Fixing Retail with the Golden Ratio

Mathematicians, scholars, artists have been fascinated by it for millennia. Leonardo da Vinci used it to study human proportions and Chopin used it to structure his musical compositions. It’s how snails design their homes, it’s found in carnivorous plants, tropical cyclones and the spiraling arms of distant galaxies. It is nature's golden ratio, the mathematic formula for near-perfect proportion. In this 2-Part series I’ll explain how savvy marketers will use it to mend the malfunctioned art of merchandising.

Why is the golden ratio important at retail?

Because, proportion is what makes things look beautiful. Proportion allows us to cognitively organize what we see into comprehensible chunks or groups. For example, we consider people with well-proportioned faces as beautiful, while shying away from those with poorer proportions. According to Wikipedia, Facial beauty "evokes a widely distributed neural network involving perceptual, decision-making and reward circuits."... [Facial attraction is] "a quick and low-effort means by which parents and infants form an internal representation, reducing the likelihood that the parent will abandon his/her offspring because of recognition failure." Gestalt psychology supports proportion, beauty and recognition theories by stating, "The brain is holistic...with self-organizing tendencies. The human eye sees objects in their entirety before perceiving their individual parts... Gestalt psychology tries to understand the laws of our ability to acquire and maintain stable percepts in a noisy world." Consumers protect themselves from being bombarded with stimuli by simply “tuning out” or blocking such stimuli from conscious awareness. And they do so out of self-protection. Perceptual Organization states that people organize mass stimuli into groups and perceive them as unified wholes. Merchandising these days is a response to an unkempt and noisy world. But without the right design strategy, the state of retailers' shelves can become an unrecognizable ocean of product. If we want consumers to see our products then we have to show them how to view them. I propose shelving, displays and products that match nature’s proportion, designed to reflect the natural order of things.

What is the golden ratio?

The golden ratio is a fascinating irrational number discovered by the Greeks (or aliens) around the sixth century. Mathematician Euclid often wrote about it in the third century BC. As I stated earlier, the golden ratio is considered near perfect proportion. However we don’t know why it occurs naturally and we don’t know why we can apply it numerically to natural events. But before we get to Part II, I’d like to first explain the math behind the golden ratio, because it is flat-out-fascinating and irrational! You’ll love how this plays out… I promise! Also, do NOT miss the photos at the end of this post.

PART I: The golden ratio

Nature's equation Images (redrawn), courtesy The golden ratio expressed algebraically like this (denoted by the Greek lowercase phi).

As a line graph, it looks like this:

Using the line graph as a baseline, turn the blue line into a square, then draw a vertical line down the middle of the box, then use that line to draw a green line diagonally to the upper right corner of the box, then use the bottom of that (green) line as an axis point to draw an arch back down to the baseline. You draw the red rectangle next to the blue box. The blue and red combined forms a new overall rectangle — the golden ratio, found everywhere in nature:

The golden ratio rectangle has the proportions of 1:1.618 or 61.8 percent. The red box area of the rectangle has the exact same proportions as the overall rectangle, at 61.8 percent.

You can continue to break up the new part of the rectangle by 61.8 percent, and you can subdivide this into boxes ad infinitum. Ta-da! This is what makes the golden ratio so fascinating.

Here's where it gets fun. There is another formula called the Fibonacci sequence; which is a series of integers in which each subsequent number is the sum of the two previous numbers, like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55...  by dividing a number early in the sequence by it's following number it produces a percentage of 2/3 (66 percent); later on in the sequence dividing 34/55=61.8 percent!

The Fibonacci sequence overlaid onto the golden ratio produces logarithmic spirals that are indiscernible from one another. Graphically the spirals look like this: Each 90 degree turn is about 61.8 percent

 Who thinks that snails are good at math? I mean, who else could have taught the Greeks the equation? This mathematical formula was around long before mankind. Who thinks this may be one of the most stunning images in the universe?

Near perfect proportion: From galaxies, to microorganisms, weather patterns, and even population migration.

 Don’t miss Part II. Proportion is not a gimmick. For traditional brick and mortar to keep up, then it will need to behave like the Internet. The Internet doesn’t sit still. Every minute of every hour, it is becoming better. Retail will need thought leaders with long-term solutions.

 Robert Millan is a Chicago based creative marketing consultant who is fascinated by the connection of people and products. You can find him at