Facial golden ratios are simple, clear and abundant.

Since my first investigation of human facial proportions in 1997, it seemed clear that the most important features that define a human face are the simplest and most obvious: An oval head and the positions and dimensions of the eyes and the mouth. As evidence, consider the “smiley face.” It expresses a variety of facial expressions with nothing more than a circular head, two eyes and a mouth line:

We immediately recognize this icon as a face, but it clearly does not represent the proportions of a human face.

Let’s instead express these same facial markers with normal human proportions, and with the simplest possible representation. This requires a vertical oval, two lines for the eyes and a line for the mouth. The resulting face will look something more like this:

This simple facial configuration is easily mapped to very natural human proportions with the use of four simple golden ratio proportions:

The next important human facial feature is the nose, most simply represented by two nostrils. These too can be mapped to very natural human proportions with golden ratio lines:

• The nostrils in relation to the pupils of the eyes
• The distance from the pupils to the nostrils to the mouth line

This basic set of facial markers has been identified and validated through my analysis of hundreds of faces. They provide a very simple and logical set of the points that are required to construct the most basic features of a human face. They identify common golden ratio proportions that can be found in many attractive human faces.

Every face is unique though, even very beautiful ones, so few faces embody every one of these these proportions exactly. Even so, I recommend these markers and ratios to researchers for their use in assessing the appearance and validity of golden ratios in studies of facial analysis and attractiveness. There are a number of additional golden ratios that can also be found in many faces, but some are not as clear and universal as these.

To distinguish this system from other facial analysis systems (e.g., the Marquardt Beauty Mask, etc.), I’ll call this the “Meisner Beauty Guide for Golden Ratio Facial Analysis,” or the “Meisner Beauty Guide” for short. The guide is based on 33 facial markers. Click on the image below for a full resolution view.

Of these 33 markers, 28 are 14 sets of symmetrical markers that appear on both sides of the face. Five other markers are on the vertical center line of the face and define proportions based on horizontal measures.

Most faces regarded as beautiful or attractive will have a significant number of markers whose proportions are very close to the golden ratio (as rounded to 1.618). The guide is simple when viewed in the individual elements shown in the slides above. It includes the following list of golden ratio facial proportions:

Why are golden ratios in the human face often missed by researchers?

A number of studies over the years have sought to determine whether golden ratio proportions exist in human facial features. Many have concluded that golden ratios do not exist, or have only a very limited presence. My review of these studies invariably reveals that the researchers simply missed the most basic golden ratios. This happened because they were measuring a different set of facial markers, and calculating a variety of alternative ratios.

As an example, one study by Italian researchers titled “The role of the golden proportion in the evaluation of facial aesthetics” captured over 30 facial markers using a very sophisticated imaging technology called 3D stereophotogrammetry (see below left). Of these, they used data on 14 facial markers for a study on attractiveness, from which they calculated 10 facial ratios (see below right).

Note how different their markers and ratios are from those in the Meisner Beauty Guide:

• Their study didn’t include the width of the face in its measures, nor were the inside and outside positions of the eyes included as markers.
• The study based half of its ratios on the hairline, which is a weak marker. The hairline is one of the most highly variable facial features by individual, and is also impacted by hair styles or male pattern baldness.
• The researchers based two other ratios on a midpoint between the eyebrows, which is certainly not as fundamental to the definition of the face as the eyes, nose and mouth.
• They used the pupils of the eyes in only two vertical measures.
• Rather than measure the very distinctive cupid’s bow of the lips in relation to the width, they omitted this marker and measured the ratio of half the width of the mouth to its height.

Their ten ratios thus did not include a single one of the ratios of the Meisner Beauty Guide. When the Meisner Beauty Guide markers are used, the face presented in their study reveals clear golden ratio proportions, horizontally and vertically. Click on image for full resolution.

The importance of facial width in attractiveness measures is illustrated by the image below. The only facial marker changed is the width of the face, and the impact on attractiveness is significant.

A 2009 study by US researchers titled “New “Golden” Ratios for Facial Beauty” made a very simplistic and invalid assumption that facial attractiveness can be reduced to one horizontal facial ratio and one vertical ratio. They announced these as the “new golden ratios” of facial attractiveness and said that true golden ratio was nowhere to be found.

The researchers properly identified the pupils to lip line as an important measure, but ignored its position on the face in relationship to the chin. Instead, they simply calculated the ratio as this dimension divided by the distance of hairline to the bottom of the chin. The importance of the relative positions of the eyes and mouth, and not just their dimensions, is illustrated in the photo below. The only change is that the eyes and mouth were both shifted downward by 20 pixels. Again, the impact on attractiveness is significant.

Horizontally, the researchers properly identified the pupils and face width as an important marker. The ratio they calculated, however, ignored the inner and outer positions of the eyes. As a result, they didn’t realize that their “new” ratio was simply a mathematical derivative of the eye width to face width golden ratio included in the Meisner Beauty Guide. The ideal face in fact embodied a number of golden ratio proportions in both its horizontal and vertical dimensions:

With this simplistic analysis based on a single female face of just average attractiveness, the researchers then made bold claims about the shortcomings in the attractiveness of famous women regarded as beautiful by most people, including Angelina Jolie, Elizabeth Hurley and Shania Twain. A more rational and valid approach would have been to start with faces that are considered beautiful and to identify a system that describes the common characteristics.

There are clearly many dozens of places on a human face that could be identified as a marker, and hundreds of ratios that can be calculated between these points. The availability of hundreds of facial ratios that do not equal the golden ratio does not mean that golden ratios do not exist. It just means that some of the most basic facial markers and simplest ratios were not included in their analysis. Many researchers apparently do not have simple gauges or software that makes identification of golden ratios easy. I urge researchers to include the Meisner Beauty Guide facial markers in the analysis of their data.

Why would the golden ratio appear in the human face?

Some have asked why golden ratios would appear in the human faces. It’s a good question. An equally appropriate question is to ask is why it would not. We find the golden ratio and the related Fibonacci series in a variety of diverse places in nature. It appears in the basic spirals of pine cones and seed pods. It is found in the spatial structure of molecules. It is even being found in quantum physics. If one is open to a spiritual perspective, the answer could be that humans were created by a superior intelligence who used the golden ratio as a constant to assure the harmony and beauty throughout the face, and in many other places in life. That answer is obviously unsatisfactory to those want a scientific explanation, and I think there is a logical answer to be found as well.

Rules of Cellular Automata

The work of Dr. Stephen Wolfram provides an insight into how individual cells are programmed to create the trillions of cells that comprise a living organism. Cellular automata proposes that a collection of cells creates a shape or design through a number of discrete time steps according to a set of rules based on the states of neighboring cells.

Consider the multitude of steps that must be required for embryonic cells to create the face of a human being through its entire growth cycle. Each cell must contain a set of rules which tells it what type of cell to become and the exact position on the face for it to appear.

Now consider that the unique mathematical properties of the golden ratio make it inherent in so many mathematical formulas and limits, as well as in many geometric constructions.

Imagine that YOU were the programmer who had to come up the rules to create the dimensions and proportions of the human face. Imagine that YOU have to choose ratios to create a facial design structure with complexity in concept, yet simplicity and harmony in execution. Would you choose a ratio like the golden ratio, with its unique mathematical ability to create a variety of different geometries? Or would you go about this by choosing a different ratio for every aspect of your design? Beauty may exist for its own sake or as an evolutionary adaptation to indicate a healthy partner for procreation. Either way, which approach do you think would result in the most aesthetically pleasing result, the use of a single ratio or different ratios for each element in the design of a face?

The Golden Ratio as the simplest and most logical solution

Our design as humans may be the result of something of higher intelligence creating a life form that is just a reflection of itself. On the other hand, it may be the evolution of individual cells uniting to create something with far more intelligence than themselves. In either case, I would submit that the golden ratio to be a more logical and likely basis for facial configurations than the use of dozens or hundreds of other independent ratios to create a face. Those in the academic community often steer away from the golden ratio because of their naturalist or humanistic leanings, and its connotation as being part of a “sacred geometry.” Its ability, however, to provide the simplest mechanism and explanation for facial dimensions should be embraced, not ignored, if we want to gain the best understanding of the dynamics at work at the cellular level in creating that wondrous face that you see every day in the mirror.

Additional evidence of golden ratios

Further support of the appearance of the golden ratio in human facial proportions is found in the work of Dr. Stephen Marquardt. The Meisner method above provides a simple way to illustrate a number of basic golden ratio proportions commonly found in the human face. It does not, however, prescribe the specific configuration of the positions and proportions facial features that create the perception of beauty.

By contrast, Dr. Marquardt’s work led to his development of his “Marquardt Beauty Mask,” a system based on a complex of numerous golden ratio based decagons that create a template or archetype for the human face. Through his research, Dr. Marquardt demonstrated that a single facial template could define human perceptions of beauty across era, race and culture. Learn more about his work on this site at “Facial Analysis and the Marquardt Beauty Mask” or in much more depth at his site at BeautyAnalysis. com. 

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Numerous studies have been done to investigate the existence and/or relationship of golden ratio proportions in the human face. Surprising few get it right, so the results of many of these studies are inaccurate and misleading. There are four important keys to selecting photographs that are suitable for facial measurements. Next, it is critical to understand and measure the facial markers that commonly reflect golden ratio proportions. In this article I’ll cover these key points, the common mistakes made and the best practices to yield results that are both accurate and meaningful.

1. Orientation of the head, and eliminating the impacts of perspective.

As simple as it sounds, one of the most important aspects of any image used for facial analysis is that the subject be looking directly into the camera. The front of the face must be parallel to the lens of the camera. There must be no tilt of the head either up, down, left or right. Doing so immediately renders a photo unreliable and usable for any accurate facial measurements.

Click on the image gallery below to see the huge impact that even slight turns of the head can have. It destroys the symmetry of the face. It also changes the relative positions and proportions of facial features in a photo.

Indicators of proper alignment include:

• Yaw (Horizontally) – Both sides of the face appear equal in size. The ears show equally on both sides of the head.
• Pitch (Vertically) – The pupils and iris will be be centered in the eyes, not looking up or down. The chin and nose will appear very square to the camera, not revealing their undersides.
• Roll (Tilt) – A vertical line can be drawn that will pass through the center point between the eyes, the center of the nose and the center line between the front teeth.

2. Distance from the camera and camera lenses, and eliminating the impacts of optical distortion.

The distance of the subject from the camera is also critical. Photos that are taken too close to the face have varying degrees of fish-eye effects. These create significant distortions in the relative positions and dimensions of facial features.

The camera lens also plays an important role. Shorter focal length lenses create more distortion than longer focal length lenses. This is because they try to wrap a larger viewing angle onto the flat surface of the camera’s light sensor, or photographic negative. It’s best to use a lens with a focal length of at least 85 mm. Photos should be taken from a distance of at least 10 feet away from the subject’s face. This immediately disqualifies any selfie photos taken at arm’s length from being usable in any facial analysis study.

Click on the image gallery below to see the impact that different distances and lenses have on facial proportions in photos.

Indications of proper distance and lens selection include:

• The ears will show fully on both sides of the head. The ears will define a clear vertical line that defines the point at which they meet the side of the face.
• The nose will not appear to be large, bulbous, broadened or showing any fish-eye effects.
• Neither the top of the head or the chin will not appear as unusually pointed.

3. Facial expressions and impacts on facial proportions.

The human face is incredibly expressive, and is capable of showing a wide range of emotions. Facial expressions can have a significant impact on the positions, dimensions and proportions of our facial features. Consider the impacts that the following have on facial measurements:

• Opening the mouth widely, on the height of the head.
• Raising of the eyebrows, on the proportion of the forehead and even on the position of the tip of the nose.
• Puckering of the lips, both in their increased height and narrowed width of the mouth.

The following photos illustrate the combined incredible impact of facial expressions and head orientation on facial proportions:

As you can see, it is be impossible to take a set of facial measurements for analysis unless there is a consistent standard. For these reason, any photo used for facial analysis must follow these guidelines:

• The teeth should be closed to gently touch in a natural, relaxed position.
• The eyes should be open, relaxed and focused directly on the camera lens.
• The mouth should be in one of two positions:
  • Reposed – Closed and relaxed, with no smile at all.
  • Smiling – With a broad, natural smile that is the same on both sides of the face, and that exposes the teeth.

Examples of facial portrait photos that have these characteristics are shown below. Photos like these are often used by modeling agencies and referred to as “headshots.”

4. Image quality and eliminating adverse impacts on accuracy.

Even with excellent results in the first two criteria, it’s critical that the image itself be of high quality so that all key facial markers are clear and easy to measure.

• Resolution – The image should be of high enough resolution. The dimension of the head in the image should be at least 400 pixels tall.
• Clarity – The image should be focused clearly. The key facial markers should have clear lines and borders.
• Lighting – The lighting should be evenly distributed to eliminate any shadows and avoid any washout of facial features. The edges of facial markers should be easy to distinguish.

5. Identifying the key facial markers and calculating the most relevant measurements.

A good facial image that meets the first four criteria is still of little value if you don’t know which points on the face to measure to get a meaningful analysis. There are many dozens of potential points on a face to take a measurement. This then creates hundreds of ratios that can be calculated between these various points. This alone is the downfall in a number of studies of the human face performed by qualified, intelligent researchers at reputable academic institutions. As an example, see my reviews of the 2009 study on facial ratios at two universities and another article interviewing another Ph.D. Both studies claimed there to be no golden ratios at all in the face.

The video below illustrates how facial markers and dimensions are measured to identify common golden ratio. See the related article on the markers used in this facial beauty analysis.

The image analysis shown in the video was done with
PhiMatrix Golden  Ratio Design and Analysis Software

Most faces regarded as beautiful will have a significant number of key facial proportions that are at, or very close to, the golden ratio. All faces are unique though and have individual variations and imperfections. So not every face has all these proportions, even beautiful ones.

These particular markers have been developed through analysis of many faces. They are based on a very simple and logical set of the points that are required to construct the basic features of a human face. They will be discussed in detail in an upcoming article

Conclusion

By following the guidelines above, you should be able to take or select photos suitable for accurate facial analysis and identify a number of golden ratio dimensions in many faces. I’d love to see the results of your analysis. See the Contact page to send some samples. You can find additional discussion and examples of golden ratio facial analysis in the Beauty section of this site.

References:

Using Facial View and Camera Angle to take Flattering Portraits by Darlene Hildebrandt

How to draw the human head from Draw as a Maniac

Lens Perspective Tutorial by Stephanie Eastwood

Fautograph Analysis on Proboards.com

Facial Exercises For Reducing Wrinkles

Kate Middleton doesn’t care!

The post How to take photos and measurements for facial beauty analysis and identification of golden ratio proportions appeared first on The Golden Ratio: Phi, 1.618.

Golden ratio facial analysis of Julia Calderone

In October 2015, Dr. Keith Devlin was interviewed by science writer Julia Calderone in an article titled “The one formula that’s supposed to ‘prove beauty’ is fundamentally wrong.”

Professor Devlin is a accomplished Ph.D. in mathematics at Stanford University and NPR’s Math Guy. His comments have reach and impact, but his views on the golden ratio are not always accurate, complete, consistent, objective or supported by evidence. Earlier in 2015, he was featured by a leading online design magazine in an article titled “The Golden Ratio: Design’s Biggest Myth – The Golden Ratio is Total Nonsense in Design. Here’s Why.” The article drew hundreds of negative responses (which were later censored and deleted by the magazine) because of its inaccuracies and misrepresentations. A highly regarded NYC designer, Darrin Crescenzi, described the article as “dangerous” and “under-informed nonsense,” motivating him to write a six page counterpoint titled “Why the Golden Ratio matters. In defense of using visual harmonies in Design.”

Do Dr. Devlin’s claims about the golden ratio and beauty “prove anything” or are they “fundamentally wrong?” Unfortunately, this latest interview resulted in another article based on a straw man argument with inaccurate information and unsupported claims. Devlin’s assertions about the golden ratio and beauty are inconsistent with statements in his own online lectures (see video below). The evidence that he says doesn’t exist is readily available, and much closer than you might ever imagine.

The evidence is “right in front of your face”

Devlin claims in the article that no evidence exists for the golden ratio in the human body. He needed look no further than to the face of his interviewer to find that evidence, as illustrated by the golden ratios in her facial analysis shown above. More examples are below, along with an explanation of why these facial markers are important.

But the evidence for the golden ratio is still denied

Despite this and a body of other evidence, here are some of the key quotes from the article:

… the allegation that it exists in the human body has little to no scientific validation.

… mathematicians haven’t found evidence that the Golden ratio proves anything, let alone beauty, in the human body.

But on the science side, there’s no evidence.” No evidence, Devlin says, that things conforming to this ratio are more beautiful, or that the ratio exists in the human body at all.

But when you try to apply it to humans, Devlin says, the theory falls flat because there’s simply no evidence that we are optimised in the same way that plants are.” Humans come in all different shapes and sizes after all.

… the belief that the Golden ratio exists outside of the garden is simply that — a belief. “It’s like Creationism. You can believe it if you want, but there’s no evidence,” Devlin says. “If you believe it, you’re not being scientific.

Those are strong statements, but isn’t the core of “being scientific” investigating and providing evidence, rather than saying there’s none to be found?

More evidence for the golden ratio in the human face

Devlin says there’s no evidence “on the science side” to show that the golden ratio appears in the human face and impacts on our perceptions of beauty. Here are a few examples:

• The extensive research on facial attractiveness by recognized beauty expert Dr. Stephen Marquardt. He’s a maxillofacial plastic surgeon and a USC/UCLA university professor. He’s also the inventor of the Marquardt Beauty Mask, which is based on the golden ratio and was awarded a US patent. His research investigated the attractiveness of hundreds of faces. He’s been featured in dozens of articles and documentaries on beauty and is recognized as the leading expert on the topic.
• The research of Dr. Eddy Levin, a pioneer in dental aesthetics and inventor of the golden mean dental gauge and grid system. His system is compulsory study in many US universities.
• A 2008 university by researchers (Dr. Kendra Schmid et al.) at the University of Nebraska titled “Computation of a Face Attractiveness Index Based on Neoclassical Canons, Symmetry, and Golden Ratios.” The study identified six facial proportions for which golden ratios were predictors of attractiveness.
• A 2009 university study on attractiveness by researchers (Dr. Pamela Pallett et al.) at the University of Toronto and University of California, San Diego titled “New ‘Golden’ Ratios for Facial Beauty.” My analysis revealed that the faces selected by study participants as the most attractive had a dozen golden ratios in their key facial markers (see below).

Other evidence is available as well, so how can Devlin make these claims?

Just another straw man argument, battling an invalid proposition

First, note that the article creates a feable straw man argument with its statement that the golden ratio is said to be a formula that “proves” beauty. No one I know with any depth of knowledge on this topic claims that the golden ratio “proves” beauty. As in the design arts, it’s not a single, all-encompassing silver bullet. It’s a tool to understanding, creating and refining natural aesthetics and beauty.

Beauty is influenced by more than one factor

There is no single magic “formula” for beauty, yet we all know it when we see it. Beauty is a concept that is dependent on human perception, not a mathematically-defined proof or law of physics. It’s influenced by many factors – proportion, symmetry, complexion, skin tone, health, facial expression, aging and more.

Proportion and symmetry are critical to beauty

Proportion and symmetry are critical factors in facial attractiveness, and the golden ratio has unique mathematical properties that no other number has to create both recursive proportionality and bilateral symmetry. The evidence shows that it provides a very good foundation in unveiling and understanding the mathematics of beauty. Below are illustrations from Dr. Marquardt’s work illustrating varying levels of conformance to his golden ratio-based beauty mask. Click on any image for high resolution:

It’s lame to suggest that that specific facial proportions are irrelevant to beauty just because “humans come in all shapes and sizes.” They do to a degree, but they’re not all equally beautiful, and they really don’t come in “all” shapes and sizes. We all have the same basic facial features that make our faces look human, rather than like the faces of ridiculous caricatures, animals or aliens in a science fiction movie. As illustrated above though, even small variations in the most basic of human facial features can create significant differences in perceived attractiveness.

This same fact was demonstrated in the 2009 study at University of Toronto and University of California, San Diego, which analyzed perceptions of attractiveness over a range of different facial proportions:

While some of the conclusions of the study were flawed, my subsequent analysis demonstrated that facial images selected as most attractive by study participants had a dozen facial proportions that were very closely aligned with golden ratios:

Keep in mind that Devlin is a mathematician, not an expert in beauty or design, and mathematics is based on formulas, equations and proofs. His viewpoint is highly theoretical, as evidenced by his statements that it’s impossible for anything in the real world to fall into the golden ratio because it’s an irrational number. By that pedantic definition, there are also no circles in this world because Pi also has an infinite number of digits. Despite that mathematical truth, our cars drive quite nicely with their non-circular tires. Dimensions based on integers have the same issue. It’s impossible, for example, to create a hole that is exactly 1″ in diameter with infinite precision. In the real world though this is all irrelevant. Most sciences outside of mathematics do not operate with such theoretical perfection and precision. We shouldn’t expect there to be a mathematical “proof” for human perceptions of beauty anymore than there is a “mathematical proof” for every scientific finding in any of the behavioral sciences (e.g., anthropology, sociology or psychology).

One needn’t look far for the evidence of golden ratios

Science is based on the best evidence available, not personal viewpoints. Let’s investigate another photo yet, take some measurements and see what the evidence tells us. We don’t need to use a photo of a super model that we’ve pre-selected to illustrate our point. Let’s just take the face of the article’s author, Julia Calderone. Here’s her portrait photo from her site at http://www.juliacalderone.com:

Now let’s use PhiMatrix software, with its pixel-level accuracy, to measure the proportions of her key facial markers to see if the golden ratio is anywhere to be found. To provide increased accuracy, I sought out a high resolution version of her portrait photo to use for the measurements. The dividing line of each rectangle shown in the images below is at the golden ratio of the lines on either side of it. Click on any image below to see the full size images:

Attractive faces usually have numerous facial markers closely aligned to golden ratio proportions

As with many other attractive faces I’ve analyzed, we find that Julia’s face has a number of key facial markers whose proportions that are very close to the golden ratio. When measured to the pixel on the high resolution photo, they average to 1.634, which is within a barely perceptible variance of less than 0.1% from the golden ratio of 1.618:

• Pupil to teeth to chin – 1.634
• Pupil to nose to chin  – 1.618
• Inside of eyes to face width -1.663 (The left side of her face was covered by hair, so its position was estimated by centering the grid on other facial features)
• Inside of eye to outside eye to face width – 1.666
• Smile width to nose width – 1.619 (Dr. Marquardt’s research revealed that smiling produces better golden ratio proportions of the mouth and nose, at the golden ratio from the center of the nose to the outside of the lips)
• Hairline to eyebrow to eye – 1.605
• Top lip to teeth line to bottom lip – 1.615
• Width of central incisor tooth to lateral incisor tooth – 1.663
• Nose width to inner edge of nostril – 1.624

There’s no reason to expect her measurements to be exactly 1.6180339887… ad infinitum in every proportion to illustrate the concept. Julia is an attractive woman, but one would not expect perfect proportions even in a supermodel. Faces are never that perfect, and everyone has some degree of variation from perfect facial symmetry.

The minimum facial markers required to express a human face

Why are these markers and their positions and dimensions important and relevant? It’s because the minimum amount of visual data required to convey the image of a human face is what led to the iconic “smiley face:” two eyes and a mouth.

The proportions of the human face though are somewhat different:

Other proportions and positions do not look as human, so there must be a certain set of proportions and positions that represent the most human, and most attractive, appearance. Imagine what a person would look like with these facial marker configurations:

Professor Keith Devlin shows the beauty created by the Golden Ratio in design

Devlin is quoted saying that there’s “No evidence that things conforming to this ratio are more beautiful.” In his own video lectures though he describes the unique impact of the golden ratio in the beauty of fractal patterns, as shown below.

He admires one fractal pattern and states, “if you want to end up with this beautiful thing (fractal pattern) … the one (ratio) that makes this beautiful is the golden ratio.” He illustrates with these fractal patterns:

So how does Devlin “prove beauty” in fractals? Is it perhaps one of these?

Beauty² – Beauty = 1

No. There is no “proof for beauty,” even in the world of fractals and mathematics. There’s no law of physics or mathematical formula tucked away in a textbook somewhere which proves a fractal based on the golden ratio to be the most “beautiful.” Devlin doesn’t offer any “scientific evidence” that a pattern based on 1.325 or 1.5 with more white space is less “beautiful.” Can he quantify the “amount” of beauty? No, not unless there’s a constant or standard by which to measure it. He knows “beauty” when he sees it, and in his own example it’s produced by the golden ratio of 1.618. It results because the parts of the pattern come together in with a harmony, balance and perfection of proportion that he perceives as the most mathematically and aesthetically pleasing.

Why does he expect a different standard for the beauty of a face?

He continues with these statements:

Certainly if you have a regular growth pattern, the golden ratio is in there.

When you have biological growth the golden ratio does pop up.

It would be unwise to discount (the golden ratio in) anything related to biological growth. It’s in there.

Isn’t the development of a human face and body the result of a biological growth function?

The same ratio that gives beauty to a fractal gives beauty to a face

The only difference in Devlin’s illustration between the beautiful fractal and the unattractive one is the ratio that led to the proportion of each new iteration of its growth. In the fractal squares example, the beautiful fractal is based on a golden ratio of 1.618 while the unattractive one is based on a ratio of 1.5.

These same two ratios are found in Dr. Marquardt’s studies of actual human faces that illustrate the ranges of attractiveness. A face with proportions based on the ratio of 1.5 is clearly far less attractive than ones based on a ratio of 1.618. Click on any image for full resolution, and to see the correlation with the same ratios in Devlin’s fractal patterns.

If we recognize the impact that the golden ratio can have on the beauty of a fractal, it shouldn’t be difficult to extrapolate that insight to understand that it can impact the beauty of a face as well. Both plants and faces develop according to genetically encoded patterns to optimize some aspect of their nature. Faces just have more complicated patterns than the simple spiral patterns of plants. Plants are optimized for spacing of seeds and access to sunlight. Faces are optimized to attract desirable, healthy mates for reproduction and other more complex biological and human functions.

Science is often based on using the best available theory until another better one comes along. Is there is a better ratio than the golden ratio to explain the proportions observed in Julia’s face, and to understand human facial beauty in general? I invite you to use PhiMatrix for free with its custom ratios to test your theory and present it. I’ll give credit, recognition and a free full license to anyone who finds a system of ratios that better explains the positions and dimensions found in an attractive face.

The Golden ratio in art, design and composition

Devlin also denies that there is any relevance or real application of the golden ratio in the design arts. Let’s give that a test as well. We learn from Julia’s site that she’s also a photographer. A good photographer would know something about composition and use this knowledge in creating the portrait photo for her site. Let’s use PhiMatrix again to find the golden ratios of her photo’s height and width:

Interestingly enough, we find that her face looks to be in rough golden ratio proportion of the width of the photo (i.e., 0.618 to 1.618). If we simply shift the grid slightly to the right to center it on her face, we find that Julia (or her photographer) cropped her portrait so that her face is in golden ratio proportion to the width of the photo, and so that her shoulder is at roughly the golden ratio of the height of the photo:

And if that weren’t enough, we find that Julia chose a dress for her portrait with a neckline that is in golden ratio proportion to the height of her head. The length of her hair is also roughly a golden ratio proportion to her hairline to her chin. It’s a good, classic, well-proportioned look. Leonardo da Vinci chose the same proportion for the Mona Lisa.

Why do humans apply the golden ratio in art and design?

Why would we find these golden ratios here? One possible and likely answer is that Julia has been unconsciously seeing golden ratio proportions in her own facial reflection and in other faces for years. This proportion probably looks natural and aesthetically pleasing to her, and perhaps just seemed “right” when she selected and cropped her own photo for her site. I’ve often seen artists create the golden ratio with surprising precision without even consciously knowing they were using it. I show them the measurements within their own works and they say that it just “looked right” to them. If humans see golden ratios in the beauty of nature and the human face, wouldn’t it be very natural to use those same proportions to create a sense of natural aesthetics and beauty in art and design?

Devlin’s statements reveal other fallacies

If it’s this simple to show the fallacies in Devlin’s statements, what about the rest of what he says?

Devlin says:

Finding the Golden ratio [in the human body] tells you nothing. In order to have something meaningful, you need a scientific explanation (for why it’s there).

We don’t have scientific reasons for why the universe exists or why specific values exist in all kinds of constants in physics and chemistry, from properties of water to the speed of light. That doesn’t mean that measuring and understanding their characteristics is any less meaningful or valuable scientifically.

Devlin claims that interest in the golden ratio is the result of a craze launched by a single book by German psychologist Adolf Zeising in 1855. This ignores historical fact and its impact throughout history on Euclid, Luca Pacioli, Leonardo da Vinci, Botticelli, Raphael, Michelangelo, Johannes Kepler and others before that time. The golden ratios of the Taj Mahal are a beautiful and elegant example of its use in architecture as early as 1632.

Despite the above evidence, Devlin states:

Unfortunately all of this fun stuff about the art gallery and music and things is just spurious, it’s a fairy tale. You can believe in fairies, you can believe in Santa Claus, and millions of people do, but it doesn’t make them true.

This comment reveals either a lack of knowledge on the topic or a very biased and limited viewpoint. Countless artists, designers and photographers have used the golden ratio as a tool for composition, so why in the world would this be a fairly tale? It’s comments like this that led designer Darrin Crescenzi to describe Devlin’s claims as “dangerous” and “under-informed nonsense,” and hundreds of other readers to post rebuttals to Devlin’s statements in the article on design at Fastco Design. Science is advanced by investigating evidence, not by mocking things you haven’t fully investigated or don’t really understand well enough to present the evidence required to support your statements. Just as with the face and beauty, there’s plenty of evidence of the golden ratio’s application in the arts that Devlin says does not exist.

Devlin is obviously an intelligent individual, so his views may be the result of one or more of the following factors:

• His information is out of date, as evidenced by illustrations in his recent presentations that he downloaded from this site sometime before 2004. The quality and depth of available information has changed significantly since then.
• His view as a mathematician that nothing in the real world can be the golden ratio because of its infinite number of digits. Infinite precision is not possible or relevant in any real world application of the sciences, engineering or the arts.
• His view as a logician that everything is false until it can be proven to be true (with logic, math or science). Many human experiences can never be “proven true,” so this approach has little relevance to aesthetics and the arts. We experience and know beauty, art, creativity, love, etc., and have general consensus on what it is, without scientific proof that it is real and true.
• His view that life is the result of a freak accident without purpose or design. This is a personal belief system, unprovable by science. It filters the way the world is seen, especially as it relates to design in nature.

If you have current information and aren’t limited by those views, the golden ratio can be found in many very interesting places and is a very useful tool for understanding beauty and design.

Even Devlin admits,

I see the world differently from anybody who’s not a mathematician. In fact I see the world differently from many mathematicians. So, in some sense, I’ve seen things that other people are not seeing.

It follows then that he’s not seeing what is seen by people with other talents, experiences, education and viewpoints. This should be clear from the evidence presented above. Devlin’s books and lectures have some very good, insightful information on mathematics, but the viewpoint of even a leading mathematician on beauty, art and design is only going to be about as valuable as the viewpoint of a leading plastic surgeon, artist or designer on mathematics.

Devlin concludes saying,

It’s not that we haven’t disproved that the Golden ratio explains the human body, it’s that we haven’t proved it. I’m not saying any of these things are false, I’m saying that as a scientist, the way they argue it is bulls#!t. There’s just no substantiation for it.

So in the end, Devlin contradicts his emphatic claims. What he said is false about the golden ratio in the human body may not be false at all. It’s just his opinion that it hasn’t been proved scientifically. He positions himself as representing science, but has he proved his own claims “scientifically?” Wouldn’t a scientist examine available data and offer specific analysis on what makes the evidence valid or invalid rather than just making unsubstantiated claims? In Devlin’s own words about proofs:

The key property of a proof is not that it is logically correct, rather that it is expressed in a manner that enables a suitably qualified reader to fill in any holes they notice, to check any steps they have any doubt about, and to correct any errors they find (as they surely will if they dig deep enough).

That standard is not met by saying there’s no evidence when there is, and offering little in exchange but unsupported opinions.

Other perspectives on beauty, mathematics, art and science

Others throughout history have held different views on this topic.

Education is the kindling of a flame, not the filling of a vessel. – Socrates (470/469 – 399 BC)

The good, of course, is always beautiful, and the beautiful never lacks proportion. – Plato (c. 424 – 348 BC)

Without mathematics there is no art. – Luca Pacioli (1447–1517)

Measure what is measurable, and make measurable what is not so. – Galileo Galilei (1564 – 1642)

Geometry has two great treasures: one is the Theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold; the second we may name a precious jewel. – Johannes Kepler (1571 – 1630)

The most beautiful thing we can experience is the mysterious. It is the source of all true art and science. – Albert Einstein  (1879-1955)

Everyone is entitled to an opinion, but facts are based on verifiable evidence, and real understanding only comes with a depth of personal study and experience in a subject. I encourage anyone reading this article to explore this topic at a deeper level, investigate the evidence with an open mind and come to your own conclusions.

You may find that those who view the world as Professor Devlin does are just a few simple measurements and a few insignificant digits away from seeing that beauty of the golden ratio extends beyond the theoretical world of fractals and mathematics to the real world of human beauty, art and design.

To Dr. Devlin: If you’re reading this and can demonstrate that any of it is inaccurate then let me know and I will change it accordingly. I understand you hold a different viewpoint, to which you are entitled, but let’s please find a way to present this topic in a way that is factual and objective. The millions of people who simply want to learn about the golden ratio deserve much more than conflicting, inaccurate information accompanied by sensational, unsupported, polarizing claims. Please understand the evidence that others present before you criticize it and dismiss it. Please share the evidence that does exist with others objectively rather than telling them none exists at all. Please give them the opportunity to do their own analysis, to come to their own conclusions and to learn something in the process.

Note: No photos in this article or on this site have been altered to match golden ratio proportions. PhiMatrix software provides golden ratios and any custom ratio accurate to the pixel, and is available for free testing by anyone on any photo. Any facial analysis should be done with the subject facing directly into the camera, and with the photo taken from at least 10 feet away to elimination optical distortion.

Other references:

http:// www.businessinsider.com.au/the-golden-ratio-fibonacci-numbers-mathematics-zeising-beauty-2015-9

http:// www.techinsider.io/the-golden-ratio-fibonacci-numbers-mathematics-zeising-beauty-2015-9

Google shortcode for this article: http://goo.gl/397U3k

The post The Golden Ratio, Beauty and Design: It’s time to ‘face’ the facts. appeared first on The Golden Ratio: Phi, 1.618.

White lines show golden ratio proportions from pupils to nose tip to lip/teeth line to bottom of the chin.

White lines show golden ratio proportions from width of face to the inside of the eyes

Click on images for full resolution.

When a joke becomes science, then science becomes a joke.

A designer in Russia morphed several celebrity faces as a joke, but it somehow morphed into “scientific evidence” in yet another attempt to debunk the golden ratio. This time it was on Wired.com, a major online magazine site. (Find article here.) Igor Kochmala created some fun images of celebrity faces that he morphed to fit nonsensical patterns of golden ratio spirals. His blog page, called “Yet-another-Fibonacci-homework,” humorously featured his “Dr. Fibonazi’s Plastic Surgery Clinic.” There he transformed five celebrity faces and the Mona Lisa to goofy looking images to supposedly “bring natural harmony” to their faces, as shown below. Click on any image for full resolution.

The blog post was picked up by dozens of online magazine sites. Smash.com described the images as “hilarious distortions.” DesignTaxi.com hailed it as “satirical.”

Every rumor about you is true? What a setback!

When the blog post was picked up by Wired.com though, the story changed. The article was titled “How Celebrity Faces Would Look if They Fit the Golden Ratio.” The celebrities were now “disfigured by the golden ratio.” The use of the golden ratio by Leonardo da Vinci and Salvador Dali was reduced to “art lore.” Its application by Le Corbusier in the design of the UN Secretariat Building was nothing more than “architecture mythology.” The author, Margaret Rhodes, concluded saying,

“Kochmala’s project is “only the most recent setback for the golden ratio, whose mythology was deconstructed in posts by Co.Design’s John Brownlee (find article here) and Stanford’s Keith Devlin (find article here). Both detail the folly in retroactively applying the golden ratio to existing works of art, and of leaning on the math as a means of making a design resonate with users. The lesson: There are no surefire formulas in beauty or good design.”

Really? If an artist intentionally applies the golden ratio then is it “folly” to study it retroactively, or maybe just a good way to learn something about art and design? Nature is filled with structures and patterns that are based on mathematics, so wouldn’t applying the same principles in design just be common sense? The lesson: Examine the evidence before believing what you read. Learn about art and design from artists and designers, not from online magazines seeking clicks with sensational articles and mathematicians who view the golden ratio as an infinitely precise theoretical construct with few possible real life applications.

Evidence and facts aren’t good click bait for traffic, but you deserve them anyway.

I’ve written an article that covers the many fallacies and misrepresentations in golden ratio article on FastcoDesign by John Brownlee (find article here). I’ve written another article the highlights many evidences of golden ratio applications that Devlin says simply do not exist. I’ve illustrated da Vinci’s intricate use of the golden ratio in Salvator Mundi, The Last Supper, The Annunciation and other paintings. I’ve shown how Le Corbusier rather brilliantly applied his golden ratio-based “Le Modulor” design philosophy to the Secretariat Building, even down to dimensions within the window frames.

So can the golden ratio also be found in the faces of the celebrities lampooned by Kochmala? I admit I’m no Ph.D. in Math. It’s been decades since I took college courses in quantitative analysis, differential equations, and statistics. I do seem to recall though that you’re supposed to look for some evidence before saying that there’s none to be found, and are required to take some measurements before coming to scientific conclusions. So let’s do just that, using PhiMatrix design and analysis software to overlay golden ratio grid lines that are accurate to the pixel. Test it yourself if you want by using the free trial of the software to create the same phi-based grid lines.

Compare the fit of celebrity faces to the golden ratio

This first gallery compares the fit of four of the celebrity faces to the horizontal golden ratio proportions often found in attractive faces. The most basic of these is found in the distance between the pupils and bottom of the chin in relation to the lip/teeth line and tip of the nose. Photos need to be taken from directly in front of the face to do this analysis. This made the image of Sylvester Stallone used in the blog unsuitable, so I found another image. Click on any image for the full resolution view:

There are some slight variances in the lengths of the noses, and the two beards make perfect alignment to the chin difficult, but the golden ratio of the distance from the pupils to the bottom of the chin is very close to the lip/teeth line in all four faces.

This second gallery illustrates how these four celebrity faces fit the vertical golden ratio proportions often found in attractive faces. The most basic of these is found in the position of the inside of the eyes in relation to the width of the face (where the inside of the ears meet the face):

Here again, the position of the eyes of all four celebrities is an extremely close fit to the golden ratio of the width of the face. Many other golden ratios can be found in attractive faces, as illustrated in my analysis of the winner of Britain’s most perfect face contest and my analysis of a 2009 university study on attractiveness.

Every face is unique, and not all fit the golden ratio.

There’s one celebrity missing. The one celebrity in the Kochmala’s blog who didn’t fit these golden ratio proportions quite as well is Jack Nicholson. Here too I had to substitute a photo taken from directly in front of the face. By applying the same golden ratio grid, you can see that either his jaw is either proportionately larger than the others, or, if holding the jaw line constant, that his nose and mouth are somewhat higher on his face than those of the others. The horizontal ratios from the width of the face show that the eyes are positioned slightly closer to the center of the face. Click on an image for full resolution.

Are Jack’s facial proportions somewhat unusual? One independent answer to that question can be found in how caricature artists interpret his face. Caricatures greatly exaggerate the unusual features of a face to create a humorous, but still very recognizable, impression of it. Look how these artists represent Jack:

Note how his jaw is shown as very prominent. Note that the nose is shown as being small and unusually close to the eyes. This portrayal is consistent with the variation we see in his face versus the golden ratio proportions found in faces of more “classic” attractiveness. A face certainly does not need to be in perfect golden ratio proportion in every dimension to be attractive, but the greater the deviations the less likely it is to be perceived by most people as being attractive. This is confirmed by the extensive research on facial beauty of Dr. Stephen Marquardt, creator of the Marquardt Beauty Mask. Jack has some golden ratios that factor into his attractiveness, despite some of his more atypical facial dimensions.

The Mona Lisa and the Golden Ratio

Leonardo da Vinci collaborated with Luca Pacioli with his illustrations for Pacioli’s “The Divine Proportion.” Pacioli’s described the golden ratio as a “subtle and secret science” for the arts. This was no secret to da Vinci, so looking to see it in his paintings isn’t folly. As one might expect, his use of this “Divine Proportion” is clearest in his paintings of religious topics such as Salvator Mundi, The Last Supper and The Annunciation. The Mona Lisa doesn’t offer many clear, decisive composition lines, nor can we find another painting with her facing directly into the camera. Here though is how the painting compares to the golden ratio:

We find that Mona Lisa’s head is roughly positioned within the two golden ratios from the center of the painting to its sides, with her eye at the center of the painting. The distances of the top of the head, bottom of the chin, neckline and her arm are positioned in close golden ratio relationships. And, while her nose is a bit long, her lips are close to the golden ratio point of the distance from the pupils of her eyes to her chin, as with the celebrities above.

The evidence speaks for itself.

The golden ratio can of course be found in the facial dimensions of attractive women as well, as illustrated below and as described in my article on “Golden Ratio Myth, Fact and Misunderstanding: The missing evidence.” Not every feature of a face need be in golden ratio proportion to create beauty, but its impact on our perceptions of attractiveness is real.

A setback for objective, evidence-based journalism.

Wired.com is quick to claim the satirical celebrity images as a “setback” for the golden ratio, but that’s hardly the case. Unfortunately, it’s a setback for the quality of information in high profile online magazines, and a setback for the level of intelligence that they attribute to their readers. Readers deserve better than tabloid journalism. You deserve facts and evidence rather than unsubstantiated rumors and opinions.

As always, I encourage you to not accept everything you read as fact, to do your own research, take your own measurements and come to your own conclusions. Most debunkers don’t even look for the evidence, and those who do usually don’t take the time to do it right. I hope this article helps you to get a better understanding of the facts, and how to test them for yourself. The golden ratio is a unique in mathematics and geometry, frequently appears in nature and is used by many as a valuable tool in understanding and applying good principles in design.

References:

https://www.behance.net/fmflkshttps://www.behance.net/gallery/13967925/Yet-another-Fibonacci-homework

http://www.smash.com/celebrity-faces-become-hilarious-distortions-made-fit-fibonaccis-golden-ratio/

https://designtaxi.com/news/374726/Satirical-Project-Uses-The-Golden-Ratio-To-Transform-Faces-Of-Celebrities/

http://designyoutrust.com/2015/04/dr-fibonazis-plastic-surgery-clinic/

https://lockerdome.com/6779865890441025/7573541621211668

the golden ratio turns famous faces into fibonacci celebrities

http://www.wired.com/2015/06/celebrities-go-golden-ratios-knife/

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The Elle article describes Joan’s background and rise to supermodel status, saying, “The hair is long and straight, the bone structure aquiline, the smile dazzling. No wonder Smalls is kicking up the kind of fashion-industry excitement that comes along only a handful of times each decade. Over the past year, she has snagged the number-one spot on Models.com, having pulled in a rumored $3.5 million—making her the eighth-highest-paid model in the world, according to Forbes.” (Follow her on Facebook, Instagram and Twitter.)

Is “flawless, unequivocal beauty” marketing hype or mathematical fact?

LA Times reporter Rene Lynch was intrigued, but wanted to do some investigative reporting on this claim of “flawless, unequivocal beauty.” Was it just hype? Could it be substantiated? She called on the Phi Guy, Gary Meisner, author of Phi: The Golden Number and developer of PhiMatrix golden ratio design and analysis software to see what some golden ratio analysis would reveal. Gary invited Dr. Stephen Marquardt, inventor of the Marquardt Beauty Mask to collaborate on the analysis.

Rene’s full article with our interview appeared as a front page feature story on beauty in the LA Times as “Puerto Rican model has ‘planet’s most perfect face’? We find out.” Below are some of the results of the facial analysis performed by Dr. Marquardt and I using our respective golden ratio based tools.

Facial beauty analysis based on the Golden Ratio

I analyzed Joan’s face with PhiMatrix software to determine the presence of the golden ratio, the classic marker of beauty, in the proportions of her facial features. Click on any image for the full size image.

On the horizontal measures, the golden ratios found were not surprising for a beautiful supermodel:

• the inside points of her eyes to the width of her face (gold lines)
• the outside points of her eyes to the distance from the center of her nose to the width of her face (white lines)
• the points of her upper lips (cupid’s bow) to the width of her mouth (green lines)
• the width of her nose to the half-width of her mouth (red lines)
• the width of her lateral incisor tooth to the width of her central incisor tooth (blue lines)

The vertical measures were a bit more surprising and atypical. Golden ratios were found at:

• the height of the eyes to the distance from the bottom of the eyes to the top of the eyebrows (gold lines)
• the flare of the nose to the distance from the pupils to the tip of the nose (aqua lines)

The surprising measures were those that showed her face to be relatively long:

• the bottom of the teeth were at a lower point than is often found in the distance from the pupils to the bottom of the chin (green lines)
• the hair line was a higher point than is often found in the distance from the bottom of the eyes to the top of the eyebrows to the hairline (white lines)

Facial beauty analysis based on the Marquardt Beauty Mask

Dr. Marquardt’s analysis with his Beauty Mask revealed similar findings. We noted that in performing the facial analysis, we had to stretch the beauty mask to 108% of its normal height to fit her face. With this revision made, many of her facial components (eyes, brows, cheeks, chin and lips) matched the mask to a striking degree. Having to narrow the mask to be able to fit it to her face immediately tells us she’s not a classic beauty. This confirms the results of the golden ratio analysis above, which also revealed that Joan’s face is relatively longer and narrower than that of most women regarded to have classic beauty.

Even after the vertical stretching, a few of the components of her face were still not completely aligned with the mask and our classic golden ratio beauty measures.  The left side of her face (on the right side of the photo below) was slightly higher than her right side and her lower jaw is rather narrow at the chin lines.

Facial symmetry analysis

Symmetry does not necessarily create beauty, but beauty is sometimes augmented by facial symmetry. If Joan has the “planet’s most perfect face” we might expect to see a high degree of symmetry between the left and right half of her face. This, though, does not seem to be the case. The right half of her face appears to be very slightly wider and higher than the left side. The visual effect of this in mirrored photos can sometimes be exaggerated by a slightly off-center angle of the face to the camera, but it still seems to be true of her face.

There’s more to beauty than what meets the eye

So, as demonstrated from the facial analysis, Joan is unquestionably beautiful, but her face has a number of features that do not merit descriptions of unequivocally “perfect” or “flawless.”  So why does Elle make such a bold claim?  First, there’s the obvious sizzle factor.  Claims like this sell more magazines than “here’s another pretty face we found to put on our next magazine cover.”

Another factor is that you have to consider what constitutes “perfection.” I would contend that there’s much more to Joan’s success and fame than the precise measurements of her facial proportions. As shown in the photos at the beginning of the article, she can very successfully adapt her look and expressions to carry off everything from exotic/mysterious to sophisticated, to the smiling, trendy school girl. Not everyone can do that. More yet, the Elle article describes a personal presence that makes those around her sense a very special quality, a confidence or air, even in the way she speaks.

A key point of this is that true beauty is measured by more than the facial proportions that we analyzed in exacting mathematical detail. It appears that Joan’s deviations from mathematical facial perfection are more than offset by many other qualities that come from her inner strength, beauty, expressiveness and style. That is an important point that anyone who is asking “how can I be more beautiful” should duly note.  Dr. Marquardt’s general research shows that a smiling face conforms more closely to golden ratio proportions than a reposed (no smile) one. A smiling face is certainly far more beautiful than a face with a look of anger or arrogance. Looks can indeed kill, and the victim is most often your own personal appearance.

Inner qualities, cosmetics, personal style and presentation are all part of beauty

Joan’s inner qualities are also profiled in the Elle article, and readers should not let those qualities be overshadowed by the headline-making claims of the physical perfection of her beauty.  Most of their readers cannot change their facial dimensions. They can change makeup, clothing and hairstyles, which all have very real impacts on our perceptions of beauty. They can aspire and learn to change their inner qualities of beauty as well. All these are critical to the beauty of a supermodel, and to everyone else.

Classical beauty versus exotic beauty

After the interview with Rene, Dr. Marquardt and I continued our discussion on non-classical beauty. We both feel that Joan fits well in this category. Joan is perceived as beautiful even though she doesn’t fit golden ratios and the beauty mask perfectly. Why is this? First, we need to acknowledge that no one’s face fits every golden ratio or the beauty mask perfectly. And, according to Dr. Marquardt, the her facial components fit the narrowed beauty mask well, so this still puts her in the realm of being beautiful.

More importantly though, in the world of supermodels classic beauty does not necessarily grab people’s attention. What generates more attention than classic beauty is classic beauty coupled with a tension that results from the conflict of beautiful versus not beautiful, good versus bad, shy versus aggressive, etc. The greater the conflict, the greater the attention and attraction. These kind of faces are classified as exotic and/or striking. In the fashion world, there are many beautiful woman.  So how does a woman stand out from all the others? By having a face that’s both beautiful but conflicted. This results in a visual confusion that causes the tension in their perceptions to rise dramatically. A beautiful face coupled with that contrast, that is what makes a woman beautifully different and intriguing in today’s world of supermodels. That’s what Joan has.

Credentials and References:

Dr. Steven R. Marquardt is the inventor of the patented Marquardt Beauty Mask, profiled on the site he authored, Marquardt Beauty Analysis (www.beautyanalysis.com.)  He received his doctorate from UCLA and completed his residency in oral and maxillofacial surgery at the UCLA medical center. He retired from active surgical practice after 27 years and currently conducts his research on human attractiveness in Orange County, California. Dr. Marquardt is an active member of the Societies of Maxillofacial Surgeons, and a Diplomate of the American Board of Oral and Maxillofacial Surgery. His university appointments have included Assistant Research Oral Surgeon and Chief of Facial Imaging at UCLA, and professorships at Loma Linda University as well as at the University of Southern California. Dr. Marquardt’s facial imaging research is acknowledged by professionals worldwide and has been presented extensively in the public media. You may have seen him on CBS, NBC, The Discovery Channel, BBC and The Learning Channel. Newspapers such as the London Times and national magazines including those in the United States, France, Germany, the United Kingdom, Holland, South Africa, Hong Kong and Australia have featured articles on his work. He currently continues his research on attractiveness and teachers lecturing to university students as well as to professionals and public groups.

Gary Meisner is the developer of PhiMatrix Golden Ratio Design and Analysis software (www.phimatrix.com), used in over seventy countries for a variety of applications including art, architecture, design, photography, financial market analysis and cosmetic surgery. He is also the author and developer of the site “Phi 1.618: The Golden Number” (www.goldennumber.net).  This is one of the Internet’s leading sites on the topic of the Golden Ratio, and presents his original research as well as content from a community of dozens of contributors from a variety of academic and professional fields.  The site serves as an online community and resource for those interested in this topic and receives over 1 million visits per year.  His work has been features in the LA Times, an educational documentary on the golden ratio by EBS Docuprime in South Korea, in Da Vinci: The Exibition and other places. Mr. Meisner has extensive business career, serving as CFO and CIO roles for five public companies, as well as a private VC-backed technology company.  He has an MBA from the University of Chicago and BS from the University of Illinois.

Elle article: http://www.elle.com/culture/celebrities/a12642/joan-smalls-profile/

LA Times article: http://www.latimes.com/nation/shareitnow/la-sh-joan-smalls-perfect-face-20140108,0,5402692.story

The post The World’s Most Perfect Face: Joan Smalls? Elle says Yes! Golden Ratio says … appeared first on The Golden Ratio: Phi, 1.618.

Dr. Stephen R. Marquardt is the world’s most recognized expert on facial analysis and beauty. He has appeared in many documentaries and been referenced in countless articles, including the Beauty episode of BBC’s 2001 documentary “The Face.” Dr. Marquardt, also CEO of Marquardt Aesthetic Imaging, has studied human beauty for decades in his practice of oral and maxillofacial surgery, and now continues his studies full time.

His work includes cross-cultural surveys on beauty, in which he found that all groups had the same perceptions of facial beauty.  He also analyzed the human face from ancient times to the modern day.  Through his research, he discovered that beauty is not only related to phi, but can be defined for both genders and for all races, cultures and eras with the beauty mask which he developed and patented. This mask uses the pentagon and decagon as its foundation. Both of these geometric shapes embody phi in all their dimensions.  For a more complete treatment and understanding of the scope of his work information see his site at Marquardt Beauty Analysis. On that site you will see the evolution and connection of the phi-based geometry of the pentagon and dodecagon to the archetypal human face of his Marquardt Beauty Mask, as illustrated in concept below:

You will also see his application of the Marquardt Beauty Mask to show the universality of our perceptions of human facial beauty across all eras of history, cultures and ethnicity, as highlighted in the examples below:

Asian	Black	Caucasian

1350 B.C. Egypt	500 B.C. Greece

164 A.D. Rome	1794 A.D.

Dr. Marquardt has another section of his site that explores face variations by age, sex and ethnic group. Here he observes that “Each archetypal mask appears to be a species non-ethnic configuration. That is the more a face, any face, looks like the mask, the more attractive it is to all humans. However no face, even the most attractive/beautiful face, exactly correlates with or matches (i.e.- exactly fits) the Mask. We are all a variation of the mask. Some of us vary only a little and some vary a lot – but most of us are somewhere between.”

A digital application of the Marquardt Beauty Mask

Dr. Marquardt of course used the concepts he discovered and perfected to achieve successful results in surgeries on his many patients during his years practice. An independent researcher and graphic artist, who calls himself “The Photoshop Surgeon,” applied Dr. Marquardt’s mask in Photoshop to demonstrate its incredible ability to transform an already attractive face into one of exquisitely striking beauty. Click on the image below to watch this independently-created Youtube video showing the Marquardt Beauty Mask being applied in Photoshop with amazing results. The illustration below shows the the before and after images, with the alignment to the Marquardt Beauty Mask as the guide for the transformation in the center:

Explore the Marquardt Beauty Mask on your own

Details on applying the Marquardt Beauty Mask to your own photo can be found at “You and the Mask” page of his site. This includes male and female versions of the mask, frontal and lateral versions, in both smiling and repose (non-smiling) position. You can download the frontal and lateral repose versions of the female mask below. Click on image for full size version.

Note:  The Marquardt Beauty Mask illustrations above are copyright 2001 by Dr. Stephen Marquardt at Marquardt Beauty Analysis and are used by permission.

I’d like to thank Dr. Marquardt for his extensive research in this area, and for allowing it to be shared in summary format here so that viewers of this site can be aware of his landmark work and visit his site to learn more about its background, concepts and application, as well as his mission for his work in this field.

Click below to see an excerpt from the BBC documentary on “The Face” featuring Dr. Marquardt at the 2:02 mark:

The post Facial Analysis and the Marquardt Beauty Mask appeared first on The Golden Ratio: Phi, 1.618.

We may never answer the question “how many angels can dance on the point of a needle,” but how about this one: “How many Divine proportions ratios are there in the face of an angel?” The YouTube video and information in this article may give some insight into the answer, with details on the contest, a recap of explanations of beauty that fall short and new insights and a video illustrating the impact of the golden ratio in beauty.

The British contest in 2012 to find “Britain’s Perfect Face” draws over 8,000 entries, and finds Florence Colgate as the winner

British company Lorraine Cosmetics sponsored a contest in 2012 to find “Britain’s Perfect Face.” Billed as the “Naked Competition,” and seeking the most perfect makeup-free face, contestants were required to have completely natural faces, without make-up, botox or cosmetic surgery. The competition drew entries from 8,045 contestants, who were initially screened by a panel that included such industry notables as Joanna Hutton, senior skincare buyer for Superdrug, and Jody Furlong, casting director and model scout.

Once the panel had selected three finalists from the 18-40 age category and three from age 41 and over, voting was opened to the public. Florence Colgate, an 18-year-old student from Kent, England, was selected as their winner.

Various sources offered incomplete explanations of beauty

News stories reporting on the event offered various explanations and analysis as to what made Florence’s face the most perfect, referring to sources such as these:

• A 2009 university study by Pallett, Link and Lee, which claimed to have discovered a “new golden ratio” of beauty based on two simple measures: the distance between the pupils at 46% of the width of the face and the distance between the pupils and mouth at 36% of the distance from the hairline to the chin. In another post on this site, I demonstrate that this study was very flawed in its conclusions. Florence’s “perfect face” has ratios that were notably different, at 44% and only 32.8%, respectively.
• A 1998 by Gillian Rhodes, which related attractiveness to symmetry of the left and right halves of the face. Florence’s face is not really all that symmetrical, as illustrated by the photo below and by the symmetry video on Florence’s Facebook page.  In addition, unattractive faces can be symmetrical as well. Other studies have shown that slight facial asymmetry is found in beautiful faces, and even adds to their uniqueness, so symmetry cannot be the determining factor either.

• General observations that Florence’s face has traits traditionally considered to be beautiful in woman, including good complexion, large eyes, full lips and high cheekbones. These though are relative terms without any specific measurements or proportions to define them.

A more complete explanation of facial beauty analysis can be found in Phi, the Golden Ratio

I would like to offer a more complete explanation as to why Florence’s face was perceived among the many entries to be the most perfect: In addition to her facial symmetry and generally attractive feminine facial features, her facial proportions are an almost perfect illustration of the Golden Ratio, 1.618, also known as phi.

How many golden ratios do you think could appear in the perfect human face? 4? 6? 12? 20, or even more? Take a guess. Then watch the YouTube video below.

The image analysis shown in the video was done with
PhiMatrix Golden  Ratio Design and Analysis Software

Were there more golden ratios in her face than you thought? The video shows a simple facial analysis of the basic golden ratio relationships on only the horizontal and vertical dimensions of the face. In the video, the golden spiral closely follows the curve of the lower half of her face. This illustrates that beauty is also a function of the shape and position of the many curves found in the human face. For example, a nose flare with sharp square edges would not be as beautiful as one with gently rounded arcs, even though both could conform to the golden ratio in their size and position. For another view on this, see the patented Beauty Mask developed by Dr. Stephen Marquardt. This mask provides an archetype for facial beauty that captures the positions and shapes of all key facial features, and is also based on the golden ratio.

Here is a list of the golden ratio proportions shown in the video:

• The Golden Ratio Analysis in the Human Face
• Beauty in the Human Face, and
• The 2009 university study on the “New” Golden Ratio

“Beauty is in the eye, or phi, of the beholder?”

It has long been said that beauty is in the eye of the beholder and thought that beauty varies by race, culture or era.  The evidence, however, shows that our perception of physical beauty is hard wired into our being and based on how closely the features of one’s face reflect phi in their proportions.

So what are your thoughts about these findings on perceptions of facial beauty? Is the Golden Ratio the most critical factor? Is the evidence presented here on facial beauty more precise, complete and compelling than symmetry alone, or the simplistic measures of the 2009 study? Your comments are welcome.

For further reading see the articles below:

http://www.goldennumber.net/facial-beauty-new-golden-ratio/

http://www.goldennumber.net/beauty/

http://www.goldennumber.net/face

https://www.facebook.com/FlorenceColgate

http://www.beautyanalysis.com/index2_mba.htm

http://www.thegloss.com/2012/04/25/beauty/florence-colgate-most-naturally-beautiful-697/#ixzz2cfnYabmq

http://newsfeed.time.com/2012/04/27/does-this-woman-have-the-perfect-face/#ixzz2cfmLphjv

http://www.youtube.com/watch?v=rKhlFic_A5A

The post Beauty, the perfect face and the Golden Ratio, featuring Florence Colgate appeared first on The Golden Ratio: Phi, 1.618.

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:

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

This is where the conclusions of the study were flawed.  The study in fact actually confirmed that perceptions of beauty are indeed based on the Golden Ratio, 1.618, as illustrated by the photo at the beginning of this article showing a dozen golden ratios.  The two “new” golden ratios are reconciled to the true golden ratios below.

The faces selected as most attractive show clear Golden Ratio proportions 

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)

The “new” golden ratio of 0.46 can then be computed from these Phi-based numbers as:

• 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

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.

References:

Pallett, P. M., et al. New ‘‘golden” ratios for facial beauty. Vision Research (2009), doi:10.1016 / j.visres.2009.11.003 (PDF)

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.

http://www.eurekalert.org/pub_releases/2009-12/uot-rdn121609.php

http://www.nbcnews.com/id/34482178/ns/health-skin_and_beauty/#.UUUBjByG1KK

http://www.smh.com.au/lifestyle/beauty/shania-twain-more-beautiful-than-angelina-jolie-20091222-lb6h.html

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The human face abounds with examples of the Golden Ratio, also known as the Golden Section or Divine Proportion.  We’ll use a succession of golden ratios to create a golden ruler to understand design in the face:

The head forms a golden rectangle with the eyes at its midpoint. The mouth and nose are each placed at golden sections of the distance between the eyes and the bottom of the chin. The beauty unfolds as you look further.

Even when viewed from the side, the human head illustrates the Divine Proportion.The first golden section (blue) from the front of the head defines the position of the ear opening. The successive golden sections define the neck (yellow), the back of the eye (green) and the front of the eye and back of the nose and mouth (magenta).  The dimensions of the face from top to bottom also exhibit the Divine Proportion, in the positions of the eye brow (blue), nose (yellow) and mouth (green and magenta).

Human beauty is based on the Divine Proportion

See the photo below which illustrates the following golden ratio proportions in the human face:

• Center of pupil : Bottom of teeth : Bottom of chin
• Outer & inner edge of eye: Center of nose
• Outer edges of lips : Upper ridges of lips
• Width of center tooth : Width of second tooth
• Width of eye : Width of iris

• The blue line defines a perfect square of the pupils and outside corners of the mouth.
• The golden section of these four blue lines defines the nose, the tip of the nose, the inside of the nostrils, the two rises of the upper lip and the inner points of the ear.
• The blue line also defines the distance from the upper lip to the bottom of the chin.
• The yellow line, a golden section of the blue line, defines the width of the nose, the distance between the eyes and eye brows and the distance from the pupils to the tip of the nose.
• The green line, a golden section of the yellow line defines the width of the eye, the distance at the pupil from the eye lash to the eye brow and the distance between the nostrils.
• The magenta line, a golden section of the green line, defines the distance from the upper lip to the bottom of the nose and several dimensions of the eye.

The golden ratio face calculator grid:

You get an actual measure of golden ratio proportion and beauty using the golden ratio face calculator that is included in PhiMatrix golden ratio design software:

PhiMatrix provides transparent grids that can be applied to any image in any other software.  In the golden ratio face grid shown above, it uses phi, or golden ratio proportions to identify the key dimensions of the human face.  It has a free two week trial and is available for Windows and Mac.

Note that the PhiMatrix golden ratio circles grid can be used to identify golden ratio proportions in the human eye:

Even the dimensions of our teeth are based on phi

The front two incisor teeth form a golden rectangle, with a phi ratio in the heighth to the width.The ratio of the width of the first tooth to the second tooth from the center is also phi.The ratio of the width of the smile to the third tooth from the center is phi as well.Visit the site of Dr. Eddy Levin for more on the Golden Section and Dentistry.

Variations and other factors in beauty

Even with a perfectly proportioned face though, there are endless variations in coloring and the shapes within this fundamental facial structure found in the Marquardt Beauty Mask. Variations in each facial feature (eyes, eyebrows, lips, nose, etc.) give rise to the distinctive appearance of each race and provide for endless variations in beauty that are as unique as each individual. The human face also communicates an incredible array of emotions which are an integral element of one’s total beauty.  The human face creates more phi elements in its appearance when we smile.  You’ll be perceived as more beautiful with a warm smile than with a cold-hearted look of anger, arrogance or contempt.

Interestingly, symmetry in the face does not necessarily equate to beauty.  Many, if not most, faces that are perceived as beautiful are usually not even close to being perfect in symmetry of the left and right sides.  Perfect symmetry tends to result in a face that appears unnatural, animated or robot-like.

Other factors influence perceptions of beauty as well, including skin tone, health and age.

More importantly, the application of the golden ratio to beauty refers only to physical beauty, and that is only one element of what defines true beauty in humans.  The saying “beauty is only skin deep” reflects this.  Physical beauty is fleeting and passes with time.  Other qualities of the mind and soul are the substance of true beauty.  These include love, joy, peace, patience, kindness, goodness, faithfulness, gentleness and self-control, to quote from the Bible in Galatians 5:22-23.  Our inner beauty is reflected in many ways, through our creative works, expressions of thought, compassion, friendship and acts of service  for others.  So while Hollywood and fashion magazines may trumpet physical beauty, true beauty in the human experience and the things that lead us to love and be loved are found in a beauty that runs much deeper, and that ultimately impacts physical beauty as well.

See also the page on Facial Beauty and the New Golden Ratio and the site at BeautyCheck.de.

Phi and Golden Number Related Jewelry

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