Golden Ratio a miracle of Kaaba, Makkah (Mecca) and Quran: A Mathematical Proof

(One of the Miracles of Noble Quran)

1.618..(or its inverse 0.618..):

Number of Golden Ratio is a mystery of Kaaba and an evidence of

God’s infinite truth within the holy Quran. The golden ratio, also known

as the divine proportion, golden mean, phi constant or golden section,

is a ratio of two numbers (in distance, weight, proportion, etc), which

is usually encountered when taking distances in geometric figures and

biological systems. It is an instrument of measurement and growth

efficiency.

It is evident in the universe as well as our own bodies.

Unbelievably, the closer a ratio to this number in an object or a

system of objects, the more beautiful it is manifested in the human eye.

You will see scientific proofs of unbelievable mysteries that have

remained hidden in the Holy City of Makkah for thousand of years with

your own eyes. Makkah is willed as direction of kowtow, convention place

for billions of Muslims and as the holy center of Islam. Those Muslims,

who can afford, are prescribed to arrive and go on a journey through

Kaaba, Muzdalifa and Arafat and to convene in the sacred city.

Phi(pronunciation: Fy like My) Constant: 1.618.., superior design

number of mathematics, is a repeating decimal, which never ends.

The Creator has always used the very

same number in numerous events in the

universe; in our heart pulses, our

arms and legs, eyebrows and teeth.

The aspect ratio of DNA spiral, in

the special design of the universe

called dodecahedron, in the leaf array rules of plants called

phyllotaxy, in the snowflake crystals, in the spiral structure of

numerous galaxies etc...(for details, See last of this booklet)

The Creator used the same number; the number of golden ratio which

is 1.618~.

It is determined that this ratio has been used for the design of

various reputable architectural structures, even including Pyramids in

Egypt. Famous astronomer Kepler defined this number as a great

treasury. Numerous famous painters, engineers and architects, like

Leonardo Da Vinci, knowingly or unknowingly, have been using this

ratio in their works of art for hundreds of years.

As a result of his 25 years long study, aesthetician Dr. Steven

Markout proves that each of human faces and bodies, created pursuant

to this ratio, are completely beautiful. If the relative ratio is

1.618 for the components of any structure, then this form will be

convenient to Golden Ratio, the perfect design.

So, where is the Golden Ratio Point of the World? The proportion of distance between Makkah and North Pole to the

distance between Makkah and South Pole is exactly 1.618, which is the

golden mean.

Moreover, the proportion of the distance between South Pole and Makkah

to the distance between both poles is again 1.618.

The miracle has not been completed yet...

The Golden Ratio Point of the World is in Makkah city

according to map of latitude and longitude, which is the common

determinant of mankind for location.

The proportion of eastern distance to the western distance of

Makkah’s solstice line is again 1.618. Moreover, as shown in the

Figure, the proportion of the distance from Makkah to the solstice line

from the west side and perimeter of world at that latitude is also

surprisingly equal to the golden ratio, 1.618.

The Golden Ratio Point of the World is always within the city

borders of Makkah, within the Holy Region that includes Kaaba

according to all mapping systems despite minor kilometrical

variations in their estimations.

At home, you can precisely measure the distance between any two points

of World by means of Google Earth’s ruler feature. If you wish, you

can easily verify the correctness of the given ratios by calculating

latitudes and longitudes or even by using a simple calculator. In

drawings, you initially see how to locate start and finish points on

Makkah city and North Pole. With respect to positive longitude and

latitude values and by taking drift angle to the land, but not to the

sea, the single Golden Ratio Point of the World is Makkah.

PhiMatrix software is an American software

used for displaying golden ratio of

pictures and drawings. If we assume the

longitude and latitude map of the World as

an everlasting painting which has an

endless depth, and open it in this

program, we will find out that the Golden

Ratio Point of the World is the City of

Makkah.

The miracles go on:

Golden Ratio Miracle is unbelievably also present in the Verse, Makkah

of Qur’an. In which God says:.

Allah has appointed proper proportions for all things. (Quran, 65:3)

Everything has its measure before His Sight. (Quran, 13:8)

The examples of the golden ratio exist in our own bodies and in all

living things in nature, are just a few of the proofs that God has

created all things with a measure.

There is one unique verse in Qur’an that includes the world

“Makkah” and an expression that mentions clear evidences within the city

which will grant faith to humanity.

The relation between the City of Makkah and the Golden Ratio is

clearly engraved in the Aale Imran Surah’s 96th verse (Quran 3:96). The

total number of all letters of this verse is 47 (In Arabic).

Translation: “First Sanctuary appointed for mankind was

that at Makkah (Mecca/Bakkah/Baca), a blessed place and

guidance for all kinds of beings.”

Calculating the golden ratio of total letters, we find out that the word

of Makkah is implied;

47 / 1.618 = 29.0...

If counted, there are miraculously 29 letters from the

beginning of the verse till the word, Makkah just as

in the world map (In Hebrew Bible Makkah is also known as

Baca/Arabic Bakkah, old name of Makkah. Psalm 84:6).

If only one single word or letter was missing, this ratio could

never been constituted.

Without pushing the limits, we have conducted the very same process that

we conducted on world map and witnessed the glorious coherence of number of

letters that reveals the relation of Makkah and Golden Ratio.

All these evidences show that, The Creator of the World and mathematics

is the same One and Single God, the indefinable and great force that has

created Kaaba, holy Region and Qur’an. He reminds whole humanity that He has

granted signs to all humanity on the basis of his foreknowledge about the

future and the common languages of humans.

Discoveries regarding the relation between Golden Ratio, Makkah, Kaaba

and Qur’an have been increasing day by day.

In the figure, it is indicated that measurements by golden ratio compass

that is also known as Leonardo compass,

prove that Makkah city itself is located on

the Golden Ratio Point of Arabia while

Kaaba is located on the Golden Ratio of

Makkah City.

According to probability calculations,

all these proofs cannot be mere

coincidence.

Other 1.618 Golden ratio Discoveries

The Human Heartbeat

A peaceful heartbeat is said by some to beat in

a Phi rhythm.

The prominent parts of an electrocardiogram

(ECG or EKG) are the P wave, a deflection

caused by the current originating in the

atrium; the QRS complex, showing the passage of the electrical activity

into the ventricles; and the T wave, as the ventricles reset themselves.

The electrocardiograms ECG or EKG) of human heartbeats vary considerably

depending on a variety of factors.

ECG's show a resemblance to the Fibonacci Convergence

As explained on the Fibonacci Series page, the ratio of each successive

pair of numbers in the Fibonacci series (0, 1, 1, 2, 3, 5, 8, 13, 21,

34, 55, 89, 144, . . .) converges on phi (1.618. . .) as you go higher

in the series.

The first numbers in the series give an approximation of phi. e.g.

1 / 0 = ∞

1 / 1 = 1

2 / 1 = 2

3 / 2 = 1.5

5 / 3 = 1.666..

8 / 5 = 1.6

13 / 8 = 1.625

21 / 13 = 1.615

34 / 21 = 1.619

55 / 34 = 1.6176

89 / 55 = 1.618...

Curiously, if you graph these approximations of phi in the series above

you get the chart below, the first part of which bears a similarity to

the ECG pattern of the human heartbeat.

DNA

The DNA spiral is a Golden Section

The DNA molecule, the program for all life, is based on the golden section. It measures 34 angstroms long by 21 angstroms wide for each full cycle of its double helix spiral.

34 and 21, of course, are numbers in the Fibonacci series and their ratio, 1.6190476 closely approximates phi, 1.6180339.

B-DNA has spirals in phi proportions

DNA in the cell appears as a double-stranded helix referred to as B-DNA.

This form of DNA has a two groove in its spirals, with a ratio of phi in the proportion of the major groove to the minor groove, or roughly 21 angstroms to 13 angstroms.

The DNA cross-section is based on Phi

A cross-sectional view from the top of the DNA double helix forms a decagon:

A decagon is in essence two pentagons, with one rotated by 36 degrees from the other, so each spiral of the double helix must trace out the shape of a pentagon.

The ratio of the diagonal of a pentagon to its side is Phi to 1. So, no matter which way you look at it, even in its smallest element, DNA, and life, is constructed using phi and the golden section!

The Human Body The human body is based on Phi and 5

The human body illustrates the Golden Section or Divine Proportion.

The Divine Proportion in the Body

The white line is the body's height.

The blue line, a golden section of the white line, defines the distance from the head to the finger tips

The yellow line, a golden section of the blue line, defines the distance from the head to the navel and the elbows.

The green line, a golden section of the yellow line, defines the distance

from the head to the pectorals and inside top of the arms, the width of

the shoulders, the length of the forearm and the shin bone.

The magenta line, a golden section of the green line, defines the distance

from the head to the base of the skull and the width of the abdomen.

The sectioned portions of the magenta line determine the position of the nose and the hairline.

Although not shown, the golden section of the magenta line (also the short section of the green line) defines the width of the head and half the width of the chest and the hips.

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.

The golden section in turn, is also based on 5, as the number phi, or 1.6180339..., is computed using 5's, as

follows:

5 ^ .5 * .5 + .5 = 1.618

In this mathematical construction "5 ̂ .5" means "5 raised to the 1/2 power," which is the square root of 5, which is then multiplied by 0.5 and to which 0.5 is then added.

Plants

Plants illustrate the Fibonacci series in the numbers and arrangements of petals, leaves, sections and seeds.

Plants that are formed in spirals, such as pinecones, pineapples and sunflowers, illustrate Fibonacci numbers. Many plants produce new branches in quantities that are based on Fibonacci numbers.

Here a sunflower seed illustrates this principal as

the number of clockwise spirals is 55 (marked in

red, with every tenth one in white) and the

number of counterclockwise spirals is 89 (marked in green, with every tenth one in white.)

Here a plant illustrates that each successive level of branches is often based on a progression through the Fibonacci series.

You might expect symmetry in plants, but if you cut a fruit or vegetable you will often find that the number of sections is a Fibonacci number:

Bananas have 3 Apples have 5

Fibonacci numbers in flower petals

Many f lowers have petals that total a number in, or very close to, the

Fibonacci series:

3 Lilies

5 Buttercups, Roses

8 Delphinium

13 Marigolds

21 Black-eyed susans

34 Pyrethrum

55/89 Daisies

The Universe

New findings in 2003 reveal that the shape of the Universe is a Dodecahedron based on Phi

In October 2001, NASA began collecting data with the Wilkinson Microwave Anisotropy Probe (WMAP) on cosmic background radiation. Like visible light from distant stars and galaxies, cosmic background radiation allows scientists to peer into the past to the time when the universe was in its infancy. Density fluctuations in this radiation can also tell scientists much about the physical nature of space.

NASA released the first WMAP cosmic background radiation data in February of 2003. In October 2003, a team including French cosmologists and Jeffrey Weeks, a freelance mathematician and recipient of a MacArthur Fellowship or "genius award," used this data to develop a model for the shape of the universe.

The study analyzed a variety of different models for the universe, including finite vs. infinite, flat, negatively curved (saddle-shaped), positively curved (spherical) space and a torus (cylindric). The study revealed that the math adds up if the universe is finite and shaped like a dodecahedron, as in the illustration below provided by Weeks:

The connection to Phi is found in the Pentagons that form the faces of the Dodecahedron

A shown on the Geometry page, A dodecahedron consists of twelve pentagons. Take a pentagon and connect all the points to form a 5-pointed star. The ratios of the lengths

of the resulting line segments are all based on phi, Φ, or 1.618!

This is still a theory, but supported by data that can be tested

Weeks cautioned that his team's model of a finite, dodecahedral-

shaped universe, while promising, is hardly a proven theory. He said, "There's more work to be done. It could be affirmed, or it could be refuted. What makes it exciting now is it's not a matter of idle speculation. There's real data

to look at and the possibility of getting a definite answer." If proven by further evidence and scrutiny, the model would represent a major discovery about the nature

of the cosmos.

Solar System

The dimensions of the Earth and Moon are in Phi relationship, forming

a Golden Triangle

The illustration above shows the relative sizes of the Earth and the Moon to scale.

Draw a radius of the Earth (1)

Draw a line from the center point of the Earth to the center point of the Moon (square root of Phi) Draw a line to connect the two lines to form a Golden Triangle (Phi).

Using dimensions from Wikipedia and geometry's classic Pythagorean Theorem, this is expressed mathematically as follows:

Dimension

(km)

Proportion

(Earth=1)

Mathematical

Expression

Radius of the Earth 6,378.10 1.000 A

Radius of the Moon 1,735.97 0.272

Earth Radius + Moon Radius 8,114.07 1.272 B

Hypotenuse 10,320.77 1.618 (Φ) C

Hypotenuse / (Earth Radius + Moon Radius) 1.618 (Φ) A²+B²=C²

This geometric construction is the same as that which appears to have been used in the construction of

the Great Pyramid of Egypt.

Certain solar system orbital periods are related to phi

Certain planets of our solar system seem to exhibit a relationship to phi, as shown by the following

table of the time it takes to orbit around the Sun:

Mercury Venus Earth Jupiter Saturn

Power of Phi -3 -1 0 5 7

Decimal Result 0.24 0.62 1.0 11.1 29.0

Actual Period 0.24 0.62 1.0 11.9 29.5

Saturn reveals a phi relationship in several of its dimensions

The diameter of Saturn is in a phi relationship with the diameter of its rings, as illustrated by the green

lines.

The inner ring division is in a phi relationship with the diameter of the rings outside the sphere of the

planet, as illustrated by the blue lines.

The Cassini division in the rings of Saturn falls at the Golden Section of the width of the lighter outside section of the rings.

Note: Phi grid showing Golden Ratio lines provided by PhiMatrix software.

A closer look at Saturn's rings reveals a darker inner ring which exhibits the same golden section

proportion as the brighter outer ring.

Venus and Earth reveal a phi relationship

Venus and the Earth are linked in an unusual relationship involving phi. Start by letting Mercury represent the basic unit of orbital distance and period in the solar system:

Planet

Distance from

the sun in km (000)

Distance where

Mercury equals 1

Period where

Mercury equals 1

Mercury 57,910 1.0000 1.0000

Venus 108,200 1.8684 2.5490

Earth 149,600 2.5833 4.1521

Curiously enough we find:

Period of Venus * Phi = Distance of the Earth

2.5833

In addition, Venus orbits the Sun in 224.695 days while Earth orbits the Sun in 365.242 days, creating

a ratio of 8/13 (both Fibonacci numbers) or 0.615 (roughly phi.) Thus 5 conjunctions of Earth and Venus occur every 8 orbits of the Earth around the Sun and every 13 orbits of Venus.

Mercury, on the other hand, orbits the Sun in 87.968 Earth days, creating a conjunction with the Earth

every 115.88 days. Thus there are 365.24/115.88 conjunctions in a year, or 22 conjunctions in 7 years, which is very close to Pi!

Relative planetary distances average to Phi

The average of the mean orbital distances of each successive planet in

relation to the one before it approximates phi:

Note: We sometimes forget about the asteroids when thinking of the planets

in our solar system. Ceres, the largest asteroid, is nearly spherical,

comprises over one-third the total mass of all the asteroids and is thus the

best of these minor planets to represent the asteroid belt. (Insight on mean orbital distances contributed by Robert Bartlett.)

2005 unveiled the discovery of a 10th planet called 2003UB313. It was

found at a distance of 97 times that of the Earth from the Sun. Its ratio to

Pluto would thus be 2.47224, much higher than any previous planet to

planet orbital distance ratio. Could it be that this is actually the 11th planet

and the 10th planet will be found at an orbit whose ratio is 1.52793 times

that of Pluto, preserving the phi average? Time will only tell, but if it happens remember that you heard it here first.

Planet

Mean distance

in million kilometers

per NASA

Relative mean

distance where

Mercury=1

Mercury 57.91 1.00000

Venus 108.21 1.86859

Earth 149.60 1.38250

Mars 227.92 1.52353

Ceres 413.79 1.81552

Jupiter 778.57 1.88154

Saturn 1,433.53 1.84123

Uranus 2,872.46 2.00377

Neptune 4,495.06 1.56488

Pluto 5,869.66 1.30580

Total 16.18736

Average 1.61874

Phi 1.61803

Degree of variance (0.00043)

Galaxies

The Golden Section in Nature

Golden ratio spiral

Body Temperatures Body temperatures and sterilization points fall near the phi points between freezing and boiling

Body temperatures vary, even within humans. The body temperatures of mammals range from around 97° to over 103° Fahrenheit. Birds

have average temperatures of around 105° Fahrenheit.

The phi point between the freezing temperature (32° F) and the boiling temperature (212° F) of water is 100.8° F, or 38.2° Centigrade.

Take the phi point from the other end of the scale of temperature and you arrive at 143°, which is

about the temperature required to kill bacteria. (Generally rounded and stated as 140° in most literature.)

Interestingly enough, if you take the phi point or 0.618 of 37 degrees centigrade, which is the average

human body temperature, you get 23 degrees centigrade or 73 degrees Farenheit, a "room"

temperature that many would consider to be just about perfect for indoor comfort and outdoor

enjoyment.

Water has a very unusual property in that it reaches maximum density in the liquid state at 4° C,

instead of in the solid one. This allows ice to float, which is vital to sustaining life beneath its surface in

cold climates. The kilogram is defined as the mass of water filling one liter at 4° C. If this critical

temperature is regarded instead of 0° C, we find that the phi point is 105.2° F, and this defines the upper end of body temperatures.

Thus even key temperatures for body heat and comfort reflect the phi points in the property of water, of which we largely consist!

Description of key temperature point Fahrenheit Centigrade

Freezing point of water 32° 0°

Middle of range of typical body temperatures of mammals 100.6° 38.1°

Phi point 2 (0.618 down from water's boiling point to freezing)

100.8° 38.2°

Average body temperature of birds 105° 40°

Phi point 2 (0.618 down from water's boiling point to maximum density)

105.2° 40.7°

Phi point 1 (sterilization point) (0.618 up from water's freezing point to boiling)

143.2° 61.8°

Boiling point of water 212° 100°

Quantum Solid State Matter

Golden Ratio Discovered in Quantum World: Hidden Symmetry Observed for the First Time in

Solid State Matter

In January 2010 Science Daily and Physics World announced the discovery of a hidden Phi symmetry in

solid state matter. As explained in the Science Daily article:

"On the atomic scale particles do not behave as we know it in the macro-atomic world. New properties emerge

which are the result of an effect known as the Heisenberg's Uncertainty Principle. In order to study

these nanoscale quantum effects the researchers have

focused on the magnetic material cobalt niobate. It consists of linked magnetic atoms, which form chains

just like a very thin bar magnet, but only one atom wide and are a useful model for describing ferromagnetism on

the nanoscale in solid state matter.

When applying a magnetic field at right angles to an

aligned spin the magnetic chain will transform into a new state called quantum critical, which can be thought

of as a quantum version of a fractal pattern. Prof. Alan Tennant, the leader of the Berlin group, explains "The

system reaches a quantum uncertain -- or a Schrödinger cat state. This is what we did in our experiments with cobalt niobate. We have tuned the system exactly in order to turn it quantum critical."

By tuning the system and artificially introducing more quantum uncertainty the researchers observed that the

chain of atoms acts like a nanoscale guitar string. Dr. Radu Coldea from Oxford University, who is the principal author of the paper and drove the international project from its inception a decade ago until the present, explains:

"Here the tension comes from the interaction between spins causing them to magnetically resonate. For these

interactions we found a series (scale) of resonant notes: The first two notes show a perfect relationship with each other. Their frequencies (pitch) are in the ratio of 1.618…, which is the golden ratio famous from art and

architecture." Radu Coldea is convinced that this is no coincidence. "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 explains."

The E8 structure itself has relationships to Phi (1.618)

Symmetry plays a fundamental role in our understanding of the physical world.

Perhaps the most intriguing of all is E8 – essentially a fantastically beautiful 8D diamond-like lattice of spheres in which each sphere is surrounded by

240 others.

E8 is a complex form of mathematical symmetry linked to string theory,

glimpsed in the real world for the first time as described above in laboratory experiments on exotic crystals.

Mathematicians discovered this complex 248-dimensional symmetry called E8 in the late 1800s. The dimensions in the structure are not necessarily spatial, like the three dimensions we live in, but they correspond to mathematical degrees of freedom, where each dimension represents a different variable. In the 1970s, the symmetrical form turned up in calculations related to string theory, a candidate for the "theory of everything" that might explain all the forces in the universe. E8 shot to fame in 2007 when the US freelance physicist Garrett Lisi posted a paper on the arXiv preprint server suggesting that E8 could underpin a theory of everything by mapping out all known particles and how they interact with each other.

The two-dimensional view above of one plane the E8 structure reveals some interesting relationships to phi. Note the light red concentric circles overlaying the illustration of E8. The red lines were added to the E8 illustratation by using PhiMatrix software, where each red line is in a phi relationship, that is 1.618 of the diameter of the one before it.

Miracles Continue…

End of the Booklet