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Photography e-Book Chapter 16 - The Golden Ratio

Loosely related to the rule of thirds is the Golden Ratio also referenced to the Golden Rectangle. This is, as far as I am able to decipher from a layperson's perspective, a mathematical look at human aesthetics. Mathematicians seem to love to apply numbers to what seemingly could or should not have numbers applied to them but what do I know, as there are many geniuses out there seeking a single mathematical formula that would explain the nature of the universe and of life itself. Mathematicians have even come up with a formula for the human decision-making process, better known as Game Theory or the Zero Sum Gain.

The Golden Ratio has purportedly been a profound influence since ancient times with Greeks utilizing the Golden Ratio in their buildings such as the Parthenon at the Temple of Athena on the Acropolis. During the Renaissance when European artists rediscovered the styles of the ancient world, the Golden Ratio was utilized for their sculptures and paintings. Leonardo da Vinci being the most prominent Renaissance artist known to have used the Golden Ratio for great works such as the Mona Lisa.

The shape of the Golden Ratio in physical form is supposed to be considered very esthetically pleasing to humans. One of the most interesting graphic forms of the Golden Ratio is the nautilus shell and the way the shell starts from a central origin and then spirals outward around itself until it reaches the horn or opening of the shell where the cephalopod's head is located. The Bowers and Wilkins speaker company of Britain, better known as B&W, designed a reference speaker with the nautilus design and called it…the Nautilus. A most intriguing and apparently an excellent sounding speaker.

The more traditional physical shape of the Golden Ratio is the golden rectangle. This rectangle is comprised of a square and one-half of another square that is the same dimension together, as seen below. It can be seen as another example of the rule of thirds as the rectangle can be comprised of three equally sized smaller rectangles. Technically, the golden rectangle is comprised of two parts that follow the Fibonacci sequence.

1,1, 2, 3, 5, 8, 13, 21, 34 etc. Each succeeding number after 1 is equal to the sum of the two preceding numbers.

Add enough golden rectangles arranged a certain way and soon you will have the golden curve that spirals aournd like a nautilus shell.

The Golden Mean or Phi and the Golden Ratio abound in nature and perhaps humanity has been genetically programmed to recognize the ratio as being pleasing. Flower petals and pinecones are two examples of spiral designs that use the Golden Ratio. Why this ratio of 1.618? This ratio provides the flower petals and leaves with maximum exposure to sunlight and allows rain drops to flow down to the root in the most effective manner. The sunflower positions its seeds in a Golden Ratio spiral because it is the most effective manner of having as many seeds in a given amount space possible and allowing them to remain un-crowded within that space.

Below is a flower that one can still see a spiral pattern emerge from the middle buds.




Ancient Greeks were not the only ones who understood the Golden Ratio. Egyptians used the Golden Ratio for their pyramids and the layout of the three great pyramids of Giza use the curve of the Golden Ratio that is predominant in a nautilus shell.

This is all heady stuff, especially for math idiots like me who can barely remember the multiplication table. I am sure I have offended the logical readers who actually know about this stuff with my most basic of descriptions for the Golden Ratio. What does this have to do with photography?

Photography is a pursuit that can be many things to different people. If we look at photography as being an art form like painting (and really they are no different) then the artist must have at least a cursory understanding of artistic principles. Aesthetics, what is it and why is something considered aesthetic?

Since it is naturally abundant, the Golden Ratio, once discovered, would obviously have profound influences on human art. Place a number of similar artifacts in a room and the one that adheres to the Golden Ratio is the one most people will choose as being the most pleasing. As humanity is a part of the natural world, it should hold that we ourselves could be some sort of derivative of the Golden Ratio in terms of the relationship of our limbs to the torso to the head.

Understanding some of the basic technique can helps us understand why it is that we find something to be pleasing to the eye. However, I still believe that the majority of the photographer's development must be borne from experience rather than theory. It is not so much what we do right that teaches us but what we do wrong or do not know. As we attempt to correct the wrong or understand what is unknown, the process has more meaning and teaches us. If we do something correctly right away, there is less incentive to understand how we did it right, if we did it correct once we will do it again. Try to keep the conceit in check on those occasions when you hit all the right factors and create a special keeper photograph. Use it as the basis to inspire you to keep on producing high quality and creative work.

There are some photographers who adhere strongly to mathematical or technical placement of the subject in the scene. I do not believe there is a need to be so strict and vigorous in composition, also because I would not even know how to use the Golden Ratio for my composition anyway. My opinion is that humans have the ability to "see" what is pleasing and what is not and the more you practice the craft the better you will develop your sense of seeing. Being rigid with your photography will reveal themselves soon enough.

We witness something and we feel compelled to explain it. We see a certain trend in how humans react to certain types of designs and try to explain that too. Sometimes it is better to look, feel, and experience rather than take cold numbers or equations to an idea or concept, especially when dealing with the creative process. Science and math have their place though for I would rather live in a house designed by a trained architect instead of an untrained artist, no matter how brilliant.

Update September 1, 2001 - As I type this now, I have just watched The Learning Channel's (TLC) special on the human face, hosted by John Cleese of Monty Python fame. A short segment of the special dealt with a ratio, a certain 1.618 ratio in fact, otherwise known as the Golden Ratio. I mentioned above that the Golden Ratio is associated with what humans consider to be attractive and the TLC special made it very clear how this ratio pops up over and over again for the human body and face. Why are models considered so attractive and why is it that only certain girls are recruited to become models? The TLC special revealed that all of the top models and faces in general that are considered beautiful have an abundance of the 1.618 ratio.

Take a measurement from you feet to your torso, then from your torso to the top of your head. The second measurement on an attrative body will be a ratio of 1.618 to the first measurement. Measure the width of your mouth at rest then measure the width of your nose, the ratio on an attractive face will be...1.618. The Golden Ratio pops up over and over again for what humans consider to be attrative and it is becoming more and more clear to me that it is a natural phenomenon so pervasive that Pythagoras called it a universal beauty so many thousands of years ago.

Now the challenge is how to incorporate this universal ratio of beauty into our photography as artists. I am going to have to research the art of the Renaissance era to gain some more insight into how the masters of old saw and created.

Reference page for more detailed and technical information on the Golden Ratio.


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