Golden Ratio Makkah hk4u

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 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 com that is also known as Leonardo com, 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 age 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. A nother 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 f ollows: 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 plant illustrates that each successive level of branches is often based on a progression through the Fibonacci series.

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.)

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 pet als 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

Pyret hrum

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 ed 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 Mathematical (Earth=1) 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)

A ²+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

-3

-1

0

5

7

Decimal Result

0.24

0.62

1.0

11.1

29.0

A ctual Period

0.24

0.62

1.0

11.9

29.5

Power of Phi

Saturn

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

Mercury

Distance f rom the sun in km (000)

Distance where Mercury equals 1

Period where Mercury equals 1

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 that you heard it here first.

Planet

Mercury

Mean Relative distance mean in million distance kilomet ers where per NA SA Mercury=1 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

Total A verage Phi Degree of variance

1.30580 16.18736 1.61874 1.61803 (0.00043)

Galaxies

The Golden Section in Nature

Golden ratio spiral

Body Temperatures Body temperatures and sterilization points f all near the phi points bet ween f reezing and boiling

Body temperatures vary, even within humans. The body temperatures of mammals range f rom 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 s urface 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

32°

0°

Middle of range of typical body temperatures of mammals

100.6°

38.1°

Phi point 2 (0.618 down f rom water's boiling point to f reezing)

100.8°

38.2°

105°

40°

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

105.2°

40.7°

Phi point 1 (sterilization point) (0.618 up f rom water's f reezing point to boiling)

143.2°

61.8°

212°

100°

Freezing point of water

A verage body temperature of birds

Boiling point of water

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 C oldea 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 w hich 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 rev eals 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