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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.




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”.


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 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 (

[4] WIKIPEDIA. 2007. “Golden Ratio”. Retrieved June 06, 2018 (

[5] THE GOLDEN RATIO. “Le Corbusier”. Retrieved June 06, 2018 (

[6] ICON. “Modulor Man by Le Corbusier”. Retrieved June 06, 2018 (

[7] THE GOLDEN NUMBER. “The UN Secretariat Building, Le Corbusier and the Golden Ratio”. Retrieved June 07, 2018 (

[8] THE GOLDEN NUMBER. “Phi and the Golden Section in Architecture”. Retrieved June 06, 2018 (

[9] THE GOLDEN NUMBER. “Phi and the Golden Section in Architecture”. Retrieved June 06, 2018 (

[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 (

[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 (
lovell house interior

Interior Design, Color and Psychology

The philosopher Alain de Botton already said that we act and feel different at different places. Jung and Cooper Marcus also believed that renovating a house can change the ones that live there. Every detail of a house can have a deeper meaning that affect us from a conscious to an unconscious level.

According to Bachelard , even the lower drawer of a shelf, parts of the basement and parts of the attic has a meaning to us and help us to spatialize our mind, feelings and personality. By design the interior of our houses, we bring things from the outside world that has some meaning to us (like a photo of a loved person or a pan that we can use to cook) and put it on a place that is accessible for us. The easier that is for our body to access something, the easier it’s for us to mentally and emotionally access them, and the harder that is to physically access something, the deeper in our unconscious it’ll be.

One architect that knew how a house can affect those who lives inside of it were Richard Neutra. He was one of the first architects to attempt to create a house that could enhance its dwellers psychology. Influenced by the Freudian idea that repressed psychical energy could be unconsciously projected into the outside world, Neutra stared to believe that he could cure some of his client’s mental issues and neurosis by acting in their environment. For him, the architect should act as a doctor, seeing his clients as patients, making diagnoses based on psychological tests and prescribing architectonic and interior design ideas as prescribing remedy.

The most important work of Neutra is the Lovell House, a house built in 1927 – 1929 for Philip and Lea Lovell. The Lovells were a couple very interested on healthy culture and the impacts on architecture on it. They already had a house, the Lovell Beach House (1922 – 1926), designed by an architect that were specialized on architecture and health, Rudolph Schildler. However, on their new house, they decided to contract Neutra to build another health home.

lovel house

In this house, as in his others houses, Neutra used the language of modern architecture and design, but in his hands, that language gain a second meaning. The first thing we can perceive is the use of glass walls and glass corners, a material that is common in modern architecture because it brings delicacy and lightness to a room. However, to Neutra, glass is a material that can be used to organize the flow of psychological energy, by letting them flow from the outside view. A material that lets natural light enters the house, keeping it not only brighter, but also psychologically cleaner. And a substance that can prevent the dwellers to project their desires into parts of the house. For him, glass could prevent us to create new neurosis and having metal issues caused by a “bad” home design.

glass wall

Going more on the inside of the house, we can see that he used preferably neutral colors, like white, gray and brown. These colors enhance our perception of the form of an object, like the roundness of a table or the quadrature of a sofa. However, in Neutra’s interior design, the colors gain an extra meaning as, for him, they create fewer emotional attachments than a colorful room.

A critique to neutra’s approach and the use of color

Overdijk says that Neutra focus on creating an environment that prevents the client from creating attachments or project unconscious energy into parts of the design. His idea was to create a therapeutic house. However, in a search for a house sterilized from any attachment and projections, Neutra didn’t perceive that a house can cause a series of emotions that could also be part of a heath home.

As the psychological researches about the impact of color in our perception evolved, we started to understand how color can impact our lives in many and positive ways. According to color psychology, the branch of psychology that studies the impact of color on our perception, color can influence the taste of food and the effectiveness of remedies, working like a placebo would. The studies in color show us that every color carry a specific meaning that is either learned or biologically innate. As we perceive a color, the color itself causes us to evaluate our surrounding, exerting an automatic influence in ourselves and in our perception of our surroundings.

Color is often used in logo design to make us feel something or act in some specific way, as show on the image above. When we design the interior of a house, we can and should consider how the colors we use in the walls and the color of the furniture can affect those who will dwell in it. We yet don’t know if color can cure someone or even if we can design a therapeutic home, but we know that it can influence us in subtle ways, changing the way that we behave in certain environments.

Even if Richard Neutra didn’t know that color can have a positive effect on us, he was the first to understand that architecture and interior design can change those who dwell in it. His works opened a space to experience the impact that material, color and design has on us. Some of his clients qualify him as a genius, but others says that his glass houses make you feel striped, all observed, like being on the outside of the house, even knowing that you are on the inside.

[1] BOTTON, Alain de. 2008. The Architecture of Happiness (Vintage International). USA: Random House LLC.

[2] JUNG, C.G. 2011. Memories, Dreams, Reflections. USA: Random House LLC.

[3] MARCUS, Claire Cooper. 2006. House as a Mirror of the Self: Exploring the Deeper Meaning of Home. USA: Nicolas-Hays Inc.

[4] BACHELARD, Gaston. 2014. The Poetics of Space. USA: Penguin Classics.

[5] WIKIPEDIA. “Lovell House”. Retrieved May 10, 2018 (

[6] MID-CENTURY HOME. “Richard Neutra’s Lovell House: Modernist Perfection”. Retrieved May 10, 2018 (

[7] OVERDIJIK, Maarten. “Richard Neutra’s Therapeutic Architecture”. Retrieved May 10, 2018 (

[8] CRAEN, A.J.; ROOS, P.J.; VRIES, A. Leonard de; KLEIJNEN, J. 1996. “Effect of Colour of Drugs: Systematic Review of Perceived Effect of Drugs and Their Effectiveness”. BMJ (Clinical research ed.). 313 (7072): 1624–1626.

[9] THE LOGO COMPANY. “Psychology of Color in Logo Design”. Retrieved May 11, 2018 (

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 (

[2] Kyoto-Araki Komuten Sukiya-Japan. “Introducing Ko-Minka”. Retrieved April 05, 2018 (

[3] Tsunagu Japan. “Simple yet beautiful: Japan's traditional homes, kominka”. Retrieved April 04, 2018 (

[4] Евгений Арсенюк Pinterest Account. “Japanese roof frame”. Retrieved April 05, 2018 (

[5] Japanese Architecture and Art Net Users System. “Fusuma”. Retrieved April 05, 2018 (

[6] Wiki Architecture. “Ward W. Willits House”. Retrieved April 04, 2018 (


Article by HL Architects and Interior Design in Durham