"0.6 18" has always had an indissoluble bond with military development, and it often happens by chance. Whether it is the beautiful wheel of the Parthenon in ancient Greece or the Terracotta Warriors and Horses in ancient China, the relationship between the vertical line and the horizontal line completely conforms to the ratio of 1: 0. 18. Genghis Khan's Mongolian cavalry swept across Eurasia, which was amazing. Through research, it is found that the combat formation of Mongolian cavalry is very different from the traditional western phalanx. In his five-column formation, the heavy cavalry and light cavalry are 2∶3, the heavy cavalry with helmet vest is 2, and the fast and flexible light cavalry is 3, which coincides with the golden section law. Europeans first consciously applied the golden section law to religion and art, and its military application began in the Black Powder Period. At that time, muskets replaced spears. Maurice, the Dutch general who took the lead in mixing musketeers and spearmen, failed to break through the shackles of traditional formations. After King Gustav of Sweden adjusted this formation, the Swedish army became the most effective army in Europe at that time. His method is to add 96 musketeers to the original 2 16 musketeers and 198 musketeers of General Morris. This change conforms to the influence law of scientific and technological development and weapons and equipment progress on tactical development, highlights the role of firearms in combat, and makes it cross the watershed of the era of cold weapons and hot weapons. The ratio of 198+96 musketeers to 2 16 spearmen once again shows us the magical effect of the golden section law. 1865438+In June 2002, Napoleon attacked Russia; In September, he entered Moscow after the Battle of Borodino. Napoleon didn't realize at this time that genius and luck were disappearing from him bit by bit, and the peak and turning point of his career came at the same time. A month later, the French army withdrew from Moscow in the heavy snow. After three months of victorious marching and two months of prosperity and decline, from the time axis, Napoleon just stepped on the golden section.

In another June after 130, Nazi Germany launched the "Barbarossa" plan against the Soviet Union. For more than two years, the Germans kept the offensive momentum until August 1943, when the "Castle" operation ended, the Germans turned to the defensive and never launched a campaign-scale attack on the Soviet Union again. 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 German army's decline from prosperity. During the Gulf War, the US military repeatedly extended the air raid time by 38 days. It was not until 38% of Iraq's 4,280 tanks, 32% of 2,280 armored vehicles and 47% of the 3 100 artillery pieces in the theater were destroyed, that is, Iraq's military strength was weakened to the golden section, that the "desert saber" was pulled out to attack Saddam. The purpose of this war was achieved in only 65,438+000 hours on the ground.

Through some scattered examples in the war, the shadow of "0.6 18" is faintly visible, swaying and wandering. If viewed in isolation, it seems to be accidental coincidence, but if too many accidents follow the same trajectory, it becomes a law, which is particularly worthy of in-depth study.

Once I accidentally played ball with my classmates on the playground and measured Newton's nose. The distance between his nostrils and the ratio to the bridge of his nose are close to 0.6 18. After that, the noses of several people were measured, and the results were all in line with the golden section. In the following life, we became very sensitive to 0.6 18. After students' speculation and practice, we found that the aspect ratio of Duo Mi Le ancient cards, the proportion of butterfly body parts and the aspect ratio of beautiful petals also conform to this law. Inquiring a lot of relevant information, such as the pyramids of Egypt, is the best application of this law.

Imagine how to make a very ordinary thin rubber band make a "Doraemon" sound. Tighten, fix and stir, which is "1", and then measure its length and do a geometric problem in Grade Three-divide this "line segment" into golden sections, and you can measure the longer one of the two line segments obtained by division, which is about 0.6 18 times the length of the original line segment. Pinch this point and pluck the longer "string" to make a "2"; Then divide the longer line into golden sections and find "3", and so on, you can also find "4, 5, 6, 7".

Have you ever seen Toronto, a famous Canadian city by the lake Ontario, where the clear water flows gently on TV? In this modern city with rows of tall buildings, the most striking building is the towering Toronto TV Tower, which is magnificent and straight into the sky. Interestingly, the flat-topped castle embedded in the middle and upper part of the tower is located at 0.6 18 times of the total length of the tower, which is the golden section of the tower height. It makes the thin TV tower look harmonious, elegant and unique. Toronto TV Tower is called "the king of towers", and this wonderful "0. 18" has played a decisive role. Similarly, the second floor of the world-famous French "father of the Eiffel Tower" is located in the prime location of the tower, which adds infinite charm to the tower.

Magnificent architecture is indispensable for "0.6 18", especially in art. On the stage, the actors are not standing in the middle or on the edge of the stage, but standing at 0.6 18 times the total length of the stage. At this point, the audience looks very comfortable. The "golden ratio"-0.618-can be found in Milos' famous statues such as Venus, Athena and Amanda the Sea Girl, so the works have reached a beautiful fairyland.

Leonardo da Vinci's Mona Lisa and Raphael's The Gentle and Handsome Virgin both used this ratio intentionally or unintentionally. Because many parts of the human body follow the golden ratio. It is recognized that the most perfect face shape-"goose egg" shape, the ratio of face width to face length is about 0.6 18. If we calculate the graceful figure of ballerinas who want to live forever, we can know that the ratio of their leg length to their body length is also around 0.6 18, which constitutes the beauty of the human body.

An erhu player in China found in his long playing career that if the "weight" of the erhu is placed somewhere on the strings, the timbre will be unparalleled. Verified by mathematicians, this is exactly the golden section of the string, 0.6 18! The golden ratio is working miracles! ?

Accidental? No, around people, there are masterpieces of 0.6 18 everywhere: people always make desktops, doors and windows into rectangles with an aspect ratio of 0.6 18. Mathematically, 0.6 18 is even more amazing. 0.6 18, the proportion of beauty, beautiful color and beautiful melody are widely reflected in people's daily life and are closely related to people. 0.6 18, a wonderful number! It has created countless beautiful scenery and unified people's aesthetics.

The joking 0.6 18 created many "coincidences". In the whole world, 0.6 18 shining like gold is everywhere! People have been creating the golden section intentionally or unintentionally. As long as you pay a little attention, you can find how close it is to our life! Mathematics is very close to us, and it is applied all the time!

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.