Entry Four - Being an introduction to perspective and more of those definitions

Few people would disagree that the Renaissance was one of the greatest periods of artistic achievement in the history of mankind. So many artistic discoveries and methods were made during this time that its influence on contemporary artists is immeasurable.

In my own personal work I am continually floored by how closely what I do and the methods in which I am taught parallel those of the great Renaissance masters. From foundation arts to graphic design and illustration it seems everything I do has some basis or beginning in the Renaissance.

As a student of sequential art the lineage of what we do as artists is clearly traceable back to the time of the Renaissance and beyond. Yet one our greatest tools in telling stories was discovered during the Renaissance and has not changed all that much. It is called Perspective and for many beginning and advanced artists it is one of the most difficult things to learn, but its power to represent the three-dimensional world on a two-dimensional surface cannot be denied.

We have a saying in sequential art that you can draw your figures as cartoony and unrealistic as you like, but if you don’t have believable backgrounds and environments then you can sell the image. The key to selling the image is perspective.

So what is perspective?

According to the Thames & Hudson Dictionary of Art Terms perspective is the method of representing a three-dimensional object, or a particular volume of space, on a flat or nearly flat surface.[1] The Thames & Hudson Dictionary goes on to classify the two major types of perspective, atmospheric and linear.

Atmospheric perspective is a means of representing distance and recession in painting, based on the way the atmosphere affects the human eye. Outlines become less precise, small details are lost, hues become noticeably more blue, colours in general become paler, color contrasts are less pronounced. These effects had already been observed by Fresco painters of the Roman period but on the whole are most typical of Naturalistic European landscape painting from the 16th century onwards. There is also an attempt at atmospheric perspective in Japanese ink painting.
Centralized perspective is linear perspective in which the eye is drawn towards a single vanishing point in the centre of the composition, usually on the horizon line. Linear perspective uses real or suggested lines converging on a vanishing point or points on the horizon or at eye level, and linking receeding planes as they do.[2]

What a mouthful! It is ironic how lengthy and difficult it can be to describe or define perspective and yet show someone a picture using perspective and they get it immediately!



[1] Edward Lucie-Smith, The Thames and Hudson Dictionary of Art Terms, 2nd. Ed. (London: Thames and Hudson Ltd, 2003), 166
[2] Ibid

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

Entry Two- The Golden Ratio, being an attempt at defining this mysterious number.

One of the things that is discussed in class is the concept of disegno. Literally translated, it is the Italian word for design. However during the Renaissance, disegno was a concept or theory that artist would try to achieve. For example if you were to say an artist has good disegno, you would be referring to the conceptual/theoretical properties of their work. Things like alignment of elements, leading diagonals, proportion, symbolism, etc would all lead a work to having good disegno.

One of the fundamentals to good disegno and design are composition and layout. As a graphic designer before beginning any project, before anything gets created, the composition of the work, the layout, the grid structure is considered first. This is certainly not a new idea either as composition has been used with great effect by just about every major successful artist throughout history.

In my study of composition in my own work and through classes one concept kept popping up that intrigued me: the Golden Ratio. Through many of my design classes as well as my foundation studies there have been lectures that made reference or were about the Golden Ratio (aka the Divine Proportion, Golden Proportion, Divine Ratio, Golden Number, etc.). Now it may be due to my own lacking mental faculties but I have never really understood what they were talking about, let alone how to use this great mysterious concept.

I don’t think I am alone in this ignorance either. Any mention of the Golden Ratio almost assuredly brings with it a deluge of complex math that most art students have spent the better part of their life avoiding. The ironic thing is that I often get the feeling my teachers don’t understand it either. Essentially they are lecturing on things they don’t fully comprehend so how can I possibly understand them? But my gut tells me that this isn’t something to be ignored. If this number, ratio, proportion shows up in the work of all these great master’s then surely there must be something to it.

So what is the Golden Ratio?

The Oxford Concise Dictionary of Art Terms offers a very thorough definition, which ironic considering the dictionary's title. Never the less, it begins by describing the Golden Ratio as such:

A harmonic proportional ratio though to have orginated in the circle of Pythagoras (6th century bc) and which was discussed by both Euclid and Vitruvius in their writings. A straight line or rectangle is divided into two unequal parts in such a way that the ratio of the smaller to the greater is the same as that of the greater to the whole. It cannot be expressed as a finite number but an approximation is 8:13 or 0.618:1. With the invention of algebra it became possible to express the ratio as Phi which equals 1 plus the square root of 5 divided by 2.[1]

The dictionary goes on to say:

The Golden Section was though to have great inherent aesthetic value and was much studied during the Renaissance, especially by the mathematician Luca Pacioli, a close friend of Leonardo Da Vinci, and Piero della Francesea. In Pacioli's book Divina Proportione (1509), illustrated drawings by Leonardo, the Golden Section is described as this "divine proportion" and Pacioli endeavors, in the true Renaissance fashion, to combine the knowledge of antiquity with the Christian faith by claiming that the ratio of the Golden Section is beyond definition and in this respect like God.

So while I still don't totally understand the math, I do understand why it is called the Golden Section or Divine Proportion or all those other names it has managed to aquire. An infinite irrational number that appears in nature repeatedly would certainly raise eyebrows and be deemed significant by any civilization either ancient or modern. Yet the actual qualities of the proportion are still a little foggy. Looking at other sources I begin to get a better sense of the term. As defined by the Artlex Art Dictionary it is:

A proportional relation (ratio) obtained by dividing a line so that the shorter part is to the longer part as the longer part is to the whole. Another way to describe this: a proportion between the two dimensions of a plane figure or the two divisions of a line, in which the ratio of the smaller to the larger is the same as the ratio of the larger to the whole: a ratio of approximately 0.618 to 1.0.[2]

The Golden Mean produces a harmonic effect called eurythmy found in nature as well as in a wide variety of works of art and design. Artists of various periods and cultures have found that dimensions determined by this formula are aesthetically appealing.

The definition by Artlex is the first that I have found to mention the term eurythmy. Eurythmy is harmony of proportion or movement.[3] Among the principles of design, eurythmy is a hybrid of three of the principles — harmony, proportion, and movement.
Well anything that can be described as having eurythmy sounds pretty darn cool to me and as an artist it sounds like something I should do my best to understand and use.

As a visual learner it would be helpful to see what this Golden Ratio is, rather than just read about it. The Internet is great for discovering things and I actually stumbled upon this really cool video that shows the Golden Ratio in all of its glory. Hopefully this will help our understanding of the Golden Ratio and ultimately lead to learning how to use it.

[1] Michael Clarke, Oxford Concise Dictionary of Art Terms (New York: Oxford University Press, 2001), page 110.

[2] ArtLex Art Dictionary, s.v. “ Golden Mean”, http://www.artlex.com/ (accessed August 3, 2008).

[3] ArtLex Art Dictionary, s.v. “Eurythmy”, http://www.artlex.com/ (accessed August 3, 2008).