The Golden Ratio is a Devine One

The Divine Ratio - Story of Phi

The Golden Ratio is an irrational mathematical constant, equals approximately 1.618. It is 0ften referred to by the letter Phi.

What is this ratio?

Dan Brown in his book De Vince Code explained how the golden ration interferes with artists work, Living creatures and Plants.

Some scientists linked it to more than 2400 years ago.

The fascination with the Golden Ratio is not confined just to mathematicians.

Biologists, artists, musicians, historians, architects, psychologists, and even mystics have pondered and debated the basis of its ubiquity and appeal. In fact, it is probably fair to say that the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics.

Ancient Greeks studied it for its frequent appearance in Geometry. They attributed the discovery to Pythagoras.

Beginning in the Renaissance, a body of literature on the aesthetics  of the golden ratio was developed.

As a result, architects, artists, book designers, and others have been encouraged to use the golden ratio in the dimensional relationships of their works.

A geometrical analysis of the Great Mosque of Kairouan, Tunisia, reveals a consistent application of the golden ratio throughout the design, according to Boussora and Mazouz.

It is found in the overall proportion of the plan and in the dimensioning of the prayer space, the court, and the minaret. Boussora and Mazouz also examined earlier archaeological theories about the mosque, and demonstrate the geometric constructions based on the golden ratio by applying these constructions to the plan of the mosque to test their hypothesis.

Speaking about Islamic Architect, it is worth mentioning that the Quran emphasized in so many verses that God created everything in proportion, Gave wealth and power in proportion, caused rain in proportion.

Miracle of Kaaba - English Version from Erdem Cetinkaya on Vimeo.
Some Islamic scholars are trying to prove that Mecca and Kaaba are good examples of the golden proportion.

This is why scientists refer to is as the Divine Ratio.

Both Egyptian pyramids and those mathematical regular square pyramids that resemble them can be analyzed with respect to the golden ratio and other ratios.

One Egyptian pyramid is remarkably close to a "golden pyramid" – the Great Pyramid of Giza (also known as the Pyramid of Cheops or Khufu).

The golden ratio is also apparent in the organization of the sections in the music of Debussy's Reflets dans l'eau (Reflections in Water), from Images  (1st series, 1905), in which "the sequence of keys is marked out by the intervals 34, 21, 13 and 8, and the main climax sits at the phi position.

Its slope of 51° 52' is extremely close to the "golden" pyramid inclination of 51° 50' and the π-based pyramid inclination of 51° 51'; other pyramids at Giza (Chephren, 52° 20', and Mycerinus, 50° 47' are also quite close.

The height of the great pyramid is equal = 146.515 meters, and its base equals 230.363 meters.

The Pharaohs used a simple math to find that half of the base is 115.182 m and the "slant height"  is 186.369 meters.

Dividing the "slant height" 186.369m by "half base" 115.182m gives 1.6180, which is practically equal to the golden ration!

The Pharaohs bring this ratio by discovering that the earth/moon relationship is the only one in the solar system that contains this unique golden section ratio that "squares the circle. 

If the base of the great pyramid is equated with the diameter of the earth, then the radius of the moon can be generated by subtracting the radius of the earth from the height of the pyramid.

The height of the great pyramid times 2p exactly equals the perimeter of the pyramid.
This proportion results from elegant design of the pyramid with the height equal two diameters of a circle and the base equal to the circumference of the circle.
The number Pi is the mathematical constant 3.1415, with the ratio of the diameter to the distance around the circle, called the circumference.

In the pyramid it is the ratio of the height to twice the length of the base.

Whether the relationship to the golden ratio in these pyramids is by design or by accident remains controversial. Several other Egyptian pyramids are very close to the rational 3:4:5 shape.

The musicologist Roy Howat has observed that the formal boundaries of La Mer correspond exactly to the golden section.

Trezise finds the intrinsic evidence "remarkable," but cautions that no written or reported evidence suggests that Debussy consciously sought such proportions.

Also, many works of Chopin, mainly Etudes (studies) and Nocturnes, are formally based on the golden ratio. This results in the biggest climax of both musical expression and technical difficulty after about 2/3 of the piece.

Pearl Drums positions the air vents on its Masters Premium models based on the golden ratio. The company claims that this arrangement improves bass response and has applied for a patent on this innovation.


Long before the advent of digital recordings, the Babylonians and Hindus, and then Pythagoras and his followers translated music into number and geometric proportions (Durant 1939).

For example, by dividing a vibrating string into various ratios they discovered that several very pleasing musical intervals could be produced.

Hence, the ratio 1:2 was found to yield an octave, 2:3 a fifth, and 3:4 a fourth, 4:5 a major third, and 5:6 a minor third (McClain 1978).

The harmonic system utilized in the nineteenth century by various composers was based on these same ratios. Indeed, Bartok utilized these ratios in his musical compositions.

These same musical ratios, the Pythagorians discovered, also were found to have the capability of reproducing themselves. That is, the ratio can reproduce itself within itself and form a unique geometrical configuration which Pythagoras and the ancient Greeks referred as the the "golden ratio" or "golden rectangle." The gold rectangle was postulated to have divine inspirational origins. Indeed, music itself was thought by early man to be magical, whereas musicians were believed by the ancient Greeks to be "prophets favored by the Gods" (Worner, 1973).

The Golden Ratio has fascinated layman and mathematician for centuries.

It seems like magic that it turns up in such different arenas as pine cones, earth-moon and planet  relationships, the Cheops Pyramid in Egypt, the Mona Lisa  and even our DNA.
Indeed its widespread appearance shows that there is a unifying mathematical principle that is more subtle than science has thus far been able to define.

It remains a mathematical mystery or should we say .......

God's Mystery...

Sami Cherkaoui

Ishtar and Easter

How much it is true that Ishtar the Ancient Goddess is the very origin of Easter, its affiliated traditions (especially Easter Eggs) and also her name is the source of the word?

As we know it, Easter is probably the most important holidays to Christians. They celebrate Jesus Christ's resurrection from the dead following his death on Good Friday.

Christians throughout the world celebrate Easter as the day Jesus Christ rose from the dead, however Easter has roots in pagan traditions as well.

In Christianity, Easter is the celebration of Christ rising from the dead three days after his crucifixion. This particular celebration is central to the Christian belief system. The celebration begins with Lent, a 40-day period of reflection and penance before Easter Sunday.

Holy week refers to the week preceding Easter and Good Friday commemorates Christ’s day of crucifixion. Holy Saturday refers to the day between the crucifixion and Christ’s resurrection. There is also a 50-day period following Easter that celebrates Christ’s ascension into heaven.

This time of Easter coincides with the arrival of spring and symbolizes the arrival of light and the awakening of life around us.

The March equinox marks the first day of various calendars including the Iranian calendar. The ancient Iranian new year's festival of Nowruz can be celebrated March 20 or March 21. According to the ancient Persian mythology Jamshid, the mythological king of Persia, ascended to the throne on this day. These festivities recall the story of creation and the ancient cosmology of Iranian and Persian people.

It is also a holiday celebrated in Azerbaijan, Afghanistan, Pakistan, Turkey, Zanzibar, Albania, and various countries of Central Asia, as well as among the Kurds.

It is also a Zoroastrian holiday, and a holy day for adherents of the Bahá'í Faith and the Nizari Ismaili Muslims.

The Bahá'í Naw-rúz is stationary; the new year always starts at sunset March 20.

Sham El Nessim was an ancient Egyptian holiday which can be traced back as far as 2700 BC. It is still one of the public holidays in Egypt. Sometime during Egypt's Christian period (c. 200–639) the date moved to Easter Monday, but before then it coincided with the vernal equinox.

In many Arab countries, Mother's Day is celebrated on the March equinox.

The Jewish Passover usually falls on the first full moon after the Northern Hemisphere vernal equinox, although occasionally (7 times every 19 years) it will occur on the second full moon.

The Christian churches calculate Easter as the first Sunday after the first full moon on or after the March equinox.

The official church definition for the equinox is March 21; however, as the Eastern Orthodox Churches use the older Julian calendar, while the Western Churches use the Gregorian calendar, both of which designate March 21 as the equinox, the actual date of Easter differs.

The earliest possible Easter date in any year is therefore March 22 on each calendar. The latest possible Easter date in any year is April 25.

According to the sidereal solar calendar Vernal Equinox is erroneously celebrated throughout South Asia on the day when the sun enters the sidereal Aries generally around 14 April.

It marks the beginning of the new year of the Tamil calendar and is celebrated in the South Indian state of Tamil Nadu.

This day is celebrated as the last day of the year according to the Bengali calendar and Assamese calendar in West Bengal, Assam, Tripura, Bangladesh and throughout the Eastern and North Eastern India. The day is known as Chaitra Sankranti in Bengali. The following is celebrated as the Bengali New Year's Day and Assamese Bihu.

Andhra Pradesh, Karnataka and Maharastra people celebrate new year ugadi set by Satavahana on the first morning after first new moon from the sidereal vernal equinox. Also the calculations of the great Indian Mathematician Bhaskaracharya proclaim the Ugadi day as the beginning of the New Year, New month and New day.

In the Indian states Orissa, this day is celebrated as the new year around April 14. It is known as 'Vishuva Sankranti' (meaning "equal" in Sanskrit).

In Kerala though the new year is on Chingam 1, the beginning of sidereal zodiac Leo, sidereal vernal equinox is celebrated much more than new year as 'Vishu'

March 20th is the first day of spring, or "vernal equinox" as astronomers would have it — vernal meaning "of or pertaining to spring," equinox meaning "equal night."

As the angle of the earth's inclination toward the sun changes throughout the year, lengthening or shortening the days according to season and hemisphere, there are two times annually when day and night are of more-or-less equal length: the spring and autumnal equinoxes.

When Julius Caesar established his calendar in 45 BC, he set March 25 as the spring equinox. Between the 4th and 16th centuries, the calendar drifted with respect to the equinox, such that the equinox began occurring on about March 21st, when Pope Gregory XIII's created his modern Gregorian calendar. The Pope was moved by the desire to restore the edicts about the date of Easter of the Council of Nicaea of AD 325.

Incidentally, the date of Easter itself is fixed by an approximation of lunar cycles used in the Hebraic calendar, but according to the historian Bede the English name comes from a pagan celebration by the Germanic tribes of the vernal (spring) equinox.

The days of February 29 of the years AD 100, AD 200, AD 300, and the day created by the irregular application of leap years between the assassination of Caesar and the decree of Augustus re-arranging the calendar in AD 8, remained in effect. This moved the equinox four days earlier than in Caesar's time.

Europeans refer Easter to a Saxon goddess who was known by the names of Oestre or Eastre, and in Germany by the name of Ostara. She is a goddess of the dawn and the spring, and her name derives from words for dawn, the shining light arising from the east. The word for the "female hormone" estrogen derives from her name. Ostara was a fertility goddess.

Ostara had a passion for new life. Her presence was felt in the flowering of plants and the birth of babies, both animal and human. The rabbit (well known for its propensity for rapid reproduction) was her sacred animal.

Eggs are an obvious symbol of fertility, and the newborn chicks an adorable representation of new growth. Brightly colored eggs, chicks, and bunnies were all used at festival time to express appreciation for Ostara's gift of abundance.

But Easter eggs and the Easter Bunny both featured in the spring festivals of Ostara, were initially held during the feasts of the goddess Ishtar.

Ishtar, goddess of romance, procreation, and war in ancient Babylon, was also worshipped as the Sumerian goddess Inanna.

She is the "mother goddesses" and the stories of her descent to the Underworld and the resurrection that follows are contained in the oldest writings that have ever been discovered.

The most famous of the myths of Ishtar tell of her descent into the realm of the dead to rescue her young lover, Tammuz, a Vegetation god forced to live half the year in the Underworld. Ishtar approached the gates of the Underworld, which was ruled by her twin sister Eresh-kigel, the goddess of death and infertility. She was refused admission.

During Ishtar's absence the earth grew barren since all acts of procreation ceased while she was away. Ishtar screamed and ranted that she would break down the gates and release all of the dead to overwhelm the world and compete with the living for the remaining food unless she was allowed to enter and plead her case with her twin.

When she won admission, the guard refused to let her pass through the first gate unless she removed her crown. At the next gate, she had to remove her earrings, then her necklace at the next, removing her garments and proud finery until she stood humbled and naked after passing through the seventh (and last) gate.

"On her head she wears the shugurra, the crown of the steppe.

Across her forehead her dark locks are carefully arranged.

Around her neck she wears the small lapis beads.

At her breast she wears the double strand of beads.

Her body is wrapped with the royal robe.

Her eyes are daubed with the ointment called, 'Let him come, let him come.'

Around her chest she wears the breast plate called 'Come, man, come!'

On her wrist she wears the gold ring.

In her hand she carries the lapis measuring rod and line."

                       

In one version, she was held captive and died but was brought back to life when her servant sprinkled her with the "water of life".

In the more widely known version of the myth, Ishtar's request was granted and she regained all of her attire and possessions as she slowly re-emerged through the gates of darkness.

Upon her return, Tammuz and the earth returned to life. Annual celebrations of this "Day of Joy", were held each year around the time of the vernal equinox.

These celebrations became the forerunners of the Ostara festivals that welcomed Oestre and the arrival of spring.

When he described his meeting with Salma Karamy in The Broken Wings, a chapter titled "Between Christ and Ishtar", Khalil Gibran the Lebanese/American intellectual wrote:

" As one enters this temple he sees on the wall at the east side an old Phoenician picture, carved in the rock depicting Ishtar, goddess of love and beauty, sitting on her throne, surrounded by seven nude virgins standing in different posses. The first one carries a torch; the second, a guitar; the third, a censer; the fourth a jug of wine; the fifth, a branch of roses; the sixth, a wreath of laurel; the seventh, a bow and arrow; and all of them look at Ishtar reverently.

On the second wall there is another picture, more modern than the first one, symbolizing Christ nailed to the cross, and at His side stand His sorrowful mother and Mary Magdalene and two other women weeping. This Byzantine picture shows that it was carved in the fifteenth or sixteenth century.

..........There is nothing else in that little temple except deep silence, revealing to the living the secrets of the goddess and speaking worldlessly of past generations and the evolution of religions.

..........In that unknown temple, I met Selma once every month and spent the hours with her, looking at those strange pictures, thinking of the crucified Christ and pondering upon the young Phoenician men and women who lived, loved and worshipped beauty in the person of Ishtar by burning incense before her statue and pouring perfume on her shrine, people for whom nothing is left to speak except the name, repeated by the march of time before the face of Eternity.

.........On another occasion she said, pointing to the carved pictures on the walls of the temple, "In the heart of this rock there are two symbols depicting the essence of a woman's desires and revealing the hidden secrets of her soul, moving between love and sorrow—between affection and sacrifice, between Ishtar sitting on the throne and Mary standing by the cross. The man buys glory and reputation, but the woman pays the price."

.........Was she to blame because she looked through the jail window upon the green fields and spacious sky? Will the people count her as being untruthful to her husband because she came from his home to sit by me between Christ and Ishtar?

And I leave you with his songs of The Rain, just to show how Ishtar was and still is the symbol of love, life and consequently the true meaning of Spring and Easter.

"

I am dotted silver threads dropped from heaven

By the gods. Nature then takes me, to adorn

Her fields and valleys.

I am beautiful pearls, plucked from the

Crown of Ishtar by the daughter of Dawn

To embellish the gardens.

When I cry the hills laugh;

When I humble myself the flowers rejoice;

When I bow, all things are elated.

The field and the cloud are lovers

And between them I am a messenger of mercy.

I quench the thirst of one;

I cure the ailment of the other.

The voice of thunder declares my arrival;

The rainbow announces my departure.

I am like earthly life, which begins at

The feet of the mad elements and ends

Under the upraised wings of death.

I emerge from the heard of the sea

Soar with the breeze. When I see a field in

Need, I descend and embrace the flowers and

The trees in a million little ways.

I touch gently at the windows with my

Soft fingers, and my announcement is a

Welcome song. All can hear, but only

The sensitive can understand.

The heat in the air gives birth to me,

But in turn I kill it,

As woman overcomes man with

The strength she takes from him.

I am the sigh of the sea;

The laughter of the field;

The tears of heaven.

So with love -

Sighs from the deep sea of affection;

Laughter from the colorful field of the spirit;

Tears from the endless heaven of memories. "

Sami Cherkaoui