Most people think that the origin of the golden ratio comes from Pythagoras. It is said that in ancient Greece, Pythagoras was walking in the street one day. Before he passed the blacksmith's shop, he heard the sound of striking the iron, so he stopped to listen. He found that the blacksmith had a regular rhythm when he was striking iron, and the proportion of this sound was expressed mathematically by Pythagoras. It has been applied in many fields, and later many people devoted themselves to it. Kepler called it "sacred division", and some people called it "golden section". Pythagoras' law appeared only 1000 years after the completion of the pyramid, which shows that it existed very early. I just don't know the answer.
It has aesthetic value in plastic arts. In the design of the length and width of arts and crafts and daily necessities, this proportion can arouse people's aesthetic feeling and is widely used in real life. The proportion of some line segments in the building adopts the golden section scientifically, and the announcer on the stage is not standing in the center of the stage, but standing on the side of the stage. Standing at the golden section of the stage length is the most beautiful and the sound spreads best. Even in the plant kingdom, the golden section is used. If you look down from the top of a twig, you will see that the leaves are arranged according to the golden section law. In many scientific experiments, a method of 0.6 18 is often used to select the scheme, that is, the optimization method, which enables us to arrange fewer experiments reasonably and find reasonable western and suitable technological conditions. It is precisely because of its extensive and important application in architecture, literature and art, industrial and agricultural production and scientific experiments that people call it the golden section.
The golden section is a mathematical proportional relationship. The golden section is strict in proportion, harmonious in art and rich in aesthetic value. Generally, it is 0.6 18 in application, just as pi is 3. 14 in application. In the elegant art hall, there are naturally golden footprints. It is also found that the themes of some famous paintings, sculptures and photographs are mostly at 0.6 18 of the picture. The artist believes that placing the bridge of a stringed instrument at 0.6 18 of the strings can make the sound softer and sweeter.
The aspect ratio of a golden rectangle is the golden ratio. In other words, the long side of a rectangle is 1.6 18 times of the short side. The golden ratio and the golden rectangle can bring aesthetic feeling to the picture, which is pleasant. It can be found in many artistic and natural works. The Parthenon in Athens, Greece is a good example. Leonardo da Vinci's Vitruvian Man fits the golden rectangle. Mona Lisa's face in Mona Lisa also conforms to the golden rectangle, and The Last Supper also applies this proportional layout.
Painters found that the ratio of leg length to height is 0.6 18: 1, and people have the most beautiful figure. However, the average length of women below the waist now only accounts for 0.58 of their height. Therefore, the 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.
The golden section and the golden section of architectural art are considered to be the most ideal proportion in architecture and art, and architects have a special preference for the number 0.6 18. Whether it is the pyramids in ancient Egypt, Notre Dame de Paris or the Eiffel Tower in France in recent centuries, there are data related to 0.6 18. The aspect ratio of the golden section to most doors and windows is also 0.618; In addition, the golden section was used in the design of ancient Greek temples.
Interestingly, this number can be seen everywhere in nature and people's lives: the navel is the golden section of the whole human body, and the knee is the golden section from the navel to the heel. The aspect ratio of most doors and windows is also 0.618. On some plants, the included angle between two adjacent petioles is137 28', which is exactly the included angle between two radii that divide the circumference into 1: 0.6 18. According to research, this angle has the best effect on ventilation and lighting of the factory building.
Architects are particularly fond of 0.6 18 in mathematics … No matter the pyramids in ancient Egypt, Notre Dame de Paris or the Eiffel Tower in France in recent centuries, there are data related to 0.6 18… It is also found that the themes of some famous paintings, sculptures and photos are mostly at 0.6 18…. The artist thinks that placing the bridge of a stringed instrument at the position of 0.6 18 can make the sound softer and sweeter.