The golden ratio also/ golden proportion/ golden mean/ golden section/ golden number/ divine proportion is that a line is divided such that the ratio of the longer part of the line to the whole is exactly the same ratio as the shorter part of the line is to the longer part.

GOLDEN RATIO

• the Greek Philosopher Pythagoras discovered the concept of harmony when he began his studies of proportion while listening to the different sounds given off when the blacksmith’s hammers hit their anvils

ORIGIN

Some twentieth-century artists and architects, including le Corbusier have proportioned their works to approximate the golden ratio— Especially in the form of the golden rectangle, in which the ratio of

the longer side to the shorter is the golden ratio— Believing this proportion to be aesthetically pleasing. The golden ratio appears in some patterns in nature, including the

spiral arrangement of leaves and other plant parts. Shapes proportioned according to the golden ratio have long been

considered aesthetically pleasing throughout many cultures, and is still used frequently in art and design, suggesting a natural balance between symmetry and asymmetry.

Why golden ratio came into existence

• Leonardo is thought to have used the golden ratio, a geometric proportion regarded as the key to creating aesthetically pleasing art, when painting the Mona Lisa.

• it is well known that the eyes take in information more efficiently when they scan side to side, as opposed to up and down. When you look at what so many people have been drawing and building, you see these proportions everywhere.“

• This is the best flowing configuration for images from plane to brain and it manifests itself frequently in human-made shapes that give the impression they were 'designed' according to the golden ratio,"

many people have spent endless hours over this simple ratio and its properties. But 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.

This symbolic potential arises because of the way the mean’s spiral shape resembles growth patterns observed in nature and its proportions are reminiscent of those in human bodies. Thus, these simple spirals and rectangles, which served to suggest the presence of a universal order underlying the world, were thereby dubbed “golden” or “divine”.

Pine cones-The seed pods are in a spiral pattern. Each cone consists of a pair of spirals, each one spiraling upwards in opposing directions

Spiral Galaxies-The Milky Way has several spiral arms.

Shells-the ratio of the sides a/b is equal to the golden mean (phi), can be repeated into infinity — takes the form of a spiral

Face-The mouth and nose are each positioned at golden sections of the distance between the eyes and the bottom of the chin. the eye and ear follows along a spiral.

The human body is also in the same ratio.

GOLDEN RATIO IN NATURE

leaves -arrangement of branches along the stems of plants and the veins in leaves

Many artists and architects have proportioned their work to approximate the golden ratio, with the belief that the outcome will be more aesthetically pleasing.  Using any of these ratios, an architect can design a door handle that has a complementary relationship to its door, which in turn has a similar relationship to its enclosing wall, and so on.  But more than this, the golden ratio has been used for the façade of great buildings from the Parthenon to the Great Mosque of Kairouan , high court , un secretariat building , villa suvoye and all the way through to modern landmarks such as the Sydney Opera House , National Gallery in London, and TAJ MAHAL

GOLDEN RATIO IN ARCHITECTURE

Parthenon, Athens Great Mosque of Kairouan high court

un secretariat building National Gallery in London,TAJ MAHAL Sydney Opera House

Golden rectangleA+B A A B

GOLDEN SPIRAL A Fibonacci spiral approximates the golden spiral using quarter-circle arcs inscribed in squares of integer Fibonacci-number side, shown for square sizes 1, 1, 2, 3, 5, 8, 13, 21, and 34.for e.g.- Mona Lisa painting

GOLDEN TRIANGLE. For e.g.-pyramids at Giza

GOLDEN RATIO

PYRAMIDS AT GIZA

The Egyptians thought that the golden ratio was sacred.  Therefore, it was very important in their religion.  They used the golden ratio when building temples and places for the dead.  If the proportions of their buildings weren't according to the golden ratio, the deceased might not make it to the afterlife or the temple would not be pleasing to the gods. 

The Egyptians used both Pi (Π) and Phi (Φ) in the design of the Great Pyramids. The Great Pyramid has a base of 230.4 meters (755.9 feet) and an estimated original height of 146.5 meters (480.6 feet).  This creates a height to base ratio of 0.636, which indicates it is indeed a Golden Triangles,

PARTHENON AT ATHENS

Golden ratio is seen in 3 aspects Height of the columnsDividing line of the root support beam Width of the columns

PARTHENON AT ATHENS

•The Parthenon was constructed using few straight or parallel lines to make it appear more visually pleasing, a brilliant feat of engineering.•It is now in ruins, making its original features and height dimension subject to some conjecture.•Even if the Golden Ratio wasn’t used intentionally in its design, •.

Height of the columns – The structural beam on top of the columns is in a golden ratio proportion to the height of the columns.

Dividing line of the root support beam - The structural beam on top of the columns has a horizontal dividing line that is in golden ratio proportion to the height of the support beam.

Width of the columns – The width of the columns is in a golden ratio proportion formed by the distance from the centre line of the columns to the outside of the columns.

PARTHENON AT ATHENS

TAJ MAHAL• In taj mahal ,golden rectangle is observed in d

height to width ratio • Also seen in plan in the relation between

charbagh and tomb.

TAJO MAHALThe TAJ MAHAL displays golden proportions in the width of its grand central arch to its width, and also in the height of the windows inside the arch to the height of the main section below the domes.

The Taj Mahal in India was also constructed using the Golden Ratio. The main building of the Taj Mahal was designed using the Golden Ratio. This is why it looks so perfect. The rectangles that served as the basic outline for the exterior of the building were all in the Golden Proportion.

GOLDEN RECTANGLEMain entrance door frame rectangle is accurately Golden rectangle. Geometry of the arc inside it is as well built after Golden regularities.

It is also observed in the lotus flower from the top of the minarets

It is also observed in the plan with .The charbagh is in the ratio with the tomb.

tomb

• Le Corbusier placed systems of harmony and proportion at the centre of his design philosophy,

• and his faith in the mathematical order of the universe was closely bound to the golden section and

• the Fibonacci series, which he described as “rhythms apparent to the eye and clear in their relations with one another.

• And these rhythms are at the very root of human activities. • The building they created also appears to have golden ratios in its design.

GOLDEN RECTANGLE UN SECRETRIAT BUILDINGDESIGNED BY-BRAZILIAN ARCHITECT OSCAR NIEMEYER AND FRENCH-SWISS ARCHITECT LE CORBUSIER.

The building features golden rectangles in the columns of its colonnade, and three vertical golden rectangles adjoined horizontally in the interior entry. The interior entry appears to use the same concept of proportion in design as the three horizontal golden rectangles adjoined vertically in the UN Secretariat Building’s height and width.

It is 154m tall skyscraper and the centrepiece of headquarters located in manhattan , New York.The first floor is slighter taller than other floors.

GOLDEN RECTANGLE

41 floors ÷ 1.618² 15.7 floors, and ≅

the visual dividing line is midway between the 15th and 16th floor.From midway to width of the building, it follows the ratio.

DESIGN OF WINDOWS AND CURTAIN WALLS

UN SECRETRIAT BUILDINGDesigned by-Brazilian architect Oscar Niemeyer and French-Swiss architect Le Corbusier.

Other golden rectangles are seen in the interiors or the small elements like the curtain walls or the entrance of the building, columns placement.

DESIGN OF MAIN ENTERANCE

• The columns that surround the centre area of the front entrance are placed at the golden ratio point of the distance from the midpoint of the entrance to the side of the entrance.

• The large open framed areas to the left and right of the centre entrance area are golden rectangles.• The doors on the left and right side of the centre entrance are golden rectangles.• The left and centre frame sections of the centre section is a golden rectangle.

GOLDEN RECTANGLE

PLAN

Even the plan is in the golden ratio with a big conference hall in the centre.

SOURCES

https://en.wikipedia.org/wiki/Parthenonhttp://allday.com/post/1186-the-hidden-history-of-the-un-headquarters/http://www.goldennumber.net/un-secretariat-building-golden-ratio-architecture/http://www.goldennumber.net/phi-pi-great-pyramid-egypt/https://sites.google.com/site/funwithfibonacci/architecture/the-taj-mahalhttp://archgeom.blogspot.in/2010/03/golden-section-in-taj-mahal.htmlhttp://fergusson.edu/public/upload/golden_ratio_and_divine_proportion_final.pdfhttps://sites.google.com/site/funwithfibonacci/architecture/the-taj-mahalhttp://www.goldennumber.net/parthenon-phi-golden-ratio/http://www.geom.uiuc.edu/~demo5337/s97b/art.htmhttp://jwilson.coe.uga.edu/emat6680/parveen/ancient_egypt.htmhttp://tempatwisata.xyz/posting/un-secretariat-building-and-the-golden-ratio-in-architecture