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Golden ratio - dividing a segment into unequal parts, with the entire segment (A) related to the larger part (B), like this most of(B) refers to the smaller part of (C), or
A: B = B: C,
C:B = B:A.
Segments golden ratio are related to each other using the infinite irrational fraction 0.618..., if C take as one A= 0.382. The numbers 0.618 and 0.382 are the coefficients of the Fibonacci sequence on which the main geometric figures.
For example, a rectangle with an aspect ratio of 0.618 and 0.382 is a golden rectangle. If you cut a square from it, you will again be left with a golden rectangle. This process can be continued indefinitely.
Another familiar example is the five-pointed star, in which each of the five lines divides the other at the golden ratio point, and the ends of the star are golden triangles.
Golden ratio and the human body
Human bones are kept in proportion close to the golden ratio. And the closer the proportions are to the golden ratio formula, the more ideal a person’s appearance looks.
If the distance between a person's foot and the navel point = 1, then the person's height = 1.618.
The distance from shoulder level to the top of the head and the size of the head is 1:1.618
The distance from the navel point to the top of the head and from shoulder level to the top of the head is 1:1.618
The distance of the navel point to the knees and from the knees to the feet is 1:1.618
Distance from tip of chin to tip upper lip and from the tip of the upper lip to the nostrils is 1:1.618
Distance from tip of chin to top line eyebrows and from the top line of the eyebrows to the crown is equal to 1:1.618
Face height/face width
The central point where the lips connect to the base of the nose/length of the nose.
Face height/distance from tip of chin to center point lip connections
Mouth width/nose width
Nose width / distance between nostrils
Interpupillary distance/eyebrow distance
The exact presence of the golden proportion in a person’s face is the ideal of beauty for the human gaze.
The golden ratio formula is visible when looking at forefinger. Each finger of the hand consists of three phalanges. The sum of the first two phalanges of the finger in relation to the entire length of the finger = golden ratio (except thumb).
Middle finger/little finger ratio = golden ratio
A person has 2 hands, the fingers on each hand consist of 3 phalanges (except for the thumb). There are 5 fingers on each hand, that is, 10 in total, but with the exception of two two-phalanx thumbs only 8 fingers were created according to the principle of the golden ratio (the numbers 2, 3, 5 and 8 are the numbers of the Fibonacci sequence).
Also worth noting is the fact that for most people, the distance between the ends of their outstretched arms is equal to their height.
A person distinguishes objects around him by their shape. Interest in the shape of an object can be dictated by vital necessity, or it can be caused by the beauty of the shape. The form, the construction of which is based on a combination of symmetry and the golden ratio, contributes to the best visual perception and the appearance of a feeling of beauty and harmony. The whole always consists of parts, parts different sizes are in a certain relationship to each other and to the whole. The principle of the golden ratio - highest manifestation structural and functional perfection of the whole and its parts in art, science, technology and nature.
Let's find out what the ancient Egyptian pyramids, Leonardo da Vinci's painting "Mona Lisa", a sunflower, a snail, a pine cone and human fingers have in common?
The answer to this question is hidden in the amazing numbers that were discovered by the Italian medieval mathematician Leonardo of Pisa, better known by the name Fibonacci (born about 1170 - died after 1228. After his discovery, these numbers began to be called by the name famous mathematician. The amazing thing about the Fibonacci number sequence is that each number in the sequence is the sum of two previous numbers.
The numbers that form the sequence 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, ... are called "Fibonacci numbers" , and the sequence itself is the Fibonacci sequence. This is in honor of the 13th century Italian mathematician Fibonacci.
In Fibonacci numbers there is one very interesting feature. When dividing any number in a sequence by the number in front of it in the series, the result will always be a value that fluctuates around irrational meaning 1.61803398875... and after a time it surpasses, That
reaching him.
(Approx. irrational number, i.e. number, decimal representation which is infinite and not periodic)
Moreover, after the 13th number in the sequence, this division result becomes constant until the infinity of the series. Exactly this constant number division in the Middle Ages was called the Divine proportion, and now in our days it is referred to as the golden section, golden average or golden proportion.
It is no coincidence that the value of the golden ratio is usually denoted Greek letter F(phi) - this was done in honor of Phidias.
So, Golden ratio = 1:1.618
233 / 144 = 1,618
377 / 233 = 1,618
610 / 377 = 1,618
987 / 610 = 1,618
1597 / 987 = 1,618
2584 / 1597 = 1,618
Golden ratio- a relationship of proportions in which the whole is related to its larger part as the larger one is to the smaller one. (If we designate the whole as C, most of A, less of B, then the golden section rule appears as the ratio C:A=A:B.) Author of the Golden Rule- Pythagoras - considered perfect a body in which the distance from the crown to the waist was related to the total length of the body as 1:3. Deviations of body weight and volume from ideal norms depend primarily on the structure of the skeleton. It is important that the body is proportional.
In creating their creations, Greek masters (Phidias, Myron, Praxiteles, etc.) used this principle of the golden proportion. Center of the golden proportion of the structure human body was located exactly at the navel.
CANON
The canon - a system of ideal proportions of the human body - was developed by the ancient Greek sculptor Polycletus in the 5th century BC. The sculptor set out to accurately determine the proportions of the human body, in accordance with his ideas about the ideal. Here are the results of his calculations: head - 1/7 of the total height, face and hand - 1/10, foot -1/6. However, to contemporaries the figures of Polykleitos seemed too massive and “square”. Nevertheless, the canons became the norm for antiquity and, with some changes, for artists of the Renaissance and classicism. Almost the canon of Polykleitos was embodied by him in the statue of Doryphoros (“Spear-bearer”). The statue of the youth is full of confidence; balance of body parts represents power physical strength. The broad shoulders are almost equal to the height of the body, half the height of the body is at the pubic fusion, the height of the head is eight times the height of the body, and the center of the “golden proportion” is at the level of the navel.
For thousands of years, people have been trying to find mathematical patterns in the proportions of the human body. For a long time individual parts of the human body served as the basis for all measurements, were natural units length. Thus, the ancient Egyptians had three units of length: a cubit (466 mm), equal to seven palms (66.5 mm), a palm, in turn, equal to four fingers. The measure of length in Greece and Rome was the foot.
The main measures of length in Russia were the sazhen and the cubit. In addition, an inch was used - the length of the joint of the thumb, a span - the distance between the spread thumb and index fingers (their heads), a palm - the width of the hand.
The human body and the golden ratio
Artists, scientists, fashion designers, designers make their calculations, drawings or sketches based on the ratio of the golden ratio. They use measurements from the human body, which was also created according to the principle of the golden ratio. Before creating their masterpieces, Leonardo Da Vinci and Le Corbusier took the parameters of the human body, created according to the law of the Golden Proportion.
The most main book of all modern architects, E. Neufert's reference book "Building Design" contains basic calculations of the parameters of the human torso, which include golden ratio.
Proportions various parts our body is a number very close to the golden ratio. If these proportions coincide with the golden ratio formula, then the person’s appearance or body is considered ideally proportioned. The principle of calculating the gold measure on the human body can be depicted in the form of a diagram 
M/m=1.618
It is characteristic that the sizes of the body parts of men and women differ significantly, but the ratios of these parts correspond in most cases to the ratios of the same integers.
The first example of the golden ratio in the structure of the human body:
If we take the navel point as the center of the human body, and the distance between a person’s foot and the navel point as a unit of measurement, then a person’s height is equivalent to the number 1.618.
In addition to this, there are several more basic golden proportions of our body:
the distance from fingertips to wrist and from wrist to elbow is 1:1.618
the distance from shoulder level to the top of the head and the size of the head is 1:1.618
the distance from the navel point to the crown of the head and from shoulder level to the crown of the head is 1:1.618
the distance of the navel point to the knees and from the knees to the feet is 1: 1.618
the distance from the tip of the chin to the tip of the upper lip and from the tip of the upper lip to the nostrils is 1:1.618
the distance from the tip of the chin to the top line of the eyebrows and from the top line of the eyebrows to the crown is 1:1.618
the distance from the tip of the chin to the top line of the eyebrows and from the top line of the eyebrows to the crown is 1:1.61
The golden ratio in human facial features as a criterion of perfect beauty.
In the structure of human facial features there are also many examples that are close in value to the golden ratio formula. However, do not immediately rush for a ruler to measure the faces of all people. Because exact correspondences to the golden ratio, according to scientists and artists, artists and sculptors, exist only in people with perfect beauty. Actually, the exact presence of the golden proportion in a person’s face is the ideal of beauty for the human gaze.
For example, if we sum up the width of the two front upper teeth and divide this sum by the height of the teeth, then, having obtained the golden ratio number, we can say that the structure of these teeth is ideal.
On human face There are other incarnations of the golden ratio rule. Here are a few of these relationships:
Face height / face width,
The central point where the lips connect to the base of the nose/length of the nose.
Face height / distance from the tip of the chin to the center point of the lips
Mouth width/nose width,
Nose width / distance between nostrils,
Distance between pupils / distance between eyebrows.
Human hand
Each finger of our hand consists of three phalanges.
The sum of the first two phalanges of the finger in relation to the entire length of the finger gives the golden number. Just bring your palm closer to you now and look carefully at the index finger, and you will immediately find in it the formula of the golden section (with the exception of the thumb).
In addition, the ratio between the middle finger and little finger is also equal to the golden ratio.
A person has 2 hands, the fingers on each hand consist of 3 phalanges (except for the thumb). There are 5 fingers on each hand, that is, 10 in total, but with the exception of two two-phalanx thumbs, only 8 fingers are created according to the principle of the golden ratio. Whereas all these numbers 2, 3, 5 and 8 are the numbers of the Fibonacci sequence.
Proportions in clothing.
The most important means Proportions are key to creating a harmonious image (for artists and architects they are of paramount importance). Harmonious proportions are based on certain mathematical relationships. This the only remedy, with the help of which it is possible to “measure” beauty. The golden ratio is the most famous example harmonious proportion. Using the principle of the golden ratio, you can create the most perfect proportions in the composition of a costume and establish an organic connection between the whole and its parts.
However, the proportions of clothing lose all meaning if they are not linked to the person. Therefore, the ratio of costume details is determined by the characteristics of the figure, its own proportions. In the human body, there are also mathematical relationships between its individual parts. If we take the height of the head as a module, i.e. a conventional unit, then (according to Vitruvius, a Roman architect and engineer of the 1st century BC, the author of the treatise “Ten Books on Architecture”) eight modules will fit in the proportional figure of an adult : from crown to chin; from chin to chest level; from chest to waist; from the waist to the groin line; from the groin line to the middle of the thigh; from mid-thigh to knee; from the knee to the middle of the shin; from shin to floor. A simplified proportion speaks of the equality of the four parts of the figure: from the top of the head to the chest line (along the armpits); from chest to hips; from the hips to the middle of the knee; from knee to floor.
The finished dress is sewn to fit an ideal, standard figure, which real life Not everyone can boast. However, a person can choose clothes in such a way as to look harmonious.
Proportions play a huge role in clothing.
Proportions in clothing are the ratio of the parts of the costume in size to each other and in comparison with the human figure. Comparative length, width, volume of the bodice and skirt, sleeves, collar, headdress, details affect visual perception a figure in a suit, to mentally assess its proportionality. The most beautiful, perfect, “correct” ratios look like those that are close to the natural proportions of the human figure. It is known that the height of the head “fits” the height about 8 times, and the waist line divides the figure in a ratio of approximately 3:5.
The most proportional human figure is considered to be the one in which these proportions are also repeated (the ratio of individual parts). The same goes for the suit.
In a costume, you can use both natural proportions and deliberately violated ones. It is impossible to go into detail here different variants, since for this you need to seriously study the laws of composition. We must remember that natural proportions, as a rule, are “advantageous” for any figure; at the same time, shortcomings of the build can be “corrected” by slightly moving, “looking” for one or another line during fitting (for example, you can slightly raise or lower the waist, narrow or widen the shoulders, change the length of the dress, sleeves, the size of the collar, pockets, belt).
The creation of clothing in many ways has something in common with architecture - both of these arts are intended for direct contact with a person, based on his natural proportions; finally, the suit, together with the person, is almost constantly surrounded by buildings and interior spaces. And the buildings, in turn, are in natural nature, in the city architectural environment. Therefore in different eras architecture and costume reflect art style of his time; and the folk costume, as it were, absorbs and preserves for centuries all the best, perfect, “eternal”.
The mass of the suit, its apparent “heaviness” or “lightness” depends on various reasons. The more “piled up” of lines, details, decorations, the more massive the figure; but when there is “nothing superfluous,” even a naturally monumental figure will be freer, as if lighter. When physically equal volumes materials that are dense, dark, embossed, and rough seem more massive than light, light, transparent, smooth, and shiny materials. At the same time, light colors “increase” volume, “reducing” heaviness, dark ones - vice versa. From here - practical conclusion: fat people You should not be afraid of light materials, but it is better to place them in the upper part of the figure, near the face.
What's happened Beautiful face? Some people think that this is a memorable face with a very expressive features, for some, a beautiful face means attractive lips and “doll” eyes, while others see beauty simply in healthy skin. In fact, the answer to this question was found a long time ago, long before the advent of aesthetic medicine as such.
A beautiful face is a harmonious face, and harmony is the correct relationship of all parts of the face to each other. Today everyone around is talking about the golden ratio - an amazing formula that reveals the secret of ideal facial proportions..
The golden ratio rule allows you to create a harmonious face
In fact, everything in our world is ideal and harmonious. Nature has built everything in such a way that under normal, natural conditions the world filled with perfect beauty. The ideal shape of snowflakes, the stunning beauty of the animal world, amazing plants and many more incredible things that amaze us every day - these are all the creations of nature.
For for long years humanity has tried to uncover the secrets of nature, to conduct mathematical analysis and understand how she manages to create beauty.
The golden ratio rule is an amazing discovery, a mathematical formula that reveals the secret of ideal facial proportions.
The main thing now is just to learn how to use it correctly.
Golden ratio:
- discovery of the secret of the golden ratio: Pythagoras, da Vinci and Egyptian priests;
- how to apply the secret of the golden ratio in aesthetic medicine.
Discovering the secret of the golden ratio: Pythagoras, da Vinci and the Egyptian priests
First amazing secret The Egyptian priests comprehended the golden ratio, and very jealously guarded it from other curious minds. It was according to the principles of ideal proportions that one of the wonders of the world was built - the Egyptian pyramids. At their base lies a square, and side edge is isosceles triangle with a right angle at the top and angles at the base of 45 degrees.
In a pyramid, the side of the base is related to its height as 1.618 - this is the main number of the golden ratio, the Divine proportion or the number “phi”. In 550 BC, the ancient Greek mathematician Pythagoras went to Egypt, and as a result of careful measurements and calculations, he managed to understand the principles of construction Egyptian pyramids and find out the same number “phi”.
More to the point in simple language, then the golden ratio is such a proportional division of a segment into two unequal parts, in which the entire segment is related to the larger part, as the larger part is related to the smaller one.
One of the greatest painters of all world history, Leonardo da Vinci, also successfully used this secret. He realized that the closer the proportions of a person’s figure and face are to the number “phi,” the more beautiful he is considered. Thus, the artist no longer needed to find amazing beauties to become his models.
Leonardo da Vinci simply drew any woman, and then adjusted the proportions of her figure and face to the proportions of the golden ratio. You will be surprised to learn that the stunning masterpiece of world painting - the portrait of Mona Lisa - is adjusted precisely according to the principle of the golden ratio. Now we can safely assume that the solution greatest secret humanity - the amazing “smile of Gioconda” lies precisely in mathematical calculations.
How to apply the secret of the golden ratio in aesthetic medicine
Everything is clear with the number “phi”, and with the Mona Lisa too, but how to apply the secret of the golden ratio in modern aesthetic medicine - you ask. The answer to this question was found by the same Leonardo da Vinci. He developed the so-called golden ruler, the aspect ratio of which is equal to the very number “phi”.
Somewhat later, contemporaries adapted this amazing discovery and designed a “beauty mask”. With its help, as well as with the help of new technologies, you can “adjust” facial features to the absolute ideal.
Modern injection, hardware and surgical techniques make it possible to fill missing volumes, tighten sagging tissues and do a lot of other things to correct facial features. But what suits one person perfectly will look completely ridiculous on another’s face.
You cannot inject everyone with the same amount of filler into their lips or correct their nose using the same template.
Beauty is in harmony, and harmony is in proportions. Use the secret of the “golden ratio” correctly, calculate the ratio of certain parts of the face to each other, and create perfect beauty.. Leave your questions, reviews and suggestions in the comments to this article.
It is enough just to bring your palm closer to you and look carefully at your index finger, and you will immediately find the formula of the golden ratio in it. Each finger of our hand consists of three phalanges. The sum of the first two phalanges of the finger in relation to the entire length of the finger gives the number of the golden ratio (with the exception of the thumb). In addition, the ratio between the middle finger and the little finger is also equal to the number of the golden ratio. 4
A person has 2 hands, the fingers on each hand consist of 3 phalanges (except for the thumb). There are 5 fingers on each hand, that is, 10 in total, but with the exception of two two-phalanx thumbs, only 8 fingers are created according to the principle of the golden ratio. Whereas all these numbers 2, 3, 5 and 8 are the numbers of the Fibonacci sequence.
The golden ratio is present in the structure of all crystals, but most crystals are microscopically small, so we cannot see them with the naked eye. However, snowflakes, which are also water crystals, are quite visible to our eyes. All the exquisitely beautiful figures that form snowflakes, all axes, circles and geometric figures in snowflakes are also always, without exception, built according to the perfect clear formula of the golden ratio. Everything in the Universe known to mankind galaxies and all the bodies in them exist in the form of a spiral, corresponding to the golden ratio formula.
The periods of revolution of the planets of the solar system are also subject to the principle of the Golden Section.
The structure of all naturally occurring living organisms and inanimate objects, having no connection or similarity with each other, are planned according to a certain mathematical formula. This is the most striking evidence of their conscious creation according to a certain project or plan. The formula of the golden section and golden proportions are very well known to all people of art, for these are the main rules of aesthetics. Any work of art designed in exact accordance with the proportions of the golden ratio is a perfect aesthetic form.
According to this law of the Great Divine Creation, galaxies were created, plants and microorganisms, the human body, crystals, living beings, the DNA molecule and the laws of physics were created, while scientists and people of art only study this law and try to imitate it, to embody this law in their creations.
There is no doubt that everything in our world, in the life around us, was created by the Almighty Lord without any similarity. Whereas people only copy and imitate the examples existing in nature that He created.
We only reproduce, with a greater or lesser degree of skill, the semblance of perfection of the life forms that surround us everywhere.