Face Beauty Rank
Beauty assessment 

Contents
You can learn from encyclopedias that beauty is a category that depends on the harmonic combination of some aspects of an object determining some category of perfection. That's it, quite a complicated definition. But you can get it that beauty is a collective characteristic. To understand beauty, one has to understand and assess some aspects… What is a beautiful face then? And where are those very aspects of an object that tell us about the category of perfection? What do these aspects depend on and can they be objectively assessed?
Beauty aspects and their objectivity. And aspects vary quite a lot! They include biological characteristics (for example, complexion…), geometric properties (symmetry), cultural peculiarities (wellknown haircuts that used to belong to the Afro culture are now popular in different parts of the world), social aspects! It is a whole bunch of various criteria and opinions that change with time. Where's the way out? We will not assess beauty depending on this variety of beauty aspects. And we do not actually need it because people of different cultures, social positions, ages may perceive these aspects quite differently… We will settle on the geometric aspects of beauty – they can be assessed objectively and they are somewhat “stable” as compared to opinions and views. We think that any other beauty assessment based on other aspects is not objective.
Geometric aspects of facial beauty. We can single out the following geometric facial characteristics: deviation from the average, deviation from symmetry and deviation from the golden section. Currently, the average height of a man on the planet is 1.65 meters and the average height of a woman on the planet is 1.54 meters. We can accept that the height of 1.54 meters is the absolutely ideal height for a woman. Then we can say how beautiful someone's figure is judging by the deviation from the average. But it is also known that the average height of people has been changing with time. Thus, people were shorter in the Middle Ages, which can be seen from the size of knights' armor. Moreover, these characteristics may vary depending on the nationality and some social and cultural preferences. Thus, beauty assessment based on average values cannot be objective enough. It is common knowledge that people with symmetrical faces are more attractive. The smaller deviation from symmetry is, the more attractive a person is. Facial symmetry can be objectively and stably assessed and can be taken as part of a Beauty Rank. This should be a major consideration when performing plastic surgery. A facelift surgery must be based on face symmetry and not the adjustment of specific facial parts as any good plastic surgeon knows. There is one more geometric aspect in beauty: deviation from the golden section.
Golden section and ideal beauty.
In order to prove the presence of the golden section in the structure of human faces, measurements were taken for certain node points on several hundred faces. Photos were used to take measurements. Faces were turned precisely towards the viewer, the emotional condition of people in the photos was neutral, there were no external attributes (for example, hats). The faces were measured and analyzed with software specifically designed for the purpose. The following geometric proportions were selected:
Distribution curve for deviation from ideal beauty. The values of eight geometric proportions were calculated. The absolute difference between these values and the golden section showed deviation from the ideal beauty. You can judge from the deviation graph that the golden section is actually present in the facial structure. The horizontal axis represents deviation from the golden section  1.618. The values close to zero are characteristic of faces with ideal beauty. The vertical axis represents the position (in percent) each person occupies in the entire sample. Thus, we see the proof that the golden section is present in the facial structure and now we have an objective, stable criterion for beauty assessment.
Beauty Rank and Deviation from Ideal Beauty. The percentage value of this deviation – Deviation from Ideal Beauty can be one of the Beauty Rank components. The distribution curve will look the same for the entire population of people. There are no values on the horizontal axis: They may change if the shape of the graph changes. And the shape may change depending on the people included in the sample. The more different people are included in this sample, the closer our curve will be to the actual regularity. Anyone can be beautiful in one group of people (the Beauty Rank is 100%) and completely ugly in another group of people (the Beauty Rank is 0%). That's the problem with calculating the Beauty Rank and it means that it is a relative value. If you calculate the Beauty Rank, you must specify the group of people it was calculated for and then you can say for sure what position on the beauty scale you occupy in this group if you have that particular Beauty Rank. At the same time, we can calculate the absolute value of the Beauty Rank for the entire population of people if we find ideally ugly people. That is why it is interesting to know the deviation from ideal beauty. It does not depend on the sample and has some other advantages. At the same time, you can compare how beautiful different people are by both the Beauty Rank and the Deviation from Ideal Beauty.
“Deviation from Ideal Beauty” sounds a bit long, isn't it? Let's call it just “Beauty” and understand it as geometric deviation from Ideal Beauty. For instance, suppose we get “Deviation” equal to 0,121. It means that our beauty differs from ideal beauty by 0,121. Now lose this zero and the value of “121” will be the Beauty. Beauty that equals to zero is Ideal Beauty. The closer the Beauty value to zero is, the more beautiful the face is. This face has small deviation from perfection.
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