A summary report entitled "The Golden Section of Life". Signed by Yang Jingsan. Summary and keywords
Abstract: 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 golden section has many manifestations in life, such as photography, medicine, biology, architecture and even the human body.
[Keywords:] golden section 0.6 18 harmonious beauty application
Fourth, the preface:
Mathematics is everywhere in our life, and the golden ratio has a long history. It can be traced back to the Parthenon in ancient Athens. The reason why it is so harmonious is that this building conforms to the golden ratio. In our life, photography, medicine, biology, architecture and even the human body have the golden section everywhere. The aspect ratio of ordinary books is the golden section; The growth of petals and branches on the trunk of some plants also hides the golden section; The themes of some famous paintings, sculptures and photographs are mostly in the picture of 0. 168? Location. The artist thinks that the bridge of stringed instruments is placed at 0. 168 of the strings. Can make the piano softer and sweeter. This shows the history of the golden ratio.
And functions. We carry out research on the topic of "golden section in life" to further understand and let students understand that there is mathematics in life, so as to love and like mathematics.
Verb (abbreviation of verb) is the main research content and method;
1, content: golden section of life
2. Methods: 1) Go to the library to find information and browse books or related books.
2) Search the Internet for relevant information.
3) ask the teacher; Group members discuss with each other.
3. Knowledge base and required resources involved in the study:
The golden ratio of mathematics, Fibonacci sequence knowledge, magazines, online content related to the golden ratio. 4. Research ideas, activity steps and schedule: 1. Divide the students into groups and assign the work and investigation direction of each group member. (the first 1 week) 2. Go to the library to find books about the golden ratio and extract relevant contents. (weeks 2-3) 3. Find the relevant golden ratio content online. (Week 2-3)
4.
Organize the data, discuss with the team members, express their opinions and show each other the research results. (the fourth week) 5. research method
Members work together, search for relevant information through the internet and library books, and summarize, select and process them. Members discuss and analyze the results according to them, and present the research results.
Research achievements of intransitive verbs
1, the golden number in art
"0.6 18", this ratio was applied to plastic arts by ancient Greek aestheticians because of its aesthetic value, because any body that conforms to the golden section law is always the most beautiful. In the history of art, it was once applied as a classic law. There are many works of art.
Economists have created many immortal reputations with it. For example, Leonardo da Vinci's Mona Lisa and Raphael's The Gentle and Handsome Virgin both used this ratio intentionally or unintentionally.
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. 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.
2. Gold content in diet and daily life:
The ratio of "golden section" is 0.6 18, which is not only a common ratio in aesthetic modeling, but also a dietary parameter. The average life expectancy of Japanese people ranks first in the world for many years, and a reasonable diet is a big factor. In their diet, the proportion of cereals, vegetarian dishes, high-quality protein and alkaline foods basically reached the golden ratio. Medical experts also found that people who eat 60% to 70% food have almost no stomach problems. Drink five glasses of water. Water in human body accounts for 6 1.8% of body weight. Excluding sweating, 2500 ml of water is lost every day, which needs to be replenished. Among them, the water supplied by semi-solid food and the water synthesized in human body are about 1500ml, accounting for about 6 1.8%. The remaining 1000ml needs to be replenished to keep the water balance. Therefore, everyone should drink 5 glasses of water every day.
Reasonable daily life should also conform to the golden section. Of the 24 hours, 2/3 are for work and life, and 1/3 is for rest and sleep. In the relationship between motion and stillness, is it "life lies in motion" or "life lies in stillness"? From a dialectical point of view and a lot of life practice, it is proved that the relationship between activity and quietness is the same as the proportion of work and rest on the same day. Four points active and six points quiet are the best health care methods. Mastering and using the golden section well can save energy consumption, delay aging and improve the quality of life.
3. Gold content in plants
The leaves of plants are full of vitality, bringing a beautiful green world to nature (as shown below).
Although the shape of leaves varies from species to species, its arrangement order on the stem (called leaf order) is very regular. You look down from the top of the plant stem, and after careful observation, you find that there is about 137.5 between the upper and lower adjacent leaves. If only one leaf is drawn on each layer, the angle difference between two adjacent leaves on the first layer and the second layer is about 137.5, and the next two to three layers, three to four layers, and four to five layers all form this angle. Botanists have calculated that this angle is the best angle for lighting and ventilation of leaves. How delicate the arrangement of leaves is!
What is the "password" hidden in 137.5 among the leaves? We know that a week is 360,360–137.5 = 222.5,137.5: 222.5 ≈ 0.618. Look, this is the "password"! The exquisite and magical arrangement of leaves actually hides 0.6 18.
Fibonacci sequence is everywhere from nature to daily life, and there is a golden ratio. The number of petals of some flowers is Fibonacci: 3 daffodils, 5 Jin Fenghua petals, 8 delphinium petals, calendula 13 petals, aster 2 1 petal, daisy 34, 55 or 89 petals, and 2 1 petal on the sunflower disk rotates clockwise. Some patterns of molluscs and crustaceans can also be found in animals, and the number of wing pairs of insects conforms to this series to some extent.
4, the amount of gold in the building
Almost all the most famous buildings in the world contain the golden ratio. Many excellent modern buildings around the world, despite their different styles, have intentionally or unintentionally applied the golden section rule in composition and layout design, giving people a harmonious and pleasing aesthetic feeling.
The world-famous Parthenon is also such an example. The outside of the temple is rectangular, with a length of 228 feet and a width of 10 1 foot. The colonnade consists of 46 Doric circular columns.
The pyramids in Egypt, an ancient civilization, are shaped like square cones and vary in size. However, the ratio of side length to base height of these pyramids is close to 0.6 18. In modern architecture, some skyscrapers adopt the treatment of "golden section", which can make the straight and monotonous tower become colorful. Arranging waistlines or decorations in the prime locations of such high-rise buildings can make the whole building complex look majestic and elegant. Such as the world-famous Eiffel Tower in Paris, France and Toronto, Canada, which is one of the tallest buildings in the world today.
The TV Tower (553.33m) was built according to the golden section principle. Shanghai Oriental Pearl Radio and Television Tower is 468 meters high. In order to beautify the tower, the designer skillfully installed a dazzling upper sphere, lower sphere and space capsule on it, which not only allowed visitors to climb high and overlook the ground scenery, but also changed the curve of the straight tower. Even better, the position of the upper sphere is 5∶8 of the total height of the tower, that is, the distance from the upper sphere to the top of the tower, and the distance from the upper sphere to the ground is about 5∶8, which is in line with the golden section ratio, making the tower tall and beautiful with aesthetic effects.
Finally, we want to tell you that we have learned a lot of mathematics knowledge in real life, but we haven't found the law yet. We can use experience and refine it into mathematics through practical activities. The essence of the golden section is the magic number of 0.6 18. As long as you pay attention, you will find its "phantom" in all aspects of life. The golden section was discovered by the ancient Greek philosopher Pythagoras, and the golden ratio of 1:0.6 18 is the most beautiful and harmonious. Mathematics is around everyone, and we should have the heart to experience and discover it.
Seven. refer to
1 、/view/ 18 16.html？ Wtp=tt 2, Application of Golden Section, Grade 8, Beijing Normal University Edition (Part Two)