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## The Golden Ratio in Design and Architecture

Mathematics and Architecture are like two peas in a pod. In the past, Architecture has done great things for geometry. In measuring the land they lived on, it was people’s need to build their buildings that caused them to first investigate the theory of form and shape (Freiberger, 2019). Ancient Greeks studied Phi and applied it in building structures by calculating the relationship between the width and height of a building, the size of the portico, and the position of columns for support (Akhtaruzzaman and Shafie, 2011). The Golden Ratio and its presence in Design and Architecture became a foundation of our modern world.

In the book entitled The Golden Ratio: The Story of Phi by Mario Livio, it was asserted that the fascination of the said Golden Ratio was not constricted to mathematicians as even primordial and contemporary architects have taken an interest and are contemplating its ubiquity. Thus, the different aspects of the Golden Ratio (ϕ) can be observed in both ancient and modern architecture as it has inspired several artists, to build structures close to perfection for distinctive purposes whether as an offering to the Gods or for the use of important people such as a significant person or even the administrative workforces.

## Golden Ratio in the Pyramid of Khufu

A pyramid built for Pharaoh Khufu 4,707 years ago in an Egyptian civilization applied the golden ratio, according to popular belief. Although several specialists have measured the height and the side of the Khufu Pyramid, the average results were 230.478m at the side, and the average height is 146.726m. Get the average height and side and divide to calculate the ratio, the ratio becomes 1.5708 which is close to the golden ratio ϕ=1.61818. The table shown below shows the measurements of the pyramid from the year 1840 until 2012.

The surveyed dimensions of the Pyramid of Khufu became evidence that early civilizations used the concept of golden ratio in structure building.

## Golden Ratio in the Parthenon

In the ancient Greek civilization, the Parthenon is one of the best-known buildings in terms of architectural design. This building was originally made to serve as a sign of dedication to the Goddess Athena. Proportions of the golden ratio can be visible along the structure and dimensions of the Parthenon.

This image illustrates the outside or the exterior of the building. In the photo, there are highlighted blue, yellow, and green lines that form rectangles. The longer parts are represented by the blue lines. The shorter parts are represented by the yellow lines. The green lines represent the entire width and the length. When the ratio of the lengths of the yellow segments and the blue segments are derived it can be equal to the ratio of the lengths between the green segments and the blue segments. If you get the ratio of the total width (31.814) and the longer part (19.69) it will result in 1.6157 close to the golden ratio.

## Golden Ratio in Taj Mahal

Known as one of the famous UNESCO World Heritage Sites, the ivory-white colored Taj Mahal also employs the Golden Ratio, specifically the phi-based proportions that can be found in the foundational aspect of the exterior outline like the relation of the width of its arch to the width of the structure and the rectangular frame bordering the windows.

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To prove the phi-based proportions, according to an article in the New World Encyclopedia, regarding the dimensions of the mausoleum, it was stated that the width of the arch is 115 feet, meanwhile, the width of the structure is 180 feet. Upon calculating the ratio, it was found that the ratio is 1.565 which is close to the value of Phi (ϕ) which is equivalent to 1.61818. In addition, measurements done by Indian architects: Richard Baraud and Ebba Kochh in 2006, had proven that the said structure equips golden rectangles, this was further supported by the study of Sanjay Surya who analyzed the proportion and symmetry of the dimensions of the Taj Mahal.

## Golden Ratio in Notre Dame Cathedral

Notre Dame Cathedral is a famous Gothic church found in Paris, France which was constructed in the beginning of 1163 and completed around 1345. According to Frederick Macody Lund, a Norwegian historian who explored the geometry of various Gothic architecture, the design of this cathedral follows the concept of the golden ratio. A number of its main significant parts such as the columns and arcs exhibit an ideal proportion that approximately meets the golden ratio values.

There are four (4) golden ratios in Notre Dame Cathedral as depicted in the photo. Each of the units that yield a value of 1:0.168 is represented by the red and yellow line segments, namely, The Portal and the Rose Window, The Rose Window and Arcade, The Towers, and The Arcade level.

## UN Secretariat Building and the Golden Ratio

One of the most notable and distinguishable paradigms of modern architecture equipping the Golden Ratio is the UN Secretariat Building located in New York, United States which was completed in the year 1961. According to a study, it was stated that the final blueprint of the said structure was based on Le Corbusier drawings which happen to be a Swiss-French architect and painter who had generated a proportional system which was named the Modulor, incorporating the Golden Ratio in the measurement of buildings.

To prove that the Golden Ratio is indeed applied to the dimension of the building, it was stated by Gary Meisner, author of the book “The Golden Ratio” and owner of GoldenNumber. Net, that the measurements of the dimensions of the structure were 1130 to 698, wherein once divided to determine the ratio would be equivalent to 1.618, which happens to be the Golden Ratio.

## Conclusion

The Parthenon is one of the best-known buildings in terms of architectural design. It was the center of religious life in the Greeks, dedicated to the Goddess Athena, whom the people of Athens considered as their patron. Mostly a sculpture manifesting the Athenian Imperium at its full power and sovereignty. The Parthenon embodies an extraordinary number of architectural refinements, which combine to give a sculptural appearance to the building.

The application of the golden ratio to architecture has paved the way for architects to impart a sense of balance to a structure. It’s used as a basis for the definition of the beauty of architecture. Architecture is perceived as pleasing and beautiful if it follows the divine proportion. In the past, the Parthenon in Greece, the Great Pyramid of Giza in Egypt, and Notre Dame Cathedral in Paris were structures that used the golden ratio (Salingaros Nikos, 2011). In the present time, the United Nations Headquarters in New York City, and the Museum of Modern Art in San Francisco are structures that use the golden ratio as well ( Bahadur and Thapa, 2018).

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