# Pi-gold ratio evaluation method in face analysis If the perception of beauty is a concept based on unconscious mechanisms, how can it create a common aesthetic sense that can transcend the ages? How did the concept of beauty come about? Is there a mathematical expression for this? Mankind has tried to find answers to these questions for years. The golden ratio is the product of this effort. This ratio, which found its ideal expression in Ancient Greece known to the Egyptians, can be defined as follows.

When a line segment is bisected by a point; Let the ratio of the large piece=a, the small piece=b be equal to the ratio of itself to the large piece, and let this ratio be mathematically 1.61803. This is called the golden ratio. To show this value, Ø=Phi, the first letter of the Greek sculptor Phidias, who lived in the 5th century BC, is used. Mathematically it is an interesting number. When 1 is subtracted from its candid, it reaches its inverse value. When 1 is planted, it reaches the square value. It is the only one among these numbers. We can see this ratio in everything we define as beautiful.

The golden ratio is a natural ratio that people realize. A rectangle with a long side of 1.61803 and a short side of 1 is called a golden rectangle. This is the most pleasing rectangle. Old architectural structures were built with this rectangle. In an isosceles triangle, if the base is 1 and the sides are 1.6803, it is called a golden triangle. In this golden triangle, the medians of the base angles divide the opposite sides in the golden ratio and make new golden triangles. In these new golden triangles, when the middle angles are drawn again, new golden triangles are obtained. We can do this multiplication in the golden rectangle. Thus, a logometric spiral is obtained. We see this in nature. Some shellfish, such as Natulius, can be found in the sequence of sunflower seeds, etc. In fact, the growth of the mandible during the postnatal growth period in humans also occurs with this logometric spiral. The golden ratios on the human face have also been studied since ancient times. Leonardo da Vinci researched the golden ratio in body and facial profile.    Techniques based on the golden ratio are currently used in facial aesthetic evaluation techniques. The first of these is the circular sector analysis developed by Baund. In this analysis, a half-ember is drawn in front of the face with the line connecting the trchion and the tragus. This circle should pass through the tip of the nose and the chin. Also, tragus in the ear; When trichion is combined with nasion and menton, the angles between them are formed and when these are proportioned to each other, they give the golden ratio. Another method was developed by Ricketts. In this method, parallel lines are drawn from the trichion, the canthus of the eye, the tip of the nose, the junction of the lips, and the mentoneum parallel to the FHL. Perpendiculars passing through the targus are drawn on these with the tip of the nose. Thus, 3 golden rectangles are drawn on the face or profile. From this drawing, E-Me/Tri-Me= Phi, Tri-En/En-Me= Phi, En-Me/E-En = 2 Phi, Em-E/Me-Em = Phi, En-E/En- Em=Phi, Me-Em/En-Em= Phi An instrument called the golden perges was developed to examine the figures with the proportion of the horse. The arms of this compass are always opened to keep the golden ratio. In 1201, the mathematician Leonardo of Pisa (Filus Bonacci) developed a number sequence. This number is based on the reproduction of rabbits and is a unique number. Each digit in the sequence is the sum of the digits before it. 0,1,1,2,3,5,8,13…..Division of each digit in the sequence by the previous digit ultimately brings us to the same mysterious number, Pi. As flowers are the most obvious example of natural beauty, the face is one of the most important examples of external beauty. Although style and fashion differ widely, cross-cultural studies have found several commonalities in people’s perceptions of beauty.

For example, large eyes and fair skin are considered beautiful in all cultures.

On the other hand, facial beauty is valid for all age groups.

There are many studies on the evaluation of facial beauty.

Although there are various percentages, there are no mathematical formulas that fully reveal the concept of beauty. On the other hand, the golden ratio values ​​(1.61803…) determined among the face elements are only valid for the ideal human face. Although the golden rule of beauty is to be self-confident and to understand that you are the only one, there have been various studies recently in order to automatically make the decision for facial beauty.

It is known that a person with perfect proportions is seven and a half times the height of his head. When viewed from the front, the human head forms a rectangle with a height of 3.5 and a width of 2.5.

The eyes are located in the middle of the height of the head. The distance between the two eyes is the width of one eye and determines the width of the nose.

The transverse head dimensions are four eyes.

In anthropometric studies, proportions are sought in beautiful body measurements as well as in the human face. Ideal women’s measurements, which are considered to be 90 – 60 – 90, actually take height into account.

not valid if not received. Venus de MiloThe real “golden ratio” in the evaluations made with the modeling coefficient, taking into account the measurements of

being measured.

The true “golden ratio”” = (98 – 70 – 100) х М, where М = height (cm) / 166.

According to the formula, for example, while the real “golden ratio” for 150 cm height is approximately 88 – 63 – 90, it is 106 – 76 – 108 for 180 cm height.