The Divine Intervention or A Mere Coincidence?!..

i am confused and i am nuts..

Somebody once told me that, the word "Intelligence" means 'Identification and Recognition of Pattern' (blessed, be that soul).. i myself do not know that whether i am intelligent yet, or not. If you are intelligent enough, you may identify/recognize the pattern in the above image at the end of this post.. Or you may end up like me..  

At first everything happens to be at random and disarranged. Then out of nowhere there emerges a pattern, a pattern that will connect all the randomness into a single unified entity. - People call this 'The Chaos Theory' (also, the Butterfly Effect - there is a thin line of connection between the flap of a Butterfly's wing to an Earth Quake that happens somewhere else around the world.)

i am so obsessed with this post, that it took me weeks to compile/complete it.

Note 1: i know that i am getting nowhere with this post, though i know this, that i have to arrive at somewhere around. Do not poke your head too much into this post, for because, i am an utter failure in simplifying things.

Note 2: I am not good at numbers (as I am not a mathematician), the more i try to sequence them, the more they get bizarre. Here i have tried my level best to simplify and sequentialize the following narration/compilation. The rest is upto you, to adjudge it. As i already said, do not poke your head too much into it.

A Little Background..

His name was Leonardo da Pisano (Leonardo of Pisa - as he was born in Pisa, Italy). Ring a bell?!.. No?!.. Let us get there the other way. We know him better by the name "Fibonacci" ('Son of Bonacci' - made his father proud, indeed). The man, who has contributed a lot to the world of Mathematics. He is the man who introduced the Decimal Number System (0,1,2,3,4,5,6,7,8,9) into Europe (till then Roman Numerals were prevalent in Europe. (As his father was a travelling merchant, he spent most of his childhood wandering through North America and the east Mediterranean lands and had his education there hopefully. His interactions with Hindu/Arab Mathematicians/Scholars gave him the impression that the Hindu/Arab Numbering System is far more superior than the European System and the world elsewhere.) He is the man who gave the Additive Rule, the Subtractive Rule, Arithmetic with Roman Numerals, the Decimal Positional System, Algorithm etc.

Above all, we know him for just one solid contribution, The FIBONACCI NUMBERS.

The Fibonacci Series as it goes, any number in the series is the sum of the two numbers prior to it.

1  1   2   3   5   8   13   21   34   55   89 . . . . 

In his book, Liber Abaci (Book of Calculations), he introduced the following problem.

"A certain man had one pair of rabbits together in a certain enclosed place, and one wishes to know how many are created from the pair in one year when it is the nature of them in a single month to bear another pair, and in the second month those born to bear also?"

That is, the number of rabbits that could be raised in a year if one began with a single pair. Fibonacci reasoned that, if the rabbits reached maturity two months after birth and produced an additional pair every month thereafter, the total population of rabbit pairs would increase monthly according to the series 1, 2, 3, 5, 8, 13, 21, 34...

Thus Fibonacci numbers were born. Born?!.. Not actually. For two good reasons.

1 - Fibonacci says his book was intended to study the 'nine Indian figures' and their arithmetic as used in various countries around and afar the Mediterranean. So, the 'rabbit problem' could probably be a mere inclusion from his eastern friends. Before Fibonacci, the sequence F(n) has been discussed explicitly by Indian Scholars (Gospaala (before 1135 AD) and Acharya Hemachandra (1150 AD - gives a detailled account on the Fibonacci Numbers, obviously not with the same name.)

2 - This happens to be the real reason why you are here, between these text blocks.

Fibonacci neither Invented the series, nor he Discovered it. Rather he ReDiscovered it, which was not too long forgotten by fellow humans (since the beginning).

You must be wondering, why such a hype for a simple one-to-one additive series, and what does this has to do with the Divine Intervention?!.. Because, the more simple it seems to be, the more mystery it holds within it.

Let us have a little dose of Mathematics here..

The relationship this sequence holds with the Golden Ratio (you will stumble upon this term more often, from now on) lies not in the actual numbers of the sequence, but in the ratio of the consecutive numbers. Let's look at the ratios of Two consecutive Fibonacci numbers:

2/1 = 2.0

3/2 = 1.5

5/3 = 1.67

8/5 = 1.6

13/8 = 1.625

21/13 = 1.615

34/21 = 1.619

55/34 = 1.618

89/55 = 1.618

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.

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As we go down the series, this number "1.618" is fixed (ofcourse rounding up to 3 decimal points) after the 13th in the series. This number, is known as the "Golden Ratio". A unique and the most irrational number (there is another number, Pi or 3.14.....).

Now let us arrive at this number Geometrically (after all, it is all about symmetry).

Consider a line such that,

If you divide the  line into two parts so that:

the longer part divided by the smaller part is also equal to the whole length divided by the longer part then you will have the Golden Ratio.

The Golden Ratio is represented by the Greek alphabet 'Phi'. (Named after the Great Greek Architect Phidias [from the school of Pythagoras, whose works immensely reflect the Golden Section] and pronounced as "Phee".)

The Golden Section (also known as Golden Ratio, Golden Mean, Golden Number, Divine Proportion, Divine Section, Golden Proportion etc..) as the number Phi, or 1.6180339..., is computed using 5's (and can not be expressed by any other means or formula except this one), as follows:

5 ^ .5 * .5 + .5 = Phi

([square root of 5 multiplied by half] + half) or

The value of Phi, 1·6180339887... goes on infinitely, just like Pi. For our purpose we are rounding it to 3 decimals. That is 1.618.

One of the special properties of the Golden Ratio is that it can be defined in terms of itself, like this:

It can be expanded into this fraction that goes on for ever (called a "continued fraction"):

The reciprocal of 1.618 is 0.618. And the reverse is also true. That is, the reciprocal of 0.618 is 1.618. No number's reciprocal's reciprocal gives the same number. ('1' is an exception ofcourse).

We know the Golden Ratio (1:1.618), better by the name 'Mean and Extreme Ratios' (Euclid 300 BC). 1.618 is referred to as 'Phi'. (There is also a small 'phi' with the value  (-)0.618[this negative small phi is related to the number of the Beast - 666, in the Bible. That is Bible Codes decoded [courtesy of various code-breakers] brothers, let us not get too much in to it)], this also belongs to the Golden Number family. This small 'phi' is nothing but the complementary (as in complex numbers) of 'Phi' (it also exhibits all the above said properties of 'Phi'.))

Now, we are arriving at the point. Why this Golden Ratio is often referred to as the Divine Proportion and what has it to do with the Divine Intervention..

Aaah.. Before that we must acquaint ourselves a little with the Golden Rectangle and the Golden Spiral. (There are also Golden Triangles, Golden Pentagrams, Golden Angle, Golden Circle, Golden Arc.. etc.. Let us stick to the basics for our purpose, for now. I will be quick with these ones)

The Golden Rectangle..

A golden rectangle is one whose side lengths are in the golden ratio, or approximately 1:1.618.

A distinctive feature of this shape is that when a square section is removed, the remainder is another golden rectangle; that is, with the same proportions as the first. Square removal can be repeated infinitely, and in each case we get another Golden Rectangle.

No other rectangle has this trait.

Construction of a Golden Rectangle..

A golden rectangle can be constructed with only straightedge (a ruler scale in Indian context) and compass by this technique:

1. Construct a simple square

2. Draw a line from the midpoint of one side of the square to an opposite corner

3. Use that line as the radius to draw an arc that defines the height of the

rectangle

4. Complete the golden rectangle

The Golden Spiral..

The Golden Spiral, sometimes called the Golden Round, is a spiral with proportions similar to the Golden Rectangle.The spiral is derived via the Golden Rectangle, a unique rectangle which has the golden ratio. When squared, it leaves a smaller rectangle behind, which has the same Golden Ratio as the previous rectangle. The squaring can continue indefinitely with the same result (as you know it already). When you connect a curve through the corners of these concentric rectangles, you have formed the golden spiral.

Back to track now..

Take a look at the following images..

Now, try to answer this..

What is common between these images?!..

All have an element of the Golden Sections in them. (the ace, the credit card, the NGC logo rectangle, the stamp are all Golden rectangles themselves. The movie posters are proportionate with Golden Section. In the Cross the ratio of the upper vertical column to the lower vertical column is 1:1.618. [and so is the ground plan of any and every orthodox Church you see])

Not only these, every single object designed and which is appealing to human eyes comply with the Golden Ratio. Your computer monitor that you are squinting at now, TV, Mobile Phones, textbook covers, automobiles, doors, furnitures, houses, buildings, machinery, equipments, instruments, music, poem, art... from the tiniest to the gigantic things that you see around now, are designed by designers in view of the Golden Proportions. (Thanks to Da Vinci, who made this cult of artists following him.)

More than 90% of the population, are known to pickup/like items which reflect the Golden Ratio. Since the Golden Ratio gives the most pleasing effect to the human eye and gives great aesthetic integrity.

So, for ages, it is known that the Golden Ratio is used to bring in aesthetic value and perfection in designing/structuring things/objects. Right from the beginning of the civilization dawn, this Golden Proportion is used invariably, through ages.

A little History here..

Euclid (300 BC) the Greek Mathematician was the first to refer to the Golden Ratio explicitly, as 'Mean and Extreme ratios (Book 6, Proposition 30 - He has written 13 books on Geometry. It was the first known book ever, available on Mathematics.).

Before that Pythagoras (500 BC) used the Golden Mean in his works, although he did not mention it in any of his works. Also the Pythagorean followers used the Golden Mean in architecture.

The Golden Mean is referred to, in the Vedas - The ancient Sanskrit sacred books of the Hindus.

The Egyptians are known to have good awareness on the Golden Number. There has been much debate in whether the Golden Ratio is used in the construction of the Pyramids.

Though the Golden ratio is evident in the ancient Egyptian Pyramids. (this might take another Post to ponder over the Great Pyramids and the Golden ratio)

The Mayans also are known to have a considerable exposure to the Golden Ratio (remember the 2012 havoc predicted by the Mayan calendar?! - it follows the Phi proportion calculations) , and also the Chinese.

Through ages humans are aware that the Golden ratio brings in harmony, perfection and aesthetic value. Hence they made good use of it in their creations. Mostly in the area of Art and Architecture.

Golden Proportion in Architecture..

The Great Pyramid of Giza (2550 BC)

Golden Ratio in the Great Pyramid

Egyptian Glyph

The Great Wall of China (450 BC- 1550 AD)

Height: 8.6m avg. Width: 5.3m (the Golden Ratio) Avg. Length: 6260 km

Parthenon, Goddess Athena Temple, Greece,(477-438 BC) -(Pythagorean Design)

Golden ratio evident throughout floor plan of Parthenon. Length is (Sq.root 5) times width.

Amphitheatre, Epidaurus, Greece (400 BC)

Golden Ratio evident in the Seating Arrangement.

Mayan Architecture, Copan, Honduras (430 -600 AD)

Mayan Pyramid

The Brahadeeswara Temple, India (1010 AD)

Chartres Cathedral, France (1194-1260 AD)

Rose Window, Chartres Cathedral

Qutb Minar, India (1288 AD)

Height: 72.55m, Base Dia.:14.4m

Victory Tower, India (1300 AD)

Taj Mahal, India (1631-1653 AD)

Workers: 22000, 1000 elephants, 22 Years, White Marble

Golden Ratios in Taj

Even The Modern Architecture..

Le Corbusier's Design

The UN Building, Hague

(A block of each 10 floors form a Golden Rectangle)

The Pentagon

The California Polytechnic Engineering Complex, The Petronas Towers, Burj Khalifa.. and so on..

and on..

The CN Tower, Canada (The Tallest stand alone structure in the Western Hemisphere)

The ratio from Top to the Observation Deck and the Observation Deck to the Bottom is 1:1.618. (553.33/342 meters)

Golden Ratio in Art..

Da Vinci's

Monalisa

Her face is a Golden Rectangle and also the whole portrait.

The Last Supper

Madonna of the Rocks

The Vitruvian Man

And more..

Michel Angelo

The Holy family

David

Creation of Adam

Raphel's Crucifiction

Seurat's Bathers

Seurat's Circus

Some Modern Art..

Picasso's Cubism is closely related to the 1:1.618 ratio.

Renaissance and Modern art adopted this concept without any conflicts.

Golden ratio in Music..

The Phi ratio incorporated in musical notes produces eternal music.

Evidence suggests that classical music composed by Mozart, Beethoven, and Bach embraces phi.

A violin is always made out of Golden Proportions.

(Thats why the sound from a violin is always soul healing and take to farther realms)

There are more, worth mentioning in the field of Accoustics in relation with the Phi statics including the Raga System of the Karnatic/Hindustani Music. (I do not want to get into much details here, if you want to know more there much information available on the net.. Its better to start from google..)

in Poems..

i do not know about the structure of English poems..

The traditional hymns of Sanskrit and the so called "Marabukkavithaigal"(traditional poetries) of Tamil right from the ages and the laws governing their structure has a close relationship with the 1:1.618 ratio. (the numbering of verses, sentences, word positioning, the style of beginning and giving an endnote to the hymn etc etc..)

So far, what we have witnessed is the Human Intervention..

it is time, to peek into the Divine Intervention..

Man has known the Golden Proportion as a value that gives aesthetically pleasing effect and perfect proportions to any object when applied to it (redundancy - will try to reduce them. Mea Culpa!). As he continued to observe through his environment, there are certain many things that exhibited identicalness with this Golden Mean that mystified him, and so are we.

For a start (believe me, just now we have started our journey), some occurrences of the Golden Number through our spiritual history. (citations needed on the below examples, since i am not sure of their validity)

In the Bible..

God commands Moses to build the Ark of the Covenant, in which to hold His Covenant with the Israelites, the Ten Commandments, saying,

"Have them make a chest of acacia wood - two and a half cubits long, a cubit and a half wide, and a cubit and a half high." - Exodus 25:10

(this is a replica, obviously..)

The ratio of 2.5 to 1.5 is 1.666..., which is as close to phi (1.618 ...) as you can come with such simple numbers and is certainly not visibly different to the eye. The Ark of the Covenant is thus constructed using the Golden Section. This ratio is also the same as 5 to 3, numbers from the Fibonacci series.

In Exodus, again we find, the altar that God commands Moses to build is based on a variation of the same 5 by 3 theme:

"Build an altar of acacia wood, three cubits high; it is to be square, five cubits long and five cubits wide." - Exodus 27:1-2

Again, God commands Noah to build an ark saying,

"And this is the fashion which thou shalt make it of: The length of the ark shall be three hundred cubits, the breadth of it fifty cubits, and the height of it thirty cubits." - Genesis 6:15

Thus the end of the ark, at 50 by 30 cubits, is also in the ratio of 5 to 3, or 1.666..., again a close approximation of Phi not visibly different to the naked eye. Noah's ark was built in the same proportion as ten arks of the covenant placed side by side.

(A similar Vessel with the similar proportions matching with Phi (although computer generated) is used in the movie 2012.)

It is believed that the Kaabaa, Holy city of Mecca is situated at the Golden Ratio point of the Earth.

(Though I have a doubt here.. Since Earth is Spherical (almost spherical) any point on the same longitude intersecting with the Phi point of the latitude could be the Golden Ratio point of the Earth, or the other way the point on the same latitude and intersected by the longitudinal Phi point. Then every point on the Earth will become its Golden Ratio point, since a sphere has no centre on its circumference.)

Also there is a mention that, the mention of the Holy city of Mecca in the Quran (which happens only once in the Quran), has a substantial relationship to the Golden Number.

The largest isosceles triangle of the sriyantra design used in ancient India, described in the Atharvana Veda (circa 1200-900 BC) is one of the face triangles of the Great Pyramid in miniature, showing almost exactly the same relationship between the Pyramid and the Golden Ratio as in its larger counterpart. (Since there is no existing works [literary] of the ancient Egyptians referring to the construction details of the Great Pyramids or any journals on how they were built - there is a popular ongoing debate between scholars, that the Egyptians could have borrowed the idea of the Pyramids from the Vedas, since Rig Veda and Atharvana Veda outdate the Pyramids. Also the design of a King's Tomb mentioned in the Atharvana Veda closely matches with the design of the Pyramids [since Pyramids are the Tombs of the Pharoahs.])

The Bakshali Manuscript (date unknown) which is written in early Sharada Script (a modified version of Sanskrit), mentions the 'Rule of Three' (traisika) was applied to solve the problems for the business community, travelers and goldsmiths. This "Rule of Three" was known to the Europeans in the thirteenth century as the famous "Golden Mean". (Now this Rule of Three is used extensively to solve business related problems [a classic example problem from the Script -

A certain King asked his goldsmith to distribute eleven gold coins among his three daughters in the ratio of a half,a quarter and one sixth. The goldsmith added one more gold coin from his own pocket and out of total twelve gold coins,he took the ratio of one half which was six and gave it to the first daughter. The second daughter got a quarter of twelve which was three gold coins. Finally, the third daughter received one sixth of twelve which amounts to two gold coins. The goldsmith took back his own gold coin but satisfied everyone.] - this Bakshali Script needs a different post, but later.)

Vedic mathematics (from Jain Sutras) denies the chaotic pattern of the infinitum of the decimals of Phi, and suggests a recursion of 24 digits (and that has been proved true, recently). Actually this 24 is derived from 12 complementary pairs of 9's. i.e.

1 1 2 3 5 8 4 3 7 1 8 9

8 8 7 6 4 1 5 6 2 8 1 9

(for more details, pls do Google). And 12 times 9 gives 108. Which is considered a sacred number by both Hindus and Christians (108 rosary beads). Hindus chant their mantra of Enlightenment - The Gayatri Mantra (one of the oldest known Divine Hymns), 108 times, and in addition, The numerology of the Gayatri Mantra is 108!

There are also mentions of the Golden Section in various Suktas of the Rig Veda (the ancient book ever known, that is available now!)

Both in the Bible and the sacred texts of Hinduism, it was mentioned that, in the beginning there was the word. Hindus called it the "Anahata Nada" (the sound that which is unmade). The "OM" also known as AUM. This sound has four elements - A, U, M and the silent element which starts and ends with it. These four elements when spelt in harmony, the resonance of the sound wave exactly matches with the Phi ratio.

Now witness the Golden Proportion in Nature..

The Plant Kingdom..

Phyllotaxy..

Phyllotaxy refers to the arrangements of leaves in a Plant's shoot system. On close observation, it shall be seen that the leaves are arranged in such a manner that each leaf gets the maximum exposure sunlight, no matter where it is placed in the plant body (whether at the top or at the bottom).

Many plants show the Fibonacci numbers in the arrangements of the leaves around their stems. If we look down on a plant, the leaves are often arranged so that leaves above do not hide leaves below (you shall witness a spiral at times). This means that each gets a good share of the sunlight and catches the most rain to channel down to the roots as it runs down the leaf to the stem.

Cactus's spines often show the same spirals.

One estimate is that 90 percent of all plants exhibit this pattern of leaves involving the Fibonacci numbers (This also implies that not all the plants of the Plant Kingdom exhibits the Phi Pattern).

In Flowers..

SeedHead Arrangement..

Seed arrangements in most of the flowers shows remarkable pattern matching with the Phi value.

For example let us consider the Sunflower Family (Asteraecea).

In the center of the Sunflower, there are two sets of logarithmic spirals, one set turning clockwise, and the other counterclockwise. The number of spirals in the two sets is different and tends to be Fibonacci numbers. Sunflowers of average size usually have 34 and 55 spirals (successive Fibonacci Numbers), but giant sunflowers 89 and 144 (Successive Fibonacci Numbers again). The reason is again efficiency, this arrangement of seeds forms an optimal packing of the seeds, no matter how large the seed head, they are uniformly packed at every stage, all the seeds being the same size, no crowding in the center and not too sparse at the edges.

The seedhead spirals need to start from a particular angle so as to attain maximum optimum packing. And here comes the Golden Angle.

360 degrees / Phi squared gives 137.5 Degrees, and this phenomenon is seen in Petal formation, Sepal formation, arrangement of leaves, buds, petals, sepals of any plant in the world.

This pattern is also observed in Daisy flowers, Pine cones, Pine apples etc etc..

Number of Petals	Flower
3 petals (or 2 sets of 3)	lily (usually in 2 sets of 3 for 6 total), iris
5 petals	buttercup, wild rose, larkspur, columbine (aquilegia), vinca
8 petals	delphinium, coreopsis
13 petals	ragwort, marigold, cineraria
21 petals	aster, black-eyed susan, chicory
34 petals	plantain, daisy, pyrethrum
55 petals	daisy, the asteraceae family
89 petals	daisy, the asteraceae family

There are exceptions to this list. Most fall into two categories - a doubling of the number of petals, and/or a version of the Fibonacci Series called the Lucas Series (2, 1, 3, 4, 7, 11, 18, 29, 47, 76, etc. ). Mutations and variations from species to species also account for exceptions but when the number of petals are averaged, the number will usually be a Fibonacci or Lucas Number.

A Daisy with 21 Petals

Pine Cone

8 and 13 - again Fibonacci Numbers.

Pine Apple

Some more illustrations..

It should be noted that the root, shoot, leaves, flowers, florets, pistils, seeds etc.. of any plant follow the Phi pattern (almost all the plants - also means that, not all).

It should also be noted that not all the plants follow the Phi pattern (redundancy again), there are certain flowers which follow the Lucas Numbers in their Petal numbering. (Lucas Numbers?! - It is the same as the Fibonacci, it is just that you have to start the sequence with 2 and 1 as the beginning numbers instead of 0 and 1). And there are also exceptions.

In the Animal Kingdom..

Let me not get in to too much details in this, because we still have got a lot to cover..

Just one phenomenon, to be mentioned here is The Nautilus..

The shell of a Nautilus shows exact match with the Golden ratio and the Golden Spiral (and also not to forget the Golden Angle part). And so is for all the shelled creatures.

Every year as the Nautilus grows it builds and shifts to a new chamber (its new house) and seals the previous chamber. These chambers are exactly in the Fibonacci Ratio, that is each successive chamber is 1.618 times that of the previous chamber. And yes, the Nautilus also grows with respect to the Phi ratio.

Did I mention that, the growth of all plants and animals (including Humans) follow the Phi pattern?!.. It is indeed, a big Yes!

Not only the growth and formation of living things, but also of abstract non-living entities. For example take the case of Snow Flakes, each Snow Flakes are formed exactly in accordance to the Phi proportion. (Imagining the amount of Snow Flakes that are formed on a normal winter hour...)

(Also look at the structure of the Snow Flake - it is as accurate as it is. The formation is remarkable with perfect symmetrical proportions.)

Back to the shell family..

Just an extended imagination on the Conch saga (the ancients knew it!..)..

A few illustrations in the Animal Kingdom..

A Spider web's prey catchment area is a carefully designed Golden Spiral.

The tail of a Sea Horse..

Mostly the limbs, body cavity of all the animals are proportionate with the ratio 1:1.618. Parts like horns, tusks, teeth, claws.. exhibit the Golden Spiral Pattern.

And now, to The Master Creation..

The Divine Proportion and the Human Body..

The entire human body is based on the Divine Proportion - right from the shape/size to the spacing of our teeth!

Do you know that, the length from your toe to your belly button is exactly 1.618 times the length from your belly button to your head top?!..

Another interesting relationship of golden section to the design of the human body is that there are:

5 appendages to the torso, in the arms, leg and head.

5 appendages on each of these, in the fingers and toes and 5 openings on the face.

5 senses in sight, sound, touch, taste and smell.

As we already know, phi can only be represented in terms of 5.

The whole human body is constructed in accordance with the Golden Proportion.

Look at your own hand,

You have ...

2 hands each of which has ..

5 fingers, each of which has ..

3 parts separated by ..

2 knuckles.

Is this just a coincidence or not?????

(This is actually a popular internet joke, but now it is getting a bit serious..)

Facial Proportions..

A human face which is most appealing is said to comply with the Golden Ratio. All the pretty faces in this world more or less comes close with Golden sections.

Pleasing faces (have more or less) approximated Phi ratios in them.

Facial beauty in an elegant manner is achieved by assembling several decagonal matrixes formed of golden-ratio sections (Thanks to aesthetician plastic surgeon Dr.Steven Markout and his 25 year research.).

Even the eyes, ears, nostrils and teeth also bear the Golden Ratio mark.

This spiral structure of the cochlea enhances better hearing.

Golden Ratio in Heart and Lungs..

The heart rhythm follows the golden ratio

When a man is at peace and calm, his Heart ECG coincides with the divine proportion. As long as the Divine Proportion within the Heart Beat is maintained, so long the man remains healthy.

A study carried out, by a team of doctors and physicists revealed the existence of the golden ratio in the structure of the lung. One feature of the network of the bronchi that constitutes the lung is that it is asymmetric. For example, the windpipe divides into two main bronchi, one long (the left) and the other short (the right). This asymmetrical division continues into the subsequent subdivisions of the bronchi. It was determined that in all these divisions the proportion of the short bronchus to the long was always 1/1.618.

So, we can say that the Golden ratio is evident in the Human Architecture. (Not altogether - there is always an element of Mutation, disproportion and deviations in beings..)

Why everything seems to follow a pattern.. a hidden symmetry..

Let us get a little deeper..

Golden Proportion in the Micro World..

Study on Viruses has unveiled some interesting phenomenon..

Before that, a little theory..

Geometrical shapes are by no means limited to triangles, squares, pentagons or hexagons. These shapes can also come together in various ways and produce new three-dimensional geometrical shapes (Platonic Solids). The cube and the pyramid are the first examples that can be cited. In addition to these, however, there are also such three-dimensional shapes as the tetrahedron (with regular four faces), octahedron, dodecahedron and icosahedron that we may never encounter in our daily lives and whose names we may never even have heard of. The dodecahedron consists of 12 pentagonal faces, and the icosahedron of 20 triangles. Scientists have discovered that these shapes can all mathematically turn into one another, and that this transformation takes place with ratios linked to the Golden Ratio.

Dodecahedron

Icosahedron

Three-dimensional forms that contain the golden ratio are very widespread in micro-organisms. Many viruses have an icosahedron shape. The best known of these is the Adeno virus. The protein sheath of the Adeno virus consists of 252 protein subunits, all regularly set out. The 12 subunits in the corners of the icosahedron are in the shape of pentagonal prisms (Golden Ratio). Rod-like structures protrude from these corners. The first virus to be known to conform to this was the polio virus. The Rhino 14 virus has the same shape as the polio virus.

The design of these viruses could be explained in terms of a generalization of icosahedral symmetry that allows identical units to be related to each other in a quasi-equivalent way with a small measure of internal flexibility.

From the most commonest Tobacco Mosaic Virus to the Most complex HIV, all follow the Phi pattern in their structures.

Marine Micro-Organisms..

The dodecahedron and icosahedron also appear in the silica skeletons of radiolarians, single-celled marine organisms.

Structures based on these two geometric shapes, like the regular dodecahedron with feet-like structures protruding from each corner, and the various formations on their surfaces make up the varying beautiful bodies of the radiolarians. Among the micro-organisms known as plankton, the bodies of globigerinae, planorbis, vortex, terebra, turitellae and trochida are all constructed on spirals. These organisms, are less than mm in size.

Why is it that virus have shapes based on the Golden Ratio, shapes that it is hard for us even to visualise in our minds?

More deeper..

The molecule in which all the physical features of living things are stored, too, has been created in a form based on the golden ratio. The DNA molecule, the very program of life, is based on the golden ratio. DNA consists of two intertwined perpendicular helixes. The length of the curve in each of these helixes is 34 angstroms and the width 21 angstroms. (1 angstrom is one hundred millionth of a cm.) 21 and 34 are two consecutive Fibonacci numbers.

Each DNA strand contains periodically recurring phosphate and sugar subunits. There are 10 such phosphate-sugar groups in each full 360 degree revolution of the DNA spiral. Thus the amount of rotation of each of these subunits around the DNA cylinder is 360 degrees divided by 10, or 36 degrees. This is exactly half the pentagon rotation, showing a close relation of the DNA sub-unit to the Golden Mean. And the cross section of the DNA helix would reveal a dodecahedron.

Even more Deeper..

The Golden Ratio in the Creations of Nature Arises in the Architecture of Atoms and Ions.

Now let us take the case of the Hydrogen atom (we take the Hydrogen atom here, because 1. Its the most abundant element in the Universe, 2. Its the most simplest atom with a single Electron in the Shell, 3. Has the highest rate of diffusion, 4. Exhibits Isotropism/Isotopism...)

The Hydrogen atom's Bohr radius when divided at the point of Electrical neutrality, gives two exact Golden Sections.
For further reading please visit (this is for tech-geeks)
http://arxiv.org/ftp/physics/papers/0509/0509207.pdf
http://www.mjcce.org.mk/PDF/25_1_132.pdf

Inter-atomic Distances, Ionic Radii, Additivity of Atomic and Ionic Radii in Chemical Bonds, Distances on Covalent Radii, Ionic Radii in Water and Distances of Oxygen and Hydrogen of Water from Ion/water Boundaries, Molar Volumes in Solids, Partial Molal and Hydrated Ionic Volumes of Alkali Halides on Covalent and Ionic Radii, Carbon to Carbon Bond Lengths and their Linear Dependence on Bond Energies.. are all inter-related via the Golden Ratio.

http://www.jh-inst.cas.cz/~rheyrovs/ (for further reading)

Even in the Periodic Table - the positioning of elements follows the Phi pattern.

Thats not all over yet..

in the Quantum World..

A simple phenomenon to observe here..

When a ray of light is held over two contiguous layers of glass, three things occur:

A part of the beam gets absorbed by the glass.

A part of the beam gets through the glass and is refracted.

A part of the beam gets reflected from the glass.

The multiple reflections that takes inside the glass (in the process of absorption, refraction and reflection), confirms solidly with the Phi proportion.

That is, the number of paths taken by the ray inside the glass before it emerges again depends on the number of reflections it is subjected to (remember Fraunhoffer's, Foucault's lines folks?!..). In conclusion, when we determine the number of rays that re-emerge, we find that they are compatible with the Fibonacci numbers.(I lost that image somehow. Will upload it as soon as I get it)

In the spectrum of light and the electromagnetic spectrum, if you see the bandwidth, wavelength and the frequency distribution of the electromagnetic waves closely.. You shall get a dose of Phi there also.

An international team, led by scientists from Oxford University, report in a recent article in Science how they spotted the symmetry, termed E8 (a simple Lie Group member of Dimension 248 - for more on it, do Google pls) , in the patterns formed by the magnetic spins in crystals of the material cobalt niobate, cooled to near absolute zero and subject to a powerful applied magnetic field.

One of the researchers (Dr.Radu Coldea) quoted that 'The tension comes from the interaction between spins causing them to magnetically resonate. We found a series of resonant modes. Close to the critical field the two lowest resonant frequencies approached closely the golden ratio 1.618…, a characteristic signature of the predicted E8 symmetry.'...'It reflects a beautiful property of the quantum system -- a hidden symmetry. Actually quite a special one called E8 by mathematicians, and this is its first observation in a material'.

He is convinced that this is no coincidence and it reflects a subtle form of order present in the quantum system.

The resonant states seen experimentally in cobalt niobate may be our first glimpse of complex symmetries that can occur in the quantum world. The results suggest that similar 'hidden' symmetries may also govern the physics of other materials near quantum critical points where electrons organize themselves according to quantum rules for strong interactions.

The research was supported by EPSRC (Engineering and Physical Sciences Research Council - A British Research Council, that provides Government funding.)

The team included Dr Radu Coldea, Dr Elisa Wheeler and Dr D Prabhakaran from Oxford University's Department of Physics, as well as researchers from Helmholtz Zentrum Berlin, ISIS Rutherford Laboratory, and Bristol University.

Golden Ratio in Fractals..

In "Quantum Physics" any basic model can be built by using THREE operators, namely The Creation Operator(Brahma), The Number Operator (Vishnu) and The Annihilation Operator (Shiva).. Similarly, the basic constituents of the particles such as proton, neutron, mesons etc., consists of the THREE fundamental particles "QUARK". (this again follows the Rule of Three [Bakshali Script] - as I told you already, a different detailed post is needed on this manuscript.)

Have you ever wondered why a Hurricane resembles a Golden Spiral?!..

There is more to wonder. It is not only the simplest/singlest of the elements that exhibit the Phi property. There are also elements that are huge/enormous/gigantic and out of our imagination level.

A few to discuss here..

Given that the Earth takes one year to orbit the Sun, the time that it takes Venus to orbit the Sun is 1.618 to the -1 years. The time it takes Mercury to orbit the Sun is approximately 1.618 to the -3 years. Mars is roughly 1.618 years, the asteroid belt is roughly 1.618 to the 3rd years (Oh yes, we have got an Asteroid belt in between Mars and Jupiter, and there is a dwarf planet called Ceres in that asteroid belt), Jupiter is approximately 1.618 to the 5th years, so on and so forth.. Uranus holds a 99% accuracy with the Phi proportion (note that Pluto does not fit).

The orbital lengths of the Planet alignment also matches roughly with the Phi ratio (the point more or less is to be noted).

Golden Ratio is evident in Saturn's rings, both outer and inner rings.

The spin of Stars and their energy levels have astounding connection with the Phi proportion.

The characteristic of Black body is determined by the Phi ratio. Its spin and Gravity is governed by the Phi factor.

Cosmic waves follow the Phi pattern.

The displacement of particles through the Universe (as it is expanding, either by the Big Bang or the Pulsating or the String Theories) follows an order coherent to the Phi factor.

There are numerous visible galaxies that relay the Golden Spiral within them.

Our own MilkyWay Galaxy..

The Andromeda Galaxy

More Galaxies..

Images from the Hubble Telescope..

There are also some recent claims, that the Universe appears to have the structure of a Dodecahedron. (Considering the recent theories on the Universe being finite and not infinite. [There is also a mention of 14 existing loka's (universes) in the Vedas]. All the modern findings that we see now, it seems is already known by our ancestors])

Time Warp Zones (as in sci-fi movies), white holes, fractal Universe and much more unheard things are claimed to follow the Phi pattern. The beauty of it is, our ancestors seem to know all these things thousands of years before, with out even a single modern gadget. (I guess I may release a sequel to this post, regarding the knowledge held by our ancient ancestors!).
This Phi can be related to anything and everything.

From the tiniest quarks to the giant galaxies.

All the known theories such as the Chaos Theory, Game Theory, String Theory, Theory of Uncertainity (Heisenberg's), Relativity Theory (Einstein even mentions the possible existence of a fractal Universe), the grand Unified theory.. etc.. follows the Phi Principle.

Life and Nature closely follows the Phi Pattern. It is often referred to as the 'Hand of God' or the 'Fingerprint of God'..

Regardless of the differences, this Phi occurs both in the Spiritual World and also modern Science. It fills the gap between them (not proved yet, and there comes our Grand Unification Theory). Astrology and Astronomy though are two extremely different fields, they somehow give us the same results.

Even the Binary codes computed in your Computer right now, and the visible spectrum through which you grasp it, and the receiver in your retina all have a dose of Phi within them.

Still more things are there, that my tiny brain has eluded me from telling you.

From Scientists to Artists, Philosophers to Prophets, Masons, Physicians.. all make use of the Phi factor in their works by someway or the other.

From the Neuron of your Nerve cell to the Lightning (a lightning fork always complies with the Phi ratio) you see on a rainy day, all share the Golden Ratio in their structure.

If you still have time.. Have a glance at this video..

(This video happens to be the sole reason, for why i am typing this post. Happened to stumble upon a Company's logo, which they boasted, is designed in strict adherence to the Golden Angle,Golden arm of the Golden Pentagram blah blah.. Nearly drowned me into this Phi world.. Damn it!)

Though there are also strong schools of thought, that maintain the Phi Factor as a mere co-incidence and could not regard it as a solid proof of Order amidst of Chaos. And they too have their own reasons to defy the Phi theory with sound reasons (as I have mentioned certain anomalies within braces, and also certain proofs are approximate and not close to accuracy).

Both working hard to get to know the truth behind the Process of Creation and Evolution (let us not forget Darwin here!).

Religion and Science both talks of the Divine Proportion in unison (though from different angles). Either the way, who ever gets there first, in decoding the mystery behind the creation and relation with the Phi Factor, we always will be previleged by getting the Grand Unification Theory)

Is there really a Hand of God that connects anything and everything through a Divine Phenomenon (let us not forget the part of Aliens [if they were allowed to exist] also).. The Divine Intervention?!..

or

Is it all nothing but just a mere co-incidence?!..

I am confused and I am nuts..

P.S: Comments.. Welcome..