2. Actual investigation method: measure some items in real life to find out the amount of gold.
3. Literature method: Euclid's >. & lt& lt abacus >> and other survey results: After investigation, the following points are found:
As early as the 6th century BC, the Pythagorean school in ancient Greece studied the drawing methods of regular pentagons and regular decagons, which showed that the golden section had been touched and even mastered at that time. In the 4th century BC, eudoxus, an ancient Greek mathematician, first studied this problem systematically and established the theory of proportion. & ltPacioli & gt absorbed the research results of eudoxus at that time, and made a further systematic discussion on the golden section, which became the earliest theoretical treatise on the golden section. The name of golden section gradually became popular in19th century. The golden section has many interesting properties and is widely used by human beings. The most famous example is the golden section method or 0.6 18 method in optimization, which was written by American mathematician Kiefer in 198.
This mathematics can be seen everywhere in nature and people's lives: the navel is the golden section of the whole length of the human body, and the knee is the golden section from the navel to the toes. The aspect ratio of most doors and windows is also 0.6 18. Architects have a special preference for mathematics, whether it is the pyramids in ancient Egypt or Notre Dame de Paris, it is related to 0.6 18.
0.6 18 was also widely used in the war. It is an extremely fascinating and mysterious number in the strategic campaign, and it also has a very pleasant name-the golden ratio, which was discovered by Pythagoras, a famous ancient Greek philosopher and mathematician, more than 2,500 years ago. Throughout the ages, this figure has been regarded as the golden rule of science and aesthetics by later generations/in the history of art, almost all outstanding works have unanimously verified this famous golden ratio. In weapons and equipment, we can easily find that the golden ratio is everywhere. In artillery firing, if the maximum range of an indirect gun is 12 km and the minimum range is 4 km, its optimal firing distance is about 9 km, which is 2/3 of the maximum range and very close to 0.6 18.
The golden section is closely related to people. In recent years, when studying the relationship between golden section and human body, it is found that there are 14 "golden section points", 12 "golden rectangles" and two "golden indexes" in human body structure. The golden index (65,438+0) reflects the nose-mouth relationship, and the eye-mouth index (2) reflects the eye-mouth relationship, which is 0.6 18. As one of the standard scales of bodybuilding,
Medicine is inextricably linked with 0.6 18, which can explain why people feel most comfortable in the environment of 22 to 24 degrees Celsius, because the product of human body temperature 37 and 0.6 18 is 22.8, and human metabolism, circadian rhythm and physiological function are in the best state at this temperature. Scientists also found that when the external environment temperature is 0.665438+ of the human body temperature,
In nature, the leaves of plants are varied and full of vitality, which brings a green world to nature. Although the shape of leaves varies from species to species, you will find it after careful observation. The growth of petals and branches on the trunk of some plants also conforms to this law. You look down from the top of the plant stem. It is found that the included angle between the upper and lower adjacent blades is about 137.5 degrees. It can be calculated that 360-137.5 = 222.5137.5/222.5 is also about 0.618. Through research and exploration, it is found that the golden section is not only used in daily life, but also in mathematics, art and fine arts. We have learned a lot, and we have also learned a lot of knowledge that is not available in textbooks. We understand that the beauty of mathematics is different from other beauties. This kind of beauty is unique and inherent, with strict proportion beauty, artistic beauty and harmonious beauty. Through this study, the biggest gain is not only to understand the golden section, but also to learn an aesthetic point of view. This aesthetic view stems from the golden ratio of everything in the world. It is not the lack of beauty, but the lack of discovery. "If you can actively seek, no matter what problems can be overcome, as long as you have perseverance, you can complete it. Mathematics, if we treat it correctly, has not only truth, but also supreme beauty, which is a kind of cold and serious beauty. This beauty is not the weak aspect that attracts our nature. It is not as gorgeous as painting or music, but it can be pure to a lofty level. I can achieve a perfect state that only great art can strictly show. Mathematics, for me, is so fascinating. As long as we are good at observing and thinking and combine what we have learned with life, we will feel the joy of life. Mathematical knowledge is applied everywhere in life, just like the golden number.