## Sunday, August 17, 2008

### Entry Three - Being an explanation on the uses of the Golden Ratio.

The easiest way to understand how the many ways golden ratio is used to show historical examples. The best known and earliest example that I have come across is the Parthenon.

The Parthenon, for those of you not in the know, is an Ancient Greek temple to the Goddess Athena. It was built in the 5th Century BC and is often considered the apex in the development of the Doric order.[1] Looking at the picture below you can see just some of the divisions based on the Golden Ratio that were used in the design of Parthenon.[2]

The image below was taken from a great website on the golden ratio by math teacher Radoslav Jovanovic. The site discusses the influence of the golden ration and fibonnacci numbers in all aspects of art and science. Interesting read if you have the time.

The Golden Ratio’s influence and importance on architecture did not end with the Ancient Greeks. In fact quite the opposite happened. Vitruvius, the Roman architect and writer, wrote in depth about the various canons of proportions used by the Greeks in their Doric, Ionic and Corinthian architectural orders.[3] According to Vitruvius these architectural orders led the Greeks to a greater understanding of the proportions of the human body. In turn, this information led Vitruvius in defining his own canon of proportion, known as the Vitruvian Man. This system of proportion later made famous in a drawing by Leonardo DaVinci, approximates the golden ratio.

I would be remiss if I did not mention that there is a lot of controversy surrounding the finding of the Golden Ratio in works of art and architecture. The fact that the Golden Ratio is an irrational number, makes it very difficult to use if not impossible to use. Generally, those using the proportion in their work will use an approximation, using rational numbers that make it easier to create even dimensions. There is a great article, or more precisely a blog entry, about the “cult of the golden ratio” and how a lot of the facts and historical uses of the proportion are just plain wrong.[4] It is a highly entertaining read but is also contains great research and citations that the author, John Hardy, uses to back up his argument.

Yet despite it’s modern detractors the Golden Ratio had a huge influence throughout the history of art and architecture, most notably during the Renaissance. You could say that the “golden age” of the golden ratio was during the Renaissance as a body of work on the aesthetics of the golden ratio was developed.[5] One of the most important works of this time was De Divina Proportione by a Franciscan friar named Luca Pacioli.[6] This three volume work was published in 1509 and explored the mathematics of the golden ratio and contained illustrations by Leonardo DaVinci. I tried to find a copy of this book and it is impossible to find. There are a few out of print versions that I found being sold by used bookstores and the like but none of those were less than \$100. As for online versions of the book, none are in existence. Apparently no one has gotten the impetus to translate from Latin or Italian to html.

Assuming the Golden Ratio is as big a deal in the Renaissance as many claim, it is no surprise then that Leonardo DaVinci is said to have used the golden ratio extensively in his work. His most famous work, the Mona Lisa, is said to be composed of several golden rectangles.[7]

There are several websites that allow you to draw golden rectangles over the painting in an attempt to explore DaVinci’s composition.[8] Yet this view of DaVinci using the golden ratio is widely disputed as there is no concrete evidence nor writings by DaVinci that can confirm or disprove the hypothesis.

Perhaps less well known but no less contested is the use of the golden ratio by Jan Vermeer. In her book Composition, author Sarah Kent discusses the use of the golden ratio by Vermeer in his painting The Artist in His Studio also called The Art of Painting.[9]

Vermeer being of the Northern Renaissance tradition creates a lot of atmosphere and focuses on soft lighting but also puts a lot of symbolism in his work. Kent explains what each of the objects in the painting mean, from the symbology of what the model is wearing to the significance of the tapestry in the background. What does symbolism have to do then with the golden ratio? Well, nothing and everything. Kent goes on to explain that by charting the placement of key items in the work you find that their position is governed by a network of lines based on the golden ratio.[10] “The map, chandelier and easel like on golden ratio divisions; the rectangle framing the artist and model is defined by golden ratio lines that follow the edge of the map, define the position of the curtain, and support the artist’s elbow as he paints the picture within the picture.”[11]
Kent suggests that because his arm actually rests on a golden ratio line means that Vermeer saw the ratio as one of the mainstays of painting. You can see this painting and all of Vermeer’s work at Essential Vermeer. It is a really awesome website that not only has great images of his work but you can also roll over the image and captions pop up explaining the symbolism of objects in the work as well as historical notes.

As objectivity in art moved to the more abstract and expressionistic, the use and study of the golden ratio gradually died down. However, there were still some proponents of its use. Salvador Dali’s The Sacrament of the Last Supper is painted on a canvas that is a golden rectangle and the picture contains a dodecahedron, with edges in golden ratio to one another.[12]

[1] http://en.wikipedia.org/wiki/parthenon
[2] http://milan.milanovic.org/math/english/golden/golden.html
[3] http://en.wikipedia.org/wiki./vitruvius
[4] http://www.laputanlogic.com/articles/2005/04/14-1647-4601.html
[5] http://www.en.wikipedia.org/wiki/golden_ratio
[6] Ibid
[7] Ibid
[8] http://demonstrations.wolfram.com/monalisaandthegoldenrectangle

[9] Sarah Kent, Composition (New York: Dorling Kindersley, 1995), 32-33.
[10] Ibid, 33
[11] Ibid
[12] http://en.wikipdeia.org/wiki/golden_ratio