What are the applications of golden section in life?

The golden section law was discovered by Pythagoras, an ancient Greek mathematician in the 6th century BC, and was later called the golden section by Plato, an ancient Greek aesthete. This is actually a numerical proportional relationship, that is, dividing a line into two parts. At this time, the ratio of long segment to short segment is exactly equal to the ratio of the whole line to long segment, and its numerical ratio is 1.6 18: 1 or 1: 0.6 18, that is to say, long. The golden section has an extremely wide and simple application both in theory and in real life, and it has also had a great influence in history. In ancient times, the ratio between the middle and the end was mainly used as a painting method. By the Renaissance, it had aroused people's great interest and attention at that time, and had a wide influence and been applied in many aspects. For example, in painting and sculpture, painters and sculptors hope to solve the problem of shape perfection and the relationship between its parts from the mathematical scale, and take this as a scientific artistic theory to guide artistic creation and reflect the perfect structure of ideal things. Leonardo da vinci, a famous painter, thinks in his book On Painting: "Aesthetic feeling is completely based on the sacred proportional relationship between the parts, and all the features must work at the same time to produce a harmonious proportion that fascinates the audience." Artists in this period were consciously tempted by the charm of the golden section, which closely combined mathematical research with artistic creation and had a great influence on later formal aesthetics and experimental aesthetics.

/kloc-in the 9th century, Cai Xin, a German aesthetician, put forward the principle of golden section, and expounded the problem of golden section in theory, holding that golden section is the key to unlock the mysteries of natural beauty and artistic beauty. He studied aesthetics by mathematical proportion method, which inspired future generations. Fechner, a German philosopher, aesthetician and psychologist, tried experimental aesthetics, established the golden section principle on the basis of extensive psychological tests, and combined aesthetic research with natural science research, which attracted wide attention. Until 1950s, the research of experimental aesthetics was still very active. Until recently, the golden section principle was still a scientific aesthetic problem full of magical mysteries. For example, in the field of quasicrystal structure research in crystallography, the problem of golden section has once again aroused the interest of physicists and mathematicians.

The biggest reason why these sculptures can arouse the audience's * * * is the harmonious beauty of their overall form of 0.6 18. This magical figure has strict proportionality, artistry and harmony, and contains rich aesthetic value. Why do people instinctively feel the existence of beauty for such a proportion? In fact, this is closely related to the evolution of human beings and the normal development of human bodies. According to research, in the process of evolution from apes to humans, the skull and leg bones changed the most and the body shape changed the least, because it was similar to gold. Many proportions in the human body structure are close to 0.6 18, so the beauty of the human body is fixed in the historical accumulation of hundreds of thousands of years. Humans are most familiar with themselves, and they will inevitably regard the beauty of the human body as the highest aesthetic standard, which is derived from things and people and from people and things. Any object similar to the human body likes it and feels beautiful. Therefore, the golden section law, as an important law of formal beauty, has become an aesthetic classic law handed down from generation to generation, and it has never failed! In recent years, when studying the relationship between the golden section and the human body, it has been found that there are 14 "golden points" (the ratio of short segment to long segment of an object is 0.6 18), 12 "golden rectangles" (the width-length ratio is 0.6 18) and two "golden rectangles".

Golden point: (1) navel: the dividing point between the top of the head and the bottom of the foot; (2) Throat: the dividing point between the top of the head and the navel; (3), (4) Knee joint: the dividing point between navel and sole; (5) and (6) Elbow joint: the dividing point between shoulder joint and middle fingertip; (7) and (8) nipple: the dividing point on the longitudinal axis of trunk nipple; (9) Eyebrow point: the dividing point between hairline and chin base 1/3 and 2/3; (10) Subnasal point: the dividing point between hairline and chin base 1/3 and 2/3; (1 1) lip bead point: the dividing point between the nose base and the chin base 1/3 and the middle and lower 2/3; (12) straight point of chin labial groove: the dividing point between 1/3 and upper middle 2/3 is the distance between nose base and chin base; (13) Left corner point: the boundary point between the left 1/3 and the right 2/3 of the horizontal line of the oral fissure; ( 14)

Right corner point: the boundary point between right 1/3 and left 2/3 of the horizontal line of the oral fissure. The golden section of the face: the face has three courts and five eyes.

Golden rectangle: (1) Body contour: shoulder width, hip breadth average width, and the height from shoulder peak to hip bottom is long; (2) Facial contour: the horizontal face of eyes is wide, and the distance from hairline to the bottom of chin is long; (3) Nose contour: the alar is wide and the distance from the nasal root to the nasal floor is long; (4) Lip contour: At rest, the distance between the peaks of the upper and lower lips is wider, and the distance between the lips is longer; (5) and (6) Hand contour: the transverse diameter of the hand is wide, and the average length is taken when the five fingers are together; (7), (8), (9), (10), (1 1), (12) Maxillary incisors, lateral incisors and canine profiles (three on the left and three on the right): the largest mesial and distal diameters. There are various golden indexes in the human body: (1) nose and lip index reflecting the relationship between nose and mouth: the ratio of the width of nose wing to the distance between corners of mouth is close to the golden number; (2) Eye-lip index reflecting the relationship between eyes and mouth: the ratio of the distance between the corners of the mouth and the outer canthus of the eyes is close to the golden number.

As one of the standard scales of bodybuilding, 0.6 18 is beyond reproach, but it has "fuzzy characteristics". Like other aesthetic parameters, it has an allowable range of change, which is restricted by ethnic, regional and individual differences. Numbers are used to express the beauty of the human body, mainly reflecting the harmonious proportional relationship. The method of judging the proportional relationship between a certain part of the same human body and the human body is called the same body method (see the middle picture). Divided into three groups: coefficient method, constant finger height and length index, such as human body sitting five times and standing seven times, that is, the height is five times the height of head when sitting, and 7 or 7.5 times when standing; Percentage method, the body length is regarded as 100%, and the proportion of all parts of the body in it; Dichotomy: that is, the human body is divided into two parts, most of which are from the foot to the navel, and a small part is from the navel to the top of the head. Standard face, its length-width ratio is coordinated, which accords with three stops and five eyes (see the right picture). Three stops refers to the length of the face, and the distance from the hairline of the head to the chin is divided into three equal parts, that is, from the hairline to the eyebrows, from the eyebrows to the tip of the nose, and from the tip of the nose to the chin. Each equal part is called one stop and three stops; Five eyes refers to the width of the face, and the frontal projection length between the two ears is the length of five-eye fissure. Except for eye fissure, the distance between the inner and outer canthus is the length of one-eye fissure, and there are two eye fissures from both sides to the ear, which is called five eyes. From different angles, the shape of the human body is different. The theory of side angle put forward by Bert and Campon is to reflect the beauty of human body through angle. Among them, Campen's theory is a method to measure the forehead inclination angle in side view based on the straight line connecting the point under the nose and the point at the ear hole, so that the complex three-dimensional head can be described by a simple contour line-this method is called side view qualitative analysis. Use a straight line connecting the tip of the nose and the submental point to observe the protruding degree of the lips and evaluate the beauty and ugliness of the lower part of the face. The nose tip, the red front edge of the lower lip and the submental point are on the same straight line, which is called the Ricketts aesthetic plane, which is a symbol of beauty.