Application and examples of golden section in life?

The Parthian Temple in ancient Greece became a world-famous perfect building because its aspect ratio was 0.6 18. Architects found that the palace designed according to this ratio is more magnificent; To design a villa, it will be more comfortable and beautiful. Even a door and window will be more harmonious and pleasing to the eye if it is designed as a golden rectangle. In the elegant art hall, there are naturally golden footprints. Painters found that the ratio of leg length to height is 0.6 18: 1, and people have the most beautiful figure. However, nowadays, the average length of women below the waist only accounts for 0.58 of their height. Therefore, the female statue of Venus in ancient Greece and the image of Apollo, the sun god, deliberately lengthened their legs so that the ratio of leg length to height reached 0.6 18, thus creating artistic beauty. No wonder many girls are willing to wear high heels, while ballerinas stand on tiptoe from time to time when dancing. Musicians found that when the proportion of "Qianjin" strings in erhu performance is 0.618:1,the timbre played is the most harmonious and pleasant. .. as long as you pay attention, you can find the footprints of "messengers" of beauty everywhere. 0.6 18 method, used in scientific experiments and optimization of industrial and agricultural production, can also bring us huge economic benefits! The golden number is 0.6 18, which is really a gorgeous treasure for the benefit of mankind! In the ancient Greek city of Athens, there was a miracle made of marble. The statue of goddess in the center of the temple hall is carved out of ivory and gold. The goddess's posture is soft and charming. According to expert research, the ratio of the distance from the heel to the navel to the height of her whole body is exactly 0.6 18. Not only is Athena so beautiful, but so are many other Greek goddesses. The ratio of 0.6 18 can be found in the familiar Milos "Venus", the image of Apollo, the sun god, and some immortal statues such as Oman. 1483 or so, an unfinished oil painting by Leonardo da Vinci, the black line around St. Jerome's body, is a golden section rectangle. At that time, Leonardo da Vinci seemed to deliberately use this golden ratio. Retrospect is an oil painting by the French impressionist painter Scherett, and its line structure ratio is also 0.6 18. In lachman's masterpiece Greek Myths and Legends, Britain painted 96 beautiful pictures. The beauty of every painting is charming and elegant. If you carefully measure their proportions, Athena is similar. The oldest guqin in China is full of the magic of golden section, with two ponds on the back, Yi Long on the left and a phoenix on the right. There are three hinges that control the pronunciation of the strings: hammer, palm and phoenix. The piano has five strings, the notes are octaves, and the segments are emblems. "With the length of the piano, three points are lost, three points are gained, and the phase is increased or decreased", the whole string is thirteen emblems. Put these together, two pools, three buttons, five strings, eight tones and thirteen emblems. What a wonderful arrangement, it happens to be Fibonacci odd numbers, and the ratio of two adjacent Fibonacci odd numbers is getting closer and closer to the golden ratio. Is it intentional or coincidental? It seems that China ancients' understanding and application of the golden section is similar to that of the West. Architecture: As early as the 5th century BC, Greek architects knew that the ratio of 0.6 18 was a harmonious and balanced structure. The Egyptian pyramids in civilized China are shaped like square cones with different sizes. However, the ratio of the side length to the bottom height of these pyramids is close to 0.6 18. In some ancient temples, the height and width were also built in proportion to the golden number. They think such a rectangle looks more beautiful. Huang Jinlv is the law that architectural art must follow. In architectural modeling, people build pavilions or design platforms in the prime location of the tower, which can make the straight and monotonous tower body colorful. We have had a preliminary taste of the great ancient buildings. Now let's look at the mystery of modern golden numbers. Pythagoras has a famous saying: all beautiful things have a common feature, that is, the harmony between parts and parts and between parts and the whole. We have done a survey, if there are two kinds of video programs on the market, one is width/length 3∶4, and the other is 9∶ 16. These two ratios are very close to 0.6 18, because the golden rectangle is the most beautiful. Gold number is also used in chemical pharmacy. If we synthesize drugs now, we don't know which temperature is between 0~ 100℃ to get the highest synthesis rate and the best curative effect. Obviously, it is not practical to try one temperature at a time. It's much easier if you use golden numbers. Mathematics is the ancestor of the golden number, so there is a lot of knowledge in this field. In fact, there is also a lot of knowledge about the golden number in biology. Our research found that the golden section number of human body has certain regularity. The golden section law was discovered by Pythagoras, an ancient Greek mathematician in the sixth 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. 0.6 18, with strict proportionality, artistry and harmony, 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 the right 1/3 and the left 2/3 of the horizontal line of the oral fissure. Golden section law of face: golden rectangle of face with three courts and five eyes: (1) Body contour: shoulder width, hip breadth average width, and height from shoulder peak to hip base; (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. Golden Index: (1) Nose and lip index reflecting the relationship between the nose and mouth: the ratio of the width of the nose wing to the distance between the corners of the 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. (2) The proportional relationship is to express the beauty of the human body with figures and compare them according to certain benchmarks. 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. (3) Angle relation From different angles, it reflects different human body shapes. 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. Our research found that plants, like animals, also contain golden numbers. The amount of gold is represented by the Greek letter φ.

Please accept it, thank you!