The golden rectangle generated by fibonacci series with the golden spiral inscribed within

What do you think a ‘perfect’ rectangle is? Do not answer in terms of scientific logic. Apply your conscience and whims and try to illustrate a rectangle that you find really normal and common- something that you think the common mass would illustrate. Next, calculate the ratio between the longer side to the shorter side.

You may think the answer will be ambiguous and will vary greatly among the people but it is not so. We had tried this very experiment in class and 99% of the class came up with a ratio hovering around 1.618. This rectangle is called a Golden rectangle. And the number 1.618 is called the Golden Ratio. It is widely represented as Phi, the Greek symbol since it was first used by Phidas, a Greek Sculptor.

All of us are acquainted with the Fibonacci series which goes like: 1-1-2-3-5-8-13-21-34-55-89. Each succeeding term is the summation of the previous two terms of the series. The ratio between two adjacent terms of the series oscillates around the golden ratio. They slowly approach it. And then again deviates away. The ratio of 55 to 34 is 1.618.

The Fibonacci pattern of increment is found in the breeding habits of rabbits; in the floral patterns of flowers, for example the number of disc florets in each circle of the disc florets increases in keeping with the Fibonacci.

You may wonder why is it so? Well, even I do not have a logical answer for you. But this ratio is found everywhere in and around the visible universe.

Phi in nature

The spiral pattern of shells and spiral galaxies, the pattern of waves and sunflower disc all follow the Golden spiral. Beautiful faces and physique can be explained in terms of Golden Ratios. The DNA molecule which measures 34 angstroms to 21 angstroms also is in Golden Ratio.

Therefore, it is often referred to as God’s fingerprint.

The employment of Golden ratio in architecture is a very old phenomena and its use was kind of evolutionary. Even before the people did realize its existence everywhere they have had been using it unconsiously in their creations. This ratio is used in art and architecture vividly for some very obvious reasons:

1. This proportion makes your design aesthetically pleasing. If you have been using this ratio as a principle in your design, you might or might not stumble upon something brilliant. But in the end whatever you produce will be acceptable and not disturbing. It is ultimate key to safe designing.
2. The ratio brings an uncanny sense of balance in buildings. Buildings built keeping in mind the golden proportions appear balanced and stable. In the same way many architects playfully construct their buildings completely against the golden ratios to bring a sense of dynamism to their buildings.
3. Sometimes even, the use of Golden Ratio in architectural forms is not conscious. However, the sense of this proportion is kind of evolutionary and architects end up employing proportions which approximate to 1.618.

## The Parthenon, Greece- mid 5th century BC

The Parthenon Greece explained within a Golden Rectangles

The very first prominent and conscious use of the pleasing aesthetic effects of the golden Ratio was brought about by Phidas a Greek sculptor in the construction of Parthenon. The elevation can be perfectly fitted into a Golden Rectangle and the even the floor plan is designed keeping in mind the  proportions of Golden Ratio.

The small relief work on the elevation of the Parthenon also can be circumscribed by Golden rectangles.

## The Pyramids- 2570 BC

Pyramid of Khufu and phi

The Egyptians too have displayed the use of Golden Ratio subtly in the construction of the Pyramids. Being one of the most ancient surviving buildings, the largest of the pyramids at Giza have employed this ratio, however with less prominence. Here the ratio of the length of the triangular sides of the pyramid to the half of length of the square side is in Golden Ratio.

However, the Golden ratio was not known to them and neither was the Pythagorean theorem. The only right angle triangle proportions they were acquainted to were 3:4:5 where 3 and 5 approximates the Golden Ratio.

## The Notre Dame

The Notre Dame

The Notre Dame is claimed to be the first Christian Church to be completely built in 1345. The west façade of the building is designed on the principles of Golden Ratio. The geometry of Phi is adopted in both horizontal and vertical arrangement of the building. The ratio of the length denoted in blue to the length denoted in red is equal to Phi.

## The Taj Mahal

The perspective form of drawing of the Taj Mahal
The entrance to the Taj

The Taj Mahal too exhibits golden proportions in is design. The entrance to the Taj is undoubtedly a Golden rectangle. The system of Phi is adopted in the vertical and horizontal arrangement of the building. The ratio of the greater red length by the shorter red length gives us Phi.

## UN secretariat building

The UN Secretariat Building

The UN Secretariat Building was built by Le Corbusier who was greatly influenced by the Golden proportions and also was the creator of the Modulor Man.

The façade of the building can be approximately divided into three Golden rectangles stacked on top of each other with less than 2.2% error. Golden Ratios also have been employed to design the windows and curtain walls. Even the entrance which flaunts a colonnade is based on Golden proportions. The height to base ratio of the free space in between the columns is a Golden rectangle.

## CN tower, Toronto

CN Tower

CN tower is the world’s 7th tallest tower and free standing structure. The ratio of the total height of the building to the height of the observation deck is a Golden ratio.The ratio of the height denoted in white is till the observation deck and the rest is shown in blue.

Therefore, we see, from the time when people actually did not know the existence of this ratio till the time when they realized its ubiquitous existence, golden ratio has been subtly used. It was there back in the depths of history during the reign of the pharaohs and continued to exist vividly during the time of the Mughals and is still there.

# Architects who use golden Proportions in their works

## Mies Van der Rohe

Farmsworth House

Architect Mies had created Farmsworth House which is a vibrant example of modern architecture which is influenced by golden ratios. The proportions between the glass walls express golden ratios where the width to height ratio approximates 1.75. The side facade are three golden rectangles placed one after another.

## Le Corbusier

Villa Savoys

As is mentioned in the discussion of UN Secretariat Building, Le Corbusier as an architect was a believer of the aesthetic properties of Golden Ratio. Villa Savoys is another work composed by him which exhibits clear Golden proportions. The elevation consists of two Golden rectangles merged together. The rectangles share a common centralized square portion.

## Mario Botta

House by Mario Botta

Mario Botta had designed a lot of private residences in Switzerland keeping mind the inclusion of golden proportions. His house at Origlio shows clear divine ratios illustrated on its elevation.