University study declares a “new” golden ratio for facial beauty but validates Phi, the Golden Ratio, as the basis for perceptions of beauty
A university study (PDF) by Pamela M. Pallett, Stephen Link and Kang Lee at the University of Toronto and University of California, San Diego announced that a “new” golden ratio had been found in perceptions of beauty in the human face. The study also said there was “little support for the Golden Ratio” that “dates back to antiquity, when the ancient Greeks believed beauty was represented by a Golden Ratio of 1:1.618.” Science Daily, in reporting on this study, quoted the one of the researchers as saying “People have tried and failed to find these ratios since antiquity” and “there was never any proof that the golden ratio was special. As it turns out, it isn’t.”
But all that glitters isn’t gold …
With this article, I think you’ll agree that the search is over, the proof exists and the real Golden Ratio is still quite special. Ironically, the results of the 2009 university study actually support this. The proof and significance of the Golden Ratio in the facial attractiveness is revealed with a simple illustration of twelve true Golden Ratios that appear in the proportions of all the key facial markers of their own ideal model:
Vertical golden ratios:
White – Hairline : Eyebrow top : Eye top
Gold – Eyebrow top : Eyebrow bottom : Eye top : Eye bottom
Blue – Eye pupil : Nose flair : Nose bottom
Green – Eye pupil : Nose bottom : Mouth
Green – Eye pupil : Nose bottom : Chin
Green – Eye pupil : Mouth : Chin
Horizontal golden ratios:
Gold – Face side : Eyebrows : Face side
Gold – Face side : Eye inside : Face side
Gold – Face side : Nose width : Face side
White – Face side : Eye outside : Nose center
Blue – Eye outside : Eye inside : Nose center
Green – Mouth outside : Lip cupid’s bow : Mouth outside
Each of the above colored rectangles is divided at its golden ratio point, accurate to the pixel and created with PhiMatrix, a golden ratio analysis and design application.
The conclusions of the study run contrary to evidence presented on this site since 2001 and its predecessor site for longer yet. The 2009 study was successful in identifying an attractive face, but the researchers apparently didn’t realize that their ideal faces contained numerous true Golden Ratios based on 1.618 and that their “new” golden ratios were simply mathematical derivations of 1.618. While this was not their intent, the study actually provided very good evidence for the validity and significance of the appearance of the true Golden Ratio of 1.618 in our perceptions of beauty in the human face, as illustrated on the Beauty and the Golden Ratio page.
Isn’t there more to beauty than two simple measures?
The study also made a critical but highly questionable assumption that human facial attractiveness is defined by two very simplistic measures:
- Vertical dimension – The distance between the pupils and mouth (AB) in relation to the distance of the hairline to the chin (CD), and
- Horizontal dimension – The distance between the pupils (EF) in relation to the width of the face (GH).
Why is it that women known for their beauty fail to measure up?
The researchers noted in one interview, “Angelina Jolie does not have golden length and width ratios. Elizabeth Hurley gets the golden ratio for length but is different from the width golden ratio by one per cent. But Canadian country pop musician Shania Twain has “both the length and width ratios.” Florence Colgate, voted in 2012 as having the most beautiful face in Britain, also failed to meet both metrics.
Is the “new” golden ratio wrong or incomplete?
So this begs this question: If women known for their beauty fail to measure up to this “new” golden ratio, could it be the metric that’s wrong? That’s actually quite easy to prove. With apologies to the pretty young lady whose face was digitally altered in the study to create their ideal attractive face, below are two digitally altered images that make her somewhat less attractive:
Despite these distortions, these faces still retain the two “new” facial proportions that the study claims to define attractiveness. The “pupil to face width” and “eye-mouth to hairline-chin” ratios are identical to those in their original ideal photo. All that was changed in the distorted photo were the eyebrows, nose and size of the lips.
The photo below retains identical sizes of every facial feature in the original .36 photo, as well as all the eye-mouth-face ratios that the study said were critical to attractiveness. Just one change was made. In the photo on the right, the positions of the eyes and mouth were shifted down by 20 pixels, with very unfavorable results on her attractiveness. This demonstrates that many other facial proportions not identified by the study are also critically important to attractiveness.
If we were to accept their two “new” golden ratios as all there is to beauty, the study would have you believe that the distorted faces should be just as attractive as the unaltered faces. And, because these distorted faces still conform to their two “new” golden ratios, the distorted faces should also be just attractive as Shania Twain and more attractive than Angelina Jolie, Elizabeth Hurley and Florence Colgate. This clearly isn’t the case, so the “new” golden ratios must not be capturing all the factors that truly define beauty. As a result, one cannot use the conclusions or “new” ratios of the 2009 to make valid assessments of relative attractiveness. A more scientifically valid approach would have been this:
- Base the study on dozens of photos of different attractive woman rather than creating digital distortions of a single woman who, while pleasantly attractive, probably would not be regarded by most to be as strikingly beautiful as Jolie, Twain, Hurley, Colgate or others.
- Have participants in the study rank the dozens of different women in order of beauty.
- Examine the photos of women ranked highest in beauty to find all the common characteristics in facial features that they all share.
Dr. Stephen Marquardt, inventor of the patented Marquardt “Beauty Mask“, is a noted plastic surgeon and recognized expert on beauty who has been referenced in hundreds of magazines, TV shows and documentaries. In an interview, Dr. Marquardt stated that the hairline is one of the most variable features on the human face and not a meaningful benchmark at all for beauty. He also commented that the width of the face is not a critical metric either. Beauty is the combination of golden ratio proportions in many facial markers, the most important of which are the positions, shapes and proportions of all aspects of the eyes, nose, mouth, chin and eyebrows.
How did the study find the Golden Ratio but not see it?
As illustrated at the top of this article, the face selected in the study as the most attractive has a significant number of facial proportions that illustrate the true golden ratio, 1.618. How did the researchers not see it? Perhaps not having the right tools or understanding of the Golden Ratio in facial proportions, but also because their “new” golden ratios are just mathematical variations on the true golden ratio.
- The “new” vertical golden ratio of 0.36 is close to 0.38, which is simply the golden ratio reciprocal variation of 1/1.618 squared. Their vertical ratio of 0.36 varies from this, but was based on the hairline at the top of the forehead, which is a highly variable feature in the human face.
- Their “new” horizontal golden ratio of 0.46 is close to 0.47, and is simply the measure that results when using the pupils rather than the inside and outside corners of the eyes, which are often based on golden ratio relationships to the width of the face. The small difference that does exist in this ratio from the pure golden ratio proportion is not visually significant, and may also be explained by the fact 0.47 was not offered as a choice in the study. In addition, the facial photo used in the study was very asymmetrical, with the left half of the face being about 8% wider than the right half. This alone created a possible range of +/- 0.037 on the ideal horizontal ratio of 0.47.
By analogy, think of it this way: A study announces a ”new” 4 inch measure for the foot has been found, and says there is little “little support for the foot that dates back to antiquity, when people believed that a foot represented a measure of about 12 inches. The researchers say “Many have tried and failed to find people with a 12 inch foot” and “there was never any proof that the 12 inch foot was special. As it turns out, it isn’t.” The study presents the “new” foot measurement of about 4 inches, but when you look deeper you find that they were measuring the width of the foot rather than its length. It’s not entirely wrong, but it certainly isn’t right.
The methodology of measuring and calculating the “new” golden ratio
Let’s take a deeper look at the study and how the “new” golden ratios are actually based on the Golden Ratio of 1.618. The researchers created a series ten derived faces from the original photos with the dimensions and positions of the eyes, nose and lips digitally altered in proportion to the facial height and width. Volunteers in the study then were shown the 110 face pairs, all with identical facial features, but with different length and width ratios, and rated the attractiveness of each, as shown below: The study reports that the researchers were “surprised to find that the preferences of the volunteers were surprisingly consistent, but with very different results from the well-known Golden Ratio of 0.618 (the reciprocal of 1.618).” The researchers concluded that they had found these two “new golden ratio” proportions that define beauty:
- Vertical facial dimensions – The distance from the eyes to the lips in relation to the that of the hairline to chin, with a ratio of 36% considered the most attractive, and
- Horizontal facial dimensions – The distance between the pupils of the eyes in relation to the width of the face at the eyes, with a ratio of 46% considered the most attractive
The conclusions were flawed in not understanding how the Golden Ratio is found in the human face
The faces selected as most attractive show clear Golden Ratio proportions
- Eyes – The inside and outside corners of the eyes
- Nose – The width of the nose
- Eyebrows – The inside edge of the eyebrows
The face below, judged as most attractive in the study for vertical proportions, illustrates the following facial features based on Golden Ratios of the height of the face:
- Nose – The base of the nose in relation to the distance from the pupils to the chin
- Lips – The center of the lip line in relation to the distance from the pupils to the chin
The “new” golden ratio of 0.46 is easily derived from the true Golden Ratio of 1.618
The “new” golden ratios declared by the study can be easily reconciled to the true Golden Ratio as shown below. The numbers shown on the photo below represent the dimensions in pixels. These dimensions give familiar variations on Phi multiplied by 100 and rounded to two decimals. Phi is the Greek letter Φ used to represent 1.618, the Golden Ratio:
- 38 = Phi to the -2 power (e..g., 1/Φ²)
- 62 = Phi to the -1 power (e.g., 1/Φ or 0.618 multiplied by 100)
- 100 = Phi to the 0 power
- 162 = Phi to the 1 power (e.g., Φ or 1.618 multiplied by 100)
- 200 = 162 + 38
- 224 = 162 + 62
- 262 = Phi to the 2 power (e.g., Φ² or 2.618 multiplied by 100)
- Position of left pupil, at the midpoint of first golden ratio line at 38 pixels and third golden ratio line at 100 pixels = (38+100)/2 = 69
- Position of right pupil, at the midpoint of fourth golden ratio line at 162 pixels and fifth golden ratio line at 224 pixels = (162+224)/2 = 193
- Distance between the pupils = 193-69 = 124
- “New” golden ratio defined as the distance between the pupils in relation to the width of the face = 124 / 262 = 0.47
The “new” golden ratio of 0.36 is just one element of other key facial dimensions based on true Golden Ratio of 1.618
These dimensions in pixels give familiar variations on phi, rounded to two decimals:
- 62 = Phi to the -1 power (e.g., 1/Φ or 0.618 multiplied by 100, rounded)
- 100 = Phi to the 0 power
- 162 = Phi to the 1 power (e.g., Φ or 1.618 multiplied by 100, rounded)
- 200 = 162 + 38
- 224 = 162 + 62
- 262 = Phi to the 2 power (e.g., Φ² or 2.618 multiplied by 100, rounded)
- 324 = 162 * 2 or 100+224
The “new” golden ratio of 0.36 can thus also be derived from these Phi-based numbers as:
- Position the eyes at the third golden ratio line at 162 pixels
- Position of the lips/teeth at the fifth golden ratio line at 262 pixels
- Distance between the teeth and the chin as 262-162 = 100
- Height of the hairline at 62 pixels to the chin at 324 pixels = 324 – 62 = 262
- “New” golden ratio defined as the distance from the eyes to the lips in relation to the distance of the hairline to the chin = 100 / 262 = 0.38
Does the Golden Ratio define beauty? The search is over, the proof exists and it’s still the Gold Standard
As referenced above, Science Daily quoted the one of the researchers as saying “People have tried and failed to find these ratios since antiquity” and “there was never any proof that the golden ratio was special. As it turns out, it isn’t.” With this article, I hope you can agree that the search is over, the proof exists, the Golden Ratio is still quite special, and now has a completely unbiased scientific study from two major universities to back it up. For more yet on illustration of the impact of the Golden Ratio on beauty, see the Beauty and Face pages.
Reference: Pallett, P. M., et al. New ‘‘golden” ratios for facial beauty. Vision Research (2009), doi:10.1016 / j.visres.2009.11.003
http://esciencenews.com/articles/2009/12/16/researchers.discover.new.golden.ratios.female.facial.beauty “Beauty is not only in the eye of the beholder but also in the relationship of the eyes and mouth of the beholden. The distance between a woman’s eyes and the distance between her eyes and her mouth are key factors in determining how attractive she is to others, according to new psychology research from the University of California, San Diego and the University of Toronto. Pamela Pallett and Stephen Link of UC San Diego and Kang Lee of the University of Toronto tested the existence of an ideal facial feature arrangement. They successfully identified the optimal relation between the eyes, the mouth and the edge of the face for individual beauty.”
http://www.sciencedaily.com/releases/2009/12/091216144141.htm “People have tried and failed to find these ratios since antiquity. The ancient Greeks found what they believed was a ‘golden ratio’ — also known as ‘phi’ or the ‘divine proportion’ — and used it in their architecture and art. Some even suggest that Leonardo Da Vinci used the golden ratio when painting his ‘Mona Lisa.’ But there was never any proof that the golden ratio was special. As it turns out, it isn’t. Instead of phi, we showed that average distances between the eyes, mouth and face contour form the true golden ratios,” said Pallett, a post-doctoral fellow in psychology at UC San Diego and also an alumna of the department.