I recently wrote a two-part series about the famous mathematical constant/artistic proportion known as the Golden Ratio, so I decided to compile a list of all the studies I could find published online about the aesthetics of the ratio: a "master list" of sorts of what people have proven about it scientifically. For background on what the golden ratio is and where it's found in math, read Part 1 of my series, and for a breakdown of some of the legends around it, check out Part 2.
Disclaimer: This list is by no means exhaustive! However, I included almost every study I encountered researching my golden ratio blog posts, including every one that was referenced by another online news article, as well as others that I found particularly interesting or high-quality. Without further ado...
This 1995 paper is easily the most robust and compelling document I've found on the golden ratio. It painstakingly compiles nearly every the empiric studies about the aesthetics of the golden ratio from the mid-19th century to the early 1990s. (The introduction is also an excellent account of the ratio's history.) I wouldn't recommend reading the 30+ page behemoth yourself; to spoil the ending, the author's personal opinion is that the evidence points toward at least some measure of preference for the golden ratio—but a very fragile one.
This study, first published in 2009, used manipulated photos to test the attractiveness of various length and width proportions in the female face. After studying the preferences of 126 university students across four experiments, they found attractiveness to be optimal "when the face’s vertical distance between the eyes and the mouth is approximately 36% of its length, and the horizontal distance between the eyes is approximately 46% of the face’s width." These proportions match the average human face.
This 2009 paper uses math and logic to argue that one's eyes will scan a rectangle most quickly when it has a length to width ratio of around 3:2. The author then argues that, because the golden ratio is so close to a 3:2 proportion, this conclusion explains why golden rectangles are so visually pleasing, or "‘breathe’ and ‘flow’ better than most other shapes," as the author puts it.
This one's filled with science jargon and concepts I have no knowledge of, although I could discern enough of the details to summarize it. Essentially, this 2015 scientific study examined the neural responses of 30 participants across 4 experiments when confronted with abstract images of various proportions. The researchers found that patterns that contained golden ratio proportions took longer for participants to visually process. They theorized that this increased length of processing time might account for the golden ratio's perceived value in art, i.e., "I've been looking at this artwork for slightly longer than usual, it must be significant!"
In this 2008 study, 36 participants used a 10-point scale to rate faces from an extensive image database. The researchers used a graphic user interface to analyze the proportions of the images (based on facial landmarks, like the inner corners of the eyes). Of the proportions tested, they found that facial attractiveness was correlated with 5 out of 6 "neoclassical canons," 3 out of 11 symmetries, and 6 out of 17 golden ratios.
This study, published in 2015, is particularly unusual both because it took place in Taiwan, rather than the western world, and because it questioned whether personality type was related to proportion preferences. 120 participants had their Myers-Briggs personality types tested and then rated each of 30 rectangles on a 1-5 scale. They found that squares were the most preferred shape, while there was moderate preference for the golden ratio, and ratios longer than the golden ratio tended to be disliked. And yes, rectangle preference varied with personality type; it also varied between males and females.
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