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August 2005

From Golden Mean to "Rule of Thirds"

Zenrock2_1The "rule of thirds" is a simplified version of the golden mean. The rule of thirds is a basic technique that photographers learn to frame their shots. Subjects placed exactly in the middle can often make for an uninteresting photo. The golden mean would be wonderful to apply when taking snaps, but obviously this is not practical. But a viewfinder can be divided by lines — real or just imagined — so that you have four intersecting lines or crossing points and 9 rectangles that resemble a tic-tac-toe board. These four crossing points (also called power points, if you can believe it) are areas you might place your main subject, rather than in the center.

There is a belief, and some research to back it up, that we are hardwired to naturally be drawn to images that have proportions approaching the golden mean, just as we are often drawn to many things in the natural environment — or even to a particular "good-looking face" — with golden-mean like proportions.

The idea of objects and visuals having proportions close to the golden section is fascinating stuff for architects, mathematicians, designers and artists. And the rule of thirds is a very basic and useful technique for photographers in many cases. But what does it mean for us? What happens if we take, say, an 800x600 PowerPoint or Keynote slide and divide it up? Dividing our "canvas" into thirds is an easier way to at least approach golden mean proportions. The rule of thirds is not really a "rule" at all, but rather a guideline. But you will find that you can apply this guideline even to PowerPoint or Keynote visuals to give them a more symmetrical and professional look. Here are some sample slides below.

   Appearing_grid     Appearing_slide
Above, the quote fills the right two thirds of the slide and is in the upper third vertically. The photo is in the remaining left third.

   Branding_grid     Branding
Notice the proportions above? Also note that the woman's eyes are looking at the text. A small thing, but reinforces the strong part of the slide, the title of the presentation.

   Sing_grid     Sing

Above, the statistics for this particular point are placed directly on two of the four "power point" crossing sections. The face of the woman is in the right third and near a crossing section.

Website_gridOut of curiosity, I placed a golden mean rectangle over the image that comprises the homepage of my website. I did not use a grid to crop the photograph or for placing the text. I went with what "felt" right. Interestingly, when I place the golden rectangle over the image, I found that the proportion of the webpage image is close to the golden rectangle, but more interesting is that the placement of my name over the image on the right is in exact golden mean proportion horizontally.


Go back and take a look at one of your recent PowerPoint or Keynote presentation slide decks. In the slide master, use the grids to divide your slides into thirds ("ctrl/command G" from your keyboard will turn the grids on/off). How can your arrange your slide content to be in better proportion? Does it make a difference?

Here is a very good, basic (and visual) explanation of the golden mean and the rule of thirds.

From Wabi-Sabi to Golden Mean

ShellEarlier I was speaking about how we can improve communication designs by looking in unexpected places. For example, by examining Wabi-Sabi concepts and sensibilities to influence our approach with designing visuals. Wabi-Sabi and Zen aesthetics are rooted in the natural world. The "design" of the natural world has a lot to teach us about symmetry, balance, beauty, and grace. Are these words you use to critique your presentation visuals — symmetry, balance, beauty, and grace?

We are drawn naturally to visuals that exhibit symmetry, balance, and beauty in proportion. Artists and designers have for centuries emulated a proportion called the "Golden Mean" or "Golden Ratio" found in nature into their works. The golden ratio is a proportion defined by the number Phi (1.618033988...). Kiberly Elam points out in her book, Geometry of Design, that "...use of the golden section rectangle, with a proportion of 1:1.618, is documented in the architecture of Stonehenge built in the 20th - 16th centuries B.C." There is evidence as well that the ancient Greeks and Egyptians applied the principle, and of course, much has been made of Renaissance artists and architects who employed the golden ratio in much of their work. offers some history on the  golden mean.

Kimberly points out at least two studies in the last 150 years or so which concluded that, given a choice, people have a significant preference for man-made objects which have proportions closest to the 5:8 ratio golden section. There is some research recently which says people prefer TVs with aspect ratios approaching the golden mean as well. A quick look at the SONY 40" flat panel shows that it has an aspect ratio or 16:9 which is not the golden mean but falls into the segment of preferred proportions. While the screen itself is not exactly a 1:1.618 rectangle, the bevels around the screen do form a golden rectangle.


We see strong golden section preferences in the natural world, of course. The sunflower, for example, consists of 21 spirals moving clockwise and 34 spirals moving counterclockwise. This 21:34 ratio is 1:1.619, very close to the golden section. Maybe the reason we are so intrigued by the things in the natural environment such as flowers, shells, fish, etc. is because of the preference we have, at least subconsciously, for shapes that have golden mean proportions.

Below, using a Bayen painting from the 12th century Japan, I applied golden section grids over the image to see what would happen. I did this by multiplying the width of the image (line A) by 0.618, which gives me line (B) and (C). Here we can see that (A) is 1.618 times (B) and (B) is 1.618 times (C). To be begin a grid, I drew a line down the page where the lines (B) and (C) intersect.


Now, I do not know if this painting uses the golden section of not. But what is interesting about this painting is that the sight line of the fishing line (including that which we imagine under the water), pole, fisherman and boat roughly run along a line that is .618 times the length of the entire image. The image is powerful and we can feel the sabi of the fisherman and the vastness of the ocean. If the subject were placed exactly center would we still get an appreciation of the waves gently carrying the boat from left to right?

Attempting to design visuals according to the golden mean proportions is impractical in most cases perhaps for us. However, the "rule of thirds" which is derived from the golden mean, is a basic design technique that can add symmetry, beauty, and professionalism to your visuals. The rule of thirds — which is not a "rule" at all — is something you can use. Photographers, for example, use the rule of thirds when framing their shots.

Next, then, we will look at using the rule of thirds in your visuals. In the mean time, please explore the world of Phi and the Fibonacci series. Once you understand the golden ratio you will begin to notice it everywhere. has an excellent explanation of Phi and the Golden Mean. It goes pretty deep yet is written in plain English and is quite easy to understand.

There are a lot of books which explore the Golden Mean and beyond. I purchased the Geometry of Design a couple of years ago and highly recommend it.