Ask for a mathematical paper on the golden section, not too abstruse, just simple. The number of words is around 2000-3000.

This semester, we learned the golden section, and we deeply felt the beauty of the golden section.

Most people think that the origin of the golden section 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 in striking iron, and the contrast 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 did not appear until 1000 years after the completion of the pyramid, so it has existed for a long time. I just don't know the answer.

Divide a line segment into two parts so that the ratio of one part to the total length is equal to the ratio of the other part to this part. The radical sign whose ratio is 5/2- 1/2 or half minus one, and the approximate value of the first three digits is 0.6 18. Because the shape designed according to this ratio is very beautiful, it is called golden section, also called Chinese-foreign ratio. This is a very interesting number. We use 0.6 18 to approximate it, and we can find it by simple calculation:

1/0.6 18= 1.6 18

( 1-0.6 18)/0.6 18=0.6 18

This kind of value is not only reflected in painting, sculpture, music, architecture and other artistic fields, but also plays an important role in management and engineering design. 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. The infinite charm of the golden section is reflected in many great works. For example, Leonardo da Vinci's Vitruvian Man fits the golden rectangle. Mona Lisa's face also conforms to the golden rectangle, and The Last Supper also applies this proportional layout.

The golden section is widely used, not only in art, but also in the pyramids of ancient Egypt, Notre Dame de Paris, or the Eiffel Tower in France in recent centuries. The approximate value of the golden section is 0.6 18, which can be said to be ubiquitous in life.

In human body structure, the ratio of umbilical cord to sole, top of head to umbilical cord; The ratio of trunk length to hip circumference; The ratio of lower limb length to upper limb length is about 0.6 18. And the closer you get to this value, the more symmetrical and perfect your whole body will be. It is most suitable for people to live at the ambient temperature of 22℃-24℃, because the normal body temperature is 36℃-37℃, and the product of this body temperature and 0.6 18 is exactly 22.4℃-22.8℃, and at this ambient temperature, the physiological function, life rhythm and other metabolic levels of the human body are in the best state. For another example, nutrition emphasizes that 60% of coarse grains and 40% of flour and rice in a staple food are eaten together, which is beneficial to the digestion and absorption of the stomach and avoids gastrointestinal diseases. This can also be included in the 0.6 18 law of diet. Anti-aging includes physiological anti-aging and psychological anti-aging, which is more important? Studies have proved that the physiological anti-aging is four and the psychological anti-aging is six, which also conforms to the golden section law. Fully mobilizing and reasonably coordinating psychological and physiological forces to delay aging can achieve the best effect of prolonging life. Reasonable daily life also conforms to the division of 0.6 18. Of the 24 hours, 2/3 are for work and life, and 1/3 is for rest and sleep. On the relationship between motion and stillness, is it "life lies in motion" or "life lies in stillness"? From the dialectical point of view and a lot of life practice, it is proved that the relationship between activity and static is the same as the proportion of work and rest on the same day. Four points of activity and six points of activity are the best health care methods. Static and dynamic: From a dialectical point of view, the static and dynamic relationship is 0.6 18, and roughly four shifts and six divisions are better health preservation methods. Diet: medical experts also found that people who eat 60% to 70% full have almost no stomach problems; The proper diet is six portions of coarse grains and four portions of refined food. According to the golden section law, the best season for getting married is 0.6 18 in one year 12 months, from the end of July to the end of August. Medical research shows that autumn is the best golden season for human immunity. Because there are the most lymphocytes in human blood from July to August, a large number of lymphatic factor resistant to various microorganisms can be produced. At this time, people's immunity is strong. Less small huxing attracts many young people who have just entered the society as owners with its "low total price, low down payment and low monthly payment". Although the market demand for small huxing is very enthusiastic, there are also investment risks. How to invest in small houses? An interesting "golden section theory" is popular in the market. Because the ratio of working time to family time just constitutes a golden section, that is, 0.6 18 to 0.382, experts believe that the most valuable position may be the golden section between work and community. Small units should be carefully calculated because of their small size. In the process of getting hotter and hotter, there is a trend in the market, that is, huxing. But absolutely small does not meet the normal needs of residents, and it will definitely not be a trend. The new consumption or investment trend shows that there is also a golden ratio in small apartment area. Between 30-80 square meters, there is a golden ratio, just over 50 square meters. Therefore, the sales volume of small-sized units of more than 50 square meters in the market exceeds other specifications. The space is mainly bedroom and living room, and 30 square meters can't subdivide any functional area at all, so it is difficult to meet the high-quality home life. More than 50 square meters is the smallest area of functional golden section, which can be divided into 30 square meters of main space and 20 square meters of supporting space to solve various functions such as independent kitchen and bathroom, balcony and storage. Therefore, according to the "golden section theory", the small apartment should not only save the apartment area and reduce the total investment, but also meet the aesthetic and functional needs of space and ensure the quality of life and home interest of residents.

The golden ratio existed in the objective world before it was discovered, and people had a clear understanding of it after unveiling this mystery. When people re-observe nature according to this law, they are surprised to find that this law can be seen in many beautiful things in nature, such as leaves, flowers, snowflakes and five-pointed stars of plants ... Many animals and insects, especially the human body, have a rich golden ratio relationship. When people know this natural law, it is widely used in human life. Since then, in our living environment, it can be seen everywhere, such as building doors and windows, cabinets and desks; Books, newspapers and magazines that we often contact; Modern movie screen. Television screens and many household appliances are made up of similar numbers. It is applied as a classic law in the history of art. Many artists have created many immortal reputations with it. The golden section can be said to have a natural connection with the composition of photographic pictures. For example, the film window ratio of a camera is 135, and the camera is 24X36, which is a ratio of 2:3, which is very typical. The 4.5X6 of 120 camera is about 3: 5. Although 6x6 is a box, most of the post-production is cut into rectangles. As long as we open the album and have a look, we will find that most of the painting forms are similar to this ratio. This may be influenced by tradition and form people's aesthetic habits. In addition, it is true that due to its pleasant nature, sometimes people do not notice this ratio in time, but deliberately use it, but often unconsciously enter this law. This also shows that the golden section itself has a beautiful nature. In photography practice, the golden section rule is applied, mainly in the application of golden section points, lines and surfaces. The golden section, in panoramic composition, is mostly the position of the main performance object or visual center, while in mid-shot and close-shot composition, it is mostly the position of the main part of the scene. In portrait composition, people's eyes are often treated near the golden section. Gold thread is often used as the location of horizon, horizontal line and skyline. Even the host's position on the stage is in line with the golden ratio. The golden section is really wonderful visually.

The golden section is also used in war. The legendary Napoleon has an indissoluble bond with the golden section. How did this happen? It turned out that June of 18 12 was the coolest and pleasant summer in Moscow. After the battle of Borokino, which failed to destroy the Russian army, Napoleon led the army into Moscow at this time. At this time, he is full of ambition and arrogance. He didn't realize that genius and luck were disappearing from him at this time, and the peak and turning point of his career came at the same time. Later, the French army withdrew from Moscow in frustration in the heavy snow and howling cold wind. Three months of triumph, two months of climax and decline, from the time axis, when the French emperor overlooked Moscow through the flame, his foot just stepped on the golden section.

194 1 On June 22nd, Nazi Germany launched the "Barbarossa" plan against the Soviet Union and conducted a blitzkrieg. In a very short period of time, it quickly occupied the vast territory of the Soviet Union and continued to advance further to China. For more than two years, the Germans kept the momentum of attack, until the "Barbarossa" operation ended in August 1943, and the Germans turned to the defensive, and they were no longer able to launch an attack that could be called a battle against the Soviets. The Battle of Stalingrad, recognized by all war historians as the turning point of the Soviet Patriotic War, took place in1July after the war broke out, which was the golden point of the 26-month timeline of the rise and fall of the German army.

We should first feel and appreciate the beauty in mathematics learning. Mathematical beauty is different from other beauty, it is unique and inherent. This kind of beauty, as Russell, a famous British philosopher and mathematical logician, said: "Mathematics, if viewed correctly, has not only truth, but also supreme beauty, just like the beauty of sculpture, which is a kind of cold and serious beauty. This beauty is not the weak aspect that attracts our nature. This beauty is not as gorgeous as painting or music. It can be pure and sublime, and it can reach the perfect state that only great art can express. " The teacher often tells us the beauty of mathematics in class. Through the study of advanced mathematics, I gradually realized the true meaning of the beauty of mathematics. This feeling is strange, subtle, understandable but difficult to express. Mathematics is so fascinating to me ... as long as we are good at observing and thinking and combine what we have learned with life, we will feel the fun of mathematics. Mathematical knowledge is everywhere in life.