# The Remarkable Golden Ratio - Part 2

Part 2 of The "Remarkable Golden Ratio" Explains how the ratio influences human perception, and delves into the uses that many architects have found for including the ratio when proportioning their work in order to make it more appealing to the human eye.

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## Influence on Human Perception

The golden proportion, as it is so prevalent in our environment, has been drilled into the human subconscious so integrally that we now expect to see it not only in organic matter, but in inorganic, human, creations. Using the golden ratio to scale the individual elements in our creations is nothing new; it’s been going on for centuries – possibly since the very beginning of time.

Despite unknowingly practicing it in our work so often, we are still fairly new to the idea of actively proportioning our tools and structures to this natural algorithm provided to use by nature, but there are a few people who pursued the belief that creating and keeping to a set of proportioning rules which take into account the golden ratio would benefit designers and architects by making the user more naturally comfortable with the creations.

## The Golden Ratio in Architecture

Swiss Architect Charles-Édouard Jeanneret (known commonly by the pseudonym Le Corbusier) used the golden ratio the form his** “**modular,”system for the scale of architectural proportion. He thought that mathematically modeling architecture, (and other products to be utilized by human beings) it would bring more comfort and pleasure to the user In order to produce this standardized architectural scale, in the scale Le Corbusier segmented a man of average height with a raised arm, and with a naval height of 1.13 meters according to the golden ratio. The raised arm made the entire figure’s height exactly twice that of the naval height.

Le Corbusier utilized this Modular scale and the Golden Ratio in many of his famous works, including Villa Stein, Villa Savoye, and Notre Dame (Paris). He intended for his Modular to become the standard for international design and architecture, and though it did not see the complete success that he vied for, it is still often studied by architects worldwide. He intended to have helped standardize international architectural and product design for the comfort of the user. He intended everything from ceiling height to doorknob level

to be standardized, leaving the world with what he thought would be a more aesthetically pleasing and comfortable living and work environment.

Le Corbusier was not the first architect to utilize the golden ratio in his designs though, in fact, there were many different architects to utilize the golden ratio in architecture – whether or not intentionally is not exactly known, as this ratio is seen in constructs predating 2000 B.C. – particularly in the Great Pyramid of Giza. Built around 2560 BC, the length of each side is 756 feet, and the height is about 481 feet. So, the ratio of the base to the height is: 756/481 = 1.5717…. remarkably, that is less than three percent difference from the golden ratio.

The Parthenon is another example of ancient architecture which can be found to have elements displaying the Golden Ratio. Just from a view of the front of the Parthenon, one can notice several aspects which are proportioned according to the golden ratio. The width to the height of the building, the height of the roof to the height of the building’s columns, and the two separate sections of decoration below the roof are all exactly proportioned to the ratio.

The Taj Mahal’s (India - 1648) doors’ and windows’ location and size are also proportioned according to the golden ratio. Today, this is continued in many modern examples of architecture, such as in the United Nations building, regardless of their individual architects and design style.

## The Divine Proportion in Art

The Vitruvian man, by Leonardo Da Vinci had a massive effect on our perception of the golden ratio, and eventually led to the Le Corbusier creating his modular system for architecture as well as many other studies into how proportions affected how we looked at things. In the world of art, there were many great artists who followed similar ideals in their own work.

Da Vinci himself featured the “Divine Proportion” in many of his paintings as well. The famous and mysterious painting*Mona Lisa* is often shown divided into golden rectangles by people studying his work. His illustrations in *De divina proportione* showed his view that the human body is proportioned to exhibit the golden ratio, which leads most scholars studying his work to believe his paintings follow this formula.

**Salvador Dali**, another famous face in the art world, paid particular attention to the golden ratio while painting *The Sacrament of the Last Supper*. The canvas itself is already a golden rectangle, and many of the elements of the painting are made to appear to fit within the golden ratio.

Some other examples can be seen in publishing as well. Page layout often utilizes the Golden Ratio to proportion page elements correctly so that they are pleasing to the eye. Many company logos, for example the newest **Pepsi** logo, are made to be aesthetically pleasing by utilizing the ratio.

After seeing the golden ratio occurring so often in the human body and nature, it soon became obvious to product designers and engineers that this ratio should be included in the tools people use every day. Some very distinct examples of this can be found within the design of musical instruments. For example, the Stradivarius violin holds extremely true to this. Antonio Stradivari produced violins which are claimed to have produced a sound quality that is impossible to reproduce (One theory states this may be because of a climate change which resulted in extraordinarily dense wood), and Stradivarius used the golden section in the design of these master violins. The body of the violin when compared to the entire length were compared create a ratio of 1 to 1.618.

Another example can be taken in a less material product, in the form of a web page. Many web designers use the golden ratio in the design of their sites in order to create the appearance of a more user friendly environment. Twitter, a social media site with millions of users who visit the site every day, has incorporated the Golden ratio in its design. Twitter’s creative director at the time, Doug Bowman, provided a picture of the new twitter layout showing the use of the Fibonacci spiral in the design of the user interface which is the main part of the site, stating that the company “didn’t leave those ratios to chance.” They used the Golden Ratio, simply because it is a ratio that the human eye is trained to recognize as something comfortable and familiar.

Many more examples are apparent in everyday product design if one looks closely. For example, the typical credit card’s width and length when compared to one another have a ratio very close to 1 to 1.618. Similarly, the IPod classic’s width and length are designed to have the same ratio. Every subsequent IPod design has been manufactured to meet that ratio, as the classic’s sales nearly tripled over the previous model, the Nano, which did not use the Golden Ratio in its design. In the same design process that resulted in Pepsi making their logo match the golden ratio, the company made their bottle designs constrain to the ratio as well.

## The Remarkable Golden Ratio Conclusion

In conclusion, the use of the mathematical model of the Golden Ratio has brought us an understanding on relationships within aesthetics and human proportion as well as the relationships which define all of biological life. It has been known to us by many different names, from the Golden Mean, to the Divine Proportion. Denoted by modern mathematicians as the letter phi, it has properties that occur remarkably often in the natural world and are deeply rooted in human perception of beauty. In ancient history, architects, inventors, and artists seemingly unknowingly used these invisible rules of proportion in their designs. Thousands of years later designers, architects, and artists are trying to utilize these rules of proportion in everyday objects and structures. From the great pyramids, to the United Nations building, to credit cards, to IPods and Twitter, the Golden Ratio is used worldwide as a medium for conveying good design to the people who are there to see it.

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