I promised I would discuss the Golden Rectangle. It is a fascinating concept for which I initially had very little interest. Afterall, not all art is based on this concept. It is not a principle of design. Whether an artist uses it or not is arbitrary. It has a long history, but that doesn’t guarantee that its use will always produce a wonderful design. It is a tool, and as such, it is up to the artist to determine its appropriateness in any work.
Having said that, I have spent a great deal of time reading about it and studying it and trying to understand the whole concept. You must realize that I am not a math person, and this is definitely a math type idea. I hate math. I can’t do multiplication tables past 2x’s. I need to use my fingers to add even small numbers. It’s just not me.
Somehow this mathematical construct or principle or whatever you want to call it has really caught my imagination. So much so, that I plan to create an entire design class based on it and intend to create several works that fit into it and fully utilize all it has to offer.
For the ancient Greeks beauty was wholly defined by whether or not a design was meticulously accurate in certain proportions.
The proportion of particular interest was the Golden Mean or Ratio. Architecture, sculpture, pottery, art, science, philosophy, and mathematics were all subject to this ideal.
During the 16th Century, the Golden Mean became known as The Divine Proportion, following its rediscovery by Luca Pacioli, a Franciscan friar. While not every artist since the 16th Century has based his work on this particular proportion, it has remained a valuable tool for both artists and architects to the present day. So what exactly is this Golden Mean?
The Pythagoreans of ancient Greece are credited with describing a mathematical pattern that occurs so frequently in nature as to be considered of divine origin. This Golden Mean divides or bisects a line by dividing the length of the line by the number Phi or 1.618. The resulting division of the line is expressed algebraically as follows: AC:AB=CB:AC (Beaird, “Grid Theory,” pg 1) It is the basis for the construction of the Golden Rectangle. It is within this rectangle that the artist creates his work.
According to the Golden Mean, when the Width is multiplied by Phi it gives us the Length of the rectangle. W x 1.618 = L. When the Length is divided by Phi it gives us the Width of the rectangle. L ÷ 1.618 = W.
One method for sectioning the Golden Rectangle is to divide every line of the Golden Rectangle using the Golden Mean and draw lines to connect the divisions. The result is a Golden Rectangle divided into 9 smaller rectangles. (Kent, 1995, pg 33) This is very much akin to the modern concept of the Rule of Thirds in which the chosen rectangle (not necessarily Golden) is divided into thirds in both directions. Areas of emphasis are then placed in the vicinity of the intersections. (Davis, “Divine Proportion”, pg 2) It is Divine Proportion simplified.
For greater accuracy in determining points for the placement of important details, the nine rectangles can be further divided by drawing a series of diagonals from and through points of division.
For the artist, the concept of the Golden Mean and subsequent Golden Rectangle provide a tools for establishing pleasing proportions and balance in his work.
Clear as mud? That’s how I felt when I first started studying about it. After a few months, it began to make sense. It may be something you might pursue in the future, but for now, it is how I determined the final size of the composition for step three, and how I decided to make the divisions seen in the previous blog entry.
If you have questions, or would like more info, I have quite a few references besides the three below and would be glad to help you out – if I can. So feel free to contact me.
Jason Beaird, “Grid Theory,” The Principles of Beautiful Web Design (2007)
<http://www.sitepoint.com/article/principles-beautiful-web-design/3.htm> Accessed 6-3-2007
Robert Davis, “Divine Proportion,” Journey from Concept to Creation (May 2007)
<http://avid.blogs.com/concept_to_creation/2007/05/divine_proporti.html>
Accessed 6-3-2007
Kent, Sarah
Composition, Dorling Kindersley, London: 1995