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Golden and Silver Ratio in Architecture

Among history, artist, designers and architects used some mathematical ratios and equations to help them with their work. Between those ratios one got famous in western tradition and other got famous in the East.

The one that got famous in the West is called golden ratio. This mathematical ratio is believed to be some kind of divine proportion (as called by Paciolli and Da Vinci in their “De Divina Proportione”[1]) that regulate the form of natural things and the human body. We can see the use of the golden ratio in the Euclid’s Elements[2], in the Renaissance art and architecture and even in modern architecture. The other that got renowned in East is called silver ratio or Japanese ratio (“Yamato-hi” for Japanese). They used the silver ratio in Buddha statues, in architecture and in anime characters, like Doraemon.

 Doraemon

Doraemon[3]

 

Each of those ratios are defined by a geometrical relation. The golden ratio is defined by dividing a section of line in two parts, part a and part b, in a way that the total length of the line (a+b) divided by the greater segment (a) is equal to the division between the two new segments (a and b) as we can see in the equation in the side and the image below, resuming: . The value of this ratio is always an irrational number that we round to 1.618. The silver ratio is quite similar, however, instead of being the total length of line (a+b) divided by the greater segment (a) that is equal to the division of the between the two segments (a and b), it’s the double of the greater segment added by the smaller segment (2a+b) divided by the greater segment (a) that is equal to the division of the between the two segments (a and b), resuming: . The value of this ratio is or, rounded, 1.414.

 

gold and silver ratios

Golden and silver ratio line[4]

 

Le Corbusier and the Golden Ratio

The famous architect Le Corbusier was one of the architects that believed and used the golden ratio in his works and advocates for its application in everyday life. To endorse the use of this ratio in any type of architectural work, interior design or product design, and inspired by Leonardo da Vinci’s Vitruvian Man, he created what he calls “Modulor”.

modulor

Image 3 – Modulor[5]

a le Corbusier sketch

A Le Corbusier’s sketch with relation between heights and the Modulor with distances in cm[6]

 

The Modulor used the golden ratio to calculate relations between parts of the human body. For this, he used, for a base, a six-foot tall man (182 cm) with one of the arms raised. However, preserving the adequate proportions, anyone could transpose it to make it work with people that are taller or smaller than the one Le Corbusier used in the Modulor. Based on this, an architect or a designer could know the best height and angle to put or to better design some furniture, doors, windows and even door handles.

One example of Le Corbusier’s architecture project designed with the help of the golden ratio is the United Nations Secretariat Building. In this building design, Le Corbusier worked with Oscar Niemeyer. Niemeyer is a famous Brazilian architect that were heavily influenced by Le Corbusier since he came to Brazil in 1935 to help Lúcio Costa (another Brazilian architect and also professor at Rio de Janeiro Federal University) and his students to design a Modernist building to the local government and teach Modernist urbanism to them. Being Niemeyer one of Costas’ student, he also learned a lot from Le Corbusier. After this, Niemeyer developed his own language, but still was influenced by what he learned from Le Corbusier.

On the building they designed together, we can see golden rectangles in the façade. We also can see the golden proportion being used in the window configuration of the building and, according to the website The Golden Number[7], we can also see the use of the golden ratio in the front entrance of the building and in the interior floor plans.

UN Secretariat Building and Golden Rectangles[8]

 

UM Secretariat Window Configuration[9]

 

The silver ratio in japanese architecture

In Japan they don’t believe much in the use of the Golden Ratio on design. To them, the use of the Silver Ratio create a design that is more beautiful and serene than the Divine Proportion. Since the Silver Ratio derives a smaller proportion (1.414), the objects that are done based on it are closer to a square than the ones done based on the western proportion.

One famous example of the use of the silver ratio is the Horyu-ji Temple in Ikagura, Nara Prefecture, Japan. This temple is a Buddhist temple with one of the oldest wooden building of the world. As we can see in the image below, the relation between the ground floor of the left building and its second floor is 1.414, and the relation between the first roof of the right floor and its last roof is also 1.414, the valor of the silver ratio.

 

Horyu-ji

Horyu-ji Temple with Pagoda[10]

 

As happened with our ratio, they were more used in the past, but we can also see contemporary works that used it, like the Tokyo Skytree. The Tokyo Skytree is one of the world’s tallest tower, having two observatories and a digital broadcasting antenna at the top. According to the image bellow, we can see a silver ratio relation between the distance of the floor to the second observatory and the distance between the floor and the top of the tower.

 

tokyo sky tree

Tokyo Skytree[11]

 

Today, neither of the two proportions is seen as a divine relation or a design rule, but we can still see projects that used them as a way to create a guidance or a feeling of harmony and serenity.

 

[1] PACIOLLI, Luca; DA VINCI, Leonardo. 2014. De Divina Proportione (On the Divine Proportion): Facsimile in Full Color of the Original Version of 1509. USA: CreateSpace Independent Publishing Platform.
[2] EUCLID. 2017. Euclid’s Elements. Kindle edition. USA: LRP.
[3] EPIC RAP BATTLES OF CARTOONS WIKI. “Doraemon”. Retrieved June 07, 2018 (http://epic-rap-battles-of-cartoons.wikia.com/wiki/Doraemon).
[4] WIKIPEDIA. 2007. “Golden Ratio”. Retrieved June 06, 2018 (https://en.wikipedia.org/wiki/Golden_ratio).
[5] THE GOLDEN RATIO. “Le Corbusier”. Retrieved June 06, 2018 (https://divinumproportione.weebly.com/le-corbusier-and-modulor.html).
[6] ICON. “Modulor Man by Le Corbusier”. Retrieved June 06, 2018 (https://www.iconeye.com/opinion/icon-of-the-month/item/3815-modulor-man-by-le-corbusier).
[7] THE GOLDEN NUMBER. “The UN Secretariat Building, Le Corbusier and the Golden Ratio”. Retrieved June 07, 2018 (https://www.goldennumber.net/un-secretariat-building-golden-ratio-architecture/).
[8] THE GOLDEN NUMBER. “Phi and the Golden Section in Architecture”. Retrieved June 06, 2018 (https://www.goldennumber.net/architecture/).
[9] THE GOLDEN NUMBER. “Phi and the Golden Section in Architecture”. Retrieved June 06, 2018 (https://www.goldennumber.net/architecture/).
[10] FANCLIP. “キティーちゃんの顔バランス。そうだったのか!!「白銀比」「黄金比」の話”. Retrieved June 08, 2018 (https://www.fanclip.jp/blog/archives/614)
[11] FANCLIP. “キティーちゃんの顔バランス。そうだったのか!!「白銀比」「黄金比」の話”. Retrieved June 08, 2018 (https://www.fanclip.jp/blog/archives/614)

Frank Lloyd Wright, the Willits House and the Traditional Japanese Architecture

The Willits House is a project made by Frank Lloyd Wright, one of the important architects of the 20th century. According to the Frank Lloyd Wright Building Conservancy, “In 1991, the AIA [The American Institute of Architects] named Wright the greatest American architect of all time”[1]. Besides not being his most famous work, the Willits House express Wright’s interest in the traditional Japanese architecture and in the simple way of living.

Wright’s interest in Japanese art started on the late 1880s, when he started to work as an art dealer as a side job, selling Japanese woodprint blocks to his clients. In 1905, when he decided to make his first trip outside of America, he decided to visit Japan, spending two months touring natural and historical landmarks. In January of 1917, Wright took a residence in Tokyo to work on projects in Japan. Apart from being designed in 1901, before his first trip to Japan, the Willits House received a lot of influences from the traditional Japanese house style.

Traditional Japanese Style

The Japanese traditional style was an architectural design that took place before the modernization made in the Meiji era (1868-1912), an era that Japan decided that it should modernize its architecture and engineering to become an industrialized country. This style is characterized by its feeling of simplicity and serenity, the attention to details, the use of wood structure and the use of wood and paper panels as walls and doors.

 

Minka in Kyoto [2]
The traditional Japanese houses are called minka, kominka or ko-minka. These houses are now slowly disappearing[3], partially because they are made of a very flammable material and partially because they aren’t appropriate for the current Japanese lifestyle. Nevertheless, they were very common in the Japan that Wright knew and visited.

Japanese roof frame [4]
To make these houses, the Japanese builders used a carpentry technique that made possible to build a house without the use of nails, with just perfect fits between wood pieces and mooring pieces together. This way of build makes it necessary to have attention to every detail of every piece used in the construction of the house so they attach together strongly.

A minka also utilizes sliding screens that worked as doors and walls. These sliding screens are called fusumashouji or fusuma, for short[5], and they can be used, when open, to turn a space wider or, when closed, to turn a room more private. These fusuma are made of wood and paper. They can be made from a very thin paper, letting light enter the house or the room, or from a very thick paper. Those paper can receiver a pure color or even some artistic painting

Willits house and its relation to Japanese traditional style

The Willits House is a house that Frank Lloyd Wright designed in 1901 for Ward W. Willits. This house received a lot of influence from the Japanese minka that we saw here before. The first characteristic that we see, analyzing the side view of the Willits House, is the white color on the wall and the wood framing the windows, mimicking the serenity found Japanese architecture and the fusuma that works as the door and wall of the minka house. We also can see a large eaves on the top of the building that are common on Japanese traditional architecture.

Floor plan

Dining room [6]
Going inside the house, we see a lot of wood frames working as structural element, as also a way to mimic fusumas, or as way of incorporate glass to make some rooms feels more permeable. Wright also used panels made of wood and glass as doors, using the glass as the Japanese use paper to fill their fusuma. We can also see that the rooms are spacious and very clean, helping to creating the feeling of serenity that are common on traditional Japanese architecture.

Wright was very interested in the Japanese culture and architecture. In this project, he could experiment some ways to incorporate his passion on the american house and in his architecture design. As we saw, this project is inspired in the Japanese minka, but also has adaptations made to work in the american style and way of living, like the use of glass and western wall material, instead of paper. These experiments were futher used on more of Wrights projects, defining part of the Praire House Style and the overall Wright style.

[1] Frank Lloyd Wright Building Conservancy. 2007. “About Frank Lloyd Wright”. Retrieved April 04, 2018 (https://www.savewright.org/who-we-are/about-frank-lloyd-wright).
[2] Kyoto-Araki Komuten Sukiya-Japan. “Introducing Ko-Minka”. Retrieved April 05, 2018 (http://sukiya-japan.com/minka/index.html).
[3] Tsunagu Japan. “Simple yet beautiful: Japan's traditional homes, kominka”. Retrieved April 04, 2018 (https://www.tsunagujapan.com/simple-yet-beautiful-japans-traditional-homes-kominka).
[4] Евгений Арсенюк Pinterest Account. “Japanese roof frame”. Retrieved April 05, 2018 (https://i.pinimg.com/originals/4a/f6/1e/4af61e02575a4c49430837c947396764.jpg).
[5] Japanese Architecture and Art Net Users System. “Fusuma”. Retrieved April 05, 2018 (http://www.aisf.or.jp/~jaanus).
[6] Wiki Architecture. “Ward W. Willits House”. Retrieved April 04, 2018 (https://en.wikiarquitectura.com/building/ward-w-willits-house).

 

Article by HL Architects and Interior Design in Durham

Architecture History: Skyscrapers Of The Past

Humanities incessant fascination with defying gravity is nothing new. It has existed throughout time and man has been in a constant battle with himself in the pursuit of building higher and higher skyscrapers. It has been a non-stop cycle wand this has led to the definition of skyscrapers to be continuously redefined through the passage of time.

Advancement in technology has enabled man to redefine the skyscraper benchmark over and over again. But if you stop for a moment to consider that skyscrapers have existed in form or another throughout history and that it is something that we share with our predecessors.

Let’s take a trip down the memory lane and let’s look at some of the skyscrapers from the history of civilizations.

 

La Venta Pyramid, La Venta

900 BC | Height: 34m-110ft

Today, if you visit the city of La Venta, located in Tabasco, Mexico, it will seem like any other city. But this is no ordinary city, it was once the capital of the great Olmec civilization and the pyramid of La Venta was truly a wonder of its time. It was the central building of the city that stood in all its might leaving spectators spell bounded.

The most interesting fact is that the pyramid of La Venta was actually a rectangular pyramid with inset corners and stepped sides. This great building was made entirely of clay and such had been its might that it has withstood 2500 years worth of corrosion.

 

La Danta Temple, El-Mirador

300 BC | Height: 72m-236 ft

If you are asked to sum up the Mayan Empire in a few words, you can safely answer – La Danta Temple.

A stone building constructed with stone-age tools, this iconic temple speaks volumes about the greatness of Mayan Empire. In its glory days, it was the pride of the city of Mirador, towering over the central Acropolis and main city plaza.

 

Pyramid of the sun, Teotihuacan, Mexico.

100 AD | Height: 71m-233ft

The third skyscraper on the list is another pyramid, which isn’t a surprise as pyramids were the structure of choice in the past.

The Pyramid is situated in the ancient city of Teotihuacán, Mexico and is the 3rd largest pyramid in the world. It is amongst the best tourist attractions in Mexico City, leaving visitors in awe because of its sheer size.

It is a common misconception that the Pyramid of the sun is an Aztec temple. However, this is incorrect as this masterpiece was constructed by the Teotihuacans, which existed at a much earlier time. Unfortunately, not much is known about the Teotihuacans and hence, the purpose for which the Pyramid of the Sun was built has been a subject of a lot of debate.

 

Step pyramid, Saqqara

2650 BC | Height: 62m-203 ft

Though pyramids have been constructed by civilizations across the globe, however, when it comes to these structures, the country that comes to mind instantly is Egypt. It can be safely said that pyramids are the most famous structures of Egypt and in this regards, let’s take at look at one of the most prestigious pyramid.

Commonly known as Step Pyramid, the Pyramid of Djoser is considered to be the first Egyptian pyramid. It isn’t a surprise that the appearance of this pyramid is quite different from the pyramids built later.

Located in the Saqqara necropolis, the Step pyramid was built during the Third dynasty for the burial of Pharaoh Djoser. It is considered as the earliest large-scale cut stone construction. The pyramid stood 62 meters tall, with a base of 109 m × 125 m and was clad in polished white limestone.

The construction of the step pyramid was a pivotal step in the history of Egypt as it led to the ambitious pyramid construction program that ultimately led to the construction of Great Pyramids at Giza.

 

Colosseum, Rome

80 AD | Height: 49m-160 ft

Moving on from pyramids, let’s take a look at an architectural wonder that is regarded as one of the most popular tourist destinations in the world – The Colosseum.

It is without a doubt that the Colosseum is the most recognizable classical building in Rome. It was constructed 2,000 years ago and has been subject to a lot of damage over the years. Despite the fact that this structure has been affected by excessive damage like being abandoned, pillaged for building materials, destroyed in numerous earthquakes, this structure has survived the test of time and still stands today.

The actual name of the Colosseum is Flavian amphitheater. However, it became to be known as the Colosseum as it gained immense fame because of the colossal statue of Nero. When it was built, it was the first permanent and the largest amphitheater in the Roman Empire. It measured around 620 by 513 feet (190 by 155 meters) and could accommodate 60,000 seated and 10,000 standing spectators.

The distinctive feature of the Colosseum was that it consisted of a freestanding structure composed of concrete and stone. This was unique as amphitheaters were traditionally dug into the hillsides in order to provide the required support. Furthermore, the structure consisted of around 80 entrances, which means that even when fully packed, all the people inside the Colosseum could easily leave in a matter of minutes.

 

Lighthouse of Alexandria

280 BC-1323 AD | Height : 137m-450 ft

The Lighthouse of Alexandria, also called the Pharos of Alexandria, is one of the seven wonders of the ancient world. It was a ground-breaking technological achievement and become the model for on which all lighthouses have been built ever since.

The lighthouse of Alexandria was constructed in the 3rd century BC and was more than 350 feet high, making it one of the tallest man-made structures for many centuries.

Unfortunately, the lighthouse of Alexandria was damaged significantly during the 14th century when the region was hit by major earthquakes.

 

Article by HL Architects Durham