key body markings of the penguin all fall at golden sections of its height.
All the key facial features of the tiger fall at golden sections of the lines defining the length and width of its face.
The body sections of an ant are defined by the golden sections of its length. Its leg sections are also golden sections of its length.
Humans and the golden ratio
We can find the golden ratio in the human body allmost everywhere , from our faces to our arms to proportions of our body with each other, in our hands even in the euturis of the female.
Some more examples
Question
you have 2 parents, they each have 2 parents, so that's 4 grand-parents you have.
They also had 2 parents each making 8 great-grand-parents in total.
Therefore you have 16 great-great-grand-parents and so on ...
So the farther you go back in your family three the more people there are.
It shows that the farther back in time we go , the more people there must have been.
So it is logical to say that the population of the world gets smaller and smaller as time goes by??
Now seeing that this mathematical numbers or ratio is seen in nature, fruit and vegetables, animals and humans to an extend we have had to search for century's to find, it is hard to believe this is all to coïncidental to have occured by chance. Even DNA the source code of life it is found in. Who originally created this mathematical resolvement? is there something we human beings are missing or haven't found yet. This subject sure in intriguing. What do you think??
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