Golden Section
The "Golden Section" We should not be unfamiliar to you!
Since the 6th century BC in ancient Greece studied the Pythagoreans are pentagons and 10 are edge-shaped plot, it was inferred modern mathematicians have been touched Pythagoreans even mastered the Golden Section. The 4th century BC, the ancient Greek mathematician Eudoxus the first systematic research of this problem and to establish the proportion of theory.
BC 300 years before Euclid wrote "Elements" absorbed when Eudoxus of research results, and further discusses the golden section system, the first of the works on the golden section. The Middle Ages, the golden section was put on the cloak of mystery, a number of Pacioli of Italy said at the end of the ratio than for the sacred, and specially the writing. German astronomer Kepler said partition gold divided into the sacred. To the 19th century, the name Golden gradually prevailing. There are many golden section number of interesting properties, the practical application of the human it is also very extensive. The most famous example is the preferred study in the golden section method or 0.618 law,
Keefer mathematician from the United States was first proposed in 1953, and 70 during the promotion in China.
Perhaps, 0.618 in the performance of science and art we have to understand a lot, but you have not heard, 0.618 grievances with fire, smoke, pieces of the tragic and brutal battlefield also ties in the military also showed that it is a great and mysterious power?枭雄generation of Napoleon the Great may they never think of how his fate will be closely linked to 0.618. June 1812, the year the climate in Moscow is the most nice and cool in summer, so long as the elimination of the Russian military force after the Battle of Borodin Connaught, now led by Napoleon in his army entered Moscow.
But he was enormously proud of his success at this time, all-powerful. He did not realize that talent and luck at this time is a little bit from him and disappeared, the cause of the peak of his life and the arrival of a turning point is at the same time. Later, the French army纷扬in the snow, cold wind whistling in the withdrawal of Moscow crestfallen. Three months plus two months of victory and failure very Sheng, from the timeline, the emperor of France in Moscow overlooking the flames raging through the city, the foot is walking on the golden section line.
Lennon Patigul ancient Greek temple is the perfect world-famous architecture, its height and width ratio is 0.618. Architects have found that, according to the proportion of this design temple, palace more magnificent and beautiful; to design the villa, the villa will be more comfortable and beautiful. Doors and windows even if a rectangular design for the gold will be even more coordination and very enjoyable.
Interestingly, the figure in nature and can be seen everywhere in people's lives: the people's navel is the golden section of the body length, the person is the navel to the knees of the golden section point heel. Most of the doors and windows wide length ratio is 0.618 ...; some sik stalks, two adjacent petiole angle is 137 degrees 28 ', which is exactly the circumference is divided into two 1:0.618 ... ... of the angle between the radius. It was found that this perspective on the plants the best ventilation and lighting. The Golden Section and the people are closely related. Latitude range of the Earth's surface is 0 - 90 °, its golden section, the 34.38 ° - 55.
62 ° is the Earth's Golden Mile. In terms of average temperature, annual sunshine hours, annual precipitation, relative humidity, etc. are available for the best areas of human life. To say it Coincidentally, this region covers almost all the world's developed countries.
To observe more than life, you will find wonderful life math!
Digital
China has a saying - "As the name suggests." As the name suggests can be many things, but there are exceptions. For example, the Arabic numerals. Many people heard Arabic numerals, the Arabs will be considered to be invented. But the fact is not. Arabic numerals 1,2,3,4,5,6,7,8,9. 0 is internationally digital. The creation of this figure is not the Arabs, but Arabs can not erase credit. In fact, the Arabic numerals from the first hands of the Indians, the ancestors of their practice in the production gradually created.
3000 BC, the Indus Valley the number of residents have been more progressive, using the decimal system of calculation. To the Vedic period (BC 1400 - BC 543), the Aryans have been aware of the digital in the production activities and the role of everyday life, creating a number of simple figures incomplete. 3rd century BC, India had a full set of figures, but all over the different wording, which is a typical Brahmin style, it is unique from 1 ~ 9 each have a dedicated number of symbols, is the modern digital in from their originated from. At that time, the "0" has not yet appeared.
To the Gupta era (300-500 years) have a "0", called "If the sun" (shunya), that is a black "●", then spread into a "0." In this way, a complete set of figures produced. This is the ancient Indian people's great contributions to world culture.
India reached the number of the first Sri Lanka, Myanmar, Cambodia and other countries. 7-8 century, as across Asia, Africa, Europe Sanzhou the rise of the Arab Empire, the Arabs hungry to learn from ancient Greece, Rome, India and other countries of advanced culture, a large number of translation of its scientific work. 771 years, the Indian astronomers, travel home to visit Mao card Abbas Arab Empire Dynasty (750-1258) is the capital of Baghdad, will carry a book of astronomy in India, "西德罕塔" dedicated to the man at the time of Caliph suhr (757-775), translated into Arabic to make Mansour, named "德欣德letter."
This book a large number of figures, so called "Indian figures", the original intent of which is "come from India."
Arab mathematicians spent close Shiraz (about 780-850) and first of all to accept海伯什such as the Indian figures, and the use of astronomical tables. They gave up their 28 letters, modified to improve in practice and to introduce it without reservation to the West. 9 the beginning of the century and spent close Shiraz published "Counting Algorithm of India", the figures of India and applications.
India replaced the long clumsy figures of Roman numerals, the spread in Europe, opposed by some Christians, but the practice has proved superior to Roman numerals. Lei Russia in 1202, Italy issued a number of the "Book of Calculation", marked in Europe the beginning of the use of the Indian figures. The book has 15 chapters, the chapter said: "The nine Indian figures are: 9, 8,7,6,5,4,3,2,1 ', using the nine figures and the Arabs called sifr (zero ) mark'0 ', any number can be expressed. "
The 14th century when printing in China spread to Europe, India, but also speeded up the number of application in Europe, gradually adopted by the Europeans.
Westerners accepted by the Arabs from India, but its creators forgotten ancestor, known as Arabic numerals.
Useful mathematical
Learn mathematics is to be applied in real life, mathematics is used to solve practical problems, in fact, mathematical problems arise in life. For example, the natural use to buy things to take to the streets to add and subtract, repair houses built drawings must be painted. Just to name a few issues like this, the knowledge generated from the life, the last was to summarize the mathematical knowledge to solve more practical problems.
I have seen such a report: A professor asked a group of foreign students: "1:00 to 12:00 between the minute hand and the clock will overlap several times?" Those students watch from his wrist, hands began to allocate; and this professors to the Chinese students mentioned the same issue, the students will apply mathematical formulas to calculate. Commented that we can see that the mathematical knowledge of Chinese students are moved from the books in mind, can not be applied with flexibility, very little thought in real life learning, master of mathematical knowledge.
From this, I began to have awareness of the link mathematics and everyday life. On one occasion, her mother烙饼, 2 cake pan can be put. I thought, this is not a mathematical problem? Bake a cake with two minutes, is branded, the opposite of the one-minute at the same time take up to two pot pie, then baked with a maximum of three minutes this cake? I thought, come to the conclusion: take 3 minutes: the first first, the second cake into the pan at the same time, 1 minute, remove the second cake, Add the third cake, the first over cake surface; one minutes and then baked, this cake is like the first, and check out. The second cake and then put the opposite, at the same time to turn over the third cake,
3 minutes to do all get on.
I told my mother the idea, she said, in fact, will not be a coincidence, there is always some error, but the algorithm is correct. It appears that we must apply what they have learned in order to better enable mathematics to serve our lives.
Mathematics should be learning in life. It was said that the knowledge in books and not the actual link. This shows that knowledge of their migration has not been sufficient training. It is precisely because the school can not be well understood and applied in daily life, that makes a lot of people do not attach importance to mathematics. Hope into the lives of secondary school students in mathematics, mathematics used in daily life, mathematics and life are inseparable, studying the deep, and thoroughly, and not surprising to find that very useful mathematical fact.
The mathematical science of
Mathematics what is it? We say that mathematics is to study the real world of space and quantity of the relationship between the form of a science. In modern life and modern production of a very wide range of learning and research of modern science and technology essential to the basic tools.
As with other science, mathematics has its past, present and future. We recognize that it's past, is to understand its present and future. The development of modern mathematics very rapidly, almost 30 years, the mathematical theory of the new century, 18,19 more than the sum of the theory. Mathematical achievements of the future is expected for each "double" or 10 years. Therefore, understanding of the mathematics in the past, the general taste of what the present and the future of mathematics is very good.
The development of modern mathematics a clear trend, that is, the science are undergoing the process of mathematics.
Such as physics, know that it has long been inextricably linked with mathematics. In colleges and universities, the Department of Mathematics ordinary students to learn Physics, Department of Physics students to learn advanced mathematics, this is a well known fact.
Another example is the chemical, to use mathematics to the quantitative study of chemical reactions. To participate in response to the concentration of the material, temperature, etc., as variables, the equation changes in the law that they, through the equation of a "stable solution" to study the chemical reaction. Here the basis of not only the application of mathematics, but also to the application of "cutting-edge on", "developing" Mathematics.
Another example is biology, it is necessary to study the heart beat, blood circulation, pulse, such as a cyclical movement. This movement can be expressed by equations, equations by seeking a "cycle solution" to study the emergence of such a solution and to maintain, to control the above-mentioned phenomenon of living nature. This shows that in recent years, biological research and development from qualitative to quantitative research, but also to the application of "development" of mathematics. This allows access to a biology major achievement.
黄金分割
The "Golden Section" We should not be unfamiliar to you!
Since the 6th century BC in ancient Greece studied the Pythagoreans are pentagons and 10 are edge-shaped plot, it was inferred modern mathematicians have been touched Pythagoreans even mastered the Golden Section. The 4th century BC, the ancient Greek mathematician Eudoxus the first systematic research of this problem and to establish the proportion of theory.
BC 300 years before Euclid wrote "Elements" absorbed when Eudoxus of research results, and further discusses the golden section system, the first of the works on the golden section. The Middle Ages, the golden section was put on the cloak of mystery, a number of Pacioli of Italy said at the end of the ratio than for the sacred, and specially the writing. German astronomer Kepler said partition gold divided into the sacred. To the 19th century, the name Golden gradually prevailing. There are many golden section number of interesting properties, the practical application of the human it is also very extensive. The most famous example is the preferred study in the golden section method or 0.618 law,
Keefer mathematician from the United States was first proposed in 1953, and 70 during the promotion in China.
Perhaps, 0.618 in the performance of science and art we have to understand a lot, but you have not heard, 0.618 grievances with fire, smoke, pieces of the tragic and brutal battlefield also ties in the military also showed that it is a great and mysterious power?枭雄generation of Napoleon the Great may they never think of how his fate will be closely linked to 0.618. June 1812, the year the climate in Moscow is the most nice and cool in summer, so long as the elimination of the Russian military force after the Battle of Borodin Connaught, now led by Napoleon in his army entered Moscow.
But he was enormously proud of his success at this time, all-powerful. He did not realize that talent and luck at this time is a little bit from him and disappeared, the cause of the peak of his life and the arrival of a turning point is at the same time. Later, the French army纷扬in the snow, cold wind whistling in the withdrawal of Moscow crestfallen. Three months plus two months of victory and failure very Sheng, from the timeline, the emperor of France in Moscow overlooking the flames raging through the city, the foot is walking on the golden section line.
Lennon Patigul ancient Greek temple is the perfect world-famous architecture, its height and width ratio is 0.618. Architects have found that, according to the proportion of this design temple, palace more magnificent and beautiful; to design the villa, the villa will be more comfortable and beautiful. Doors and windows even if a rectangular design for the gold will be even more coordination and very enjoyable.
Interestingly, the figure in nature and can be seen everywhere in people's lives: the people's navel is the golden section of the body length, the person is the navel to the knees of the golden section point heel. Most of the doors and windows wide length ratio is 0.618 ...; some sik stalks, two adjacent petiole angle is 137 degrees 28 ', which is exactly the circumference is divided into two 1:0.618 ... ... of the angle between the radius. It was found that this perspective on the plants the best ventilation and lighting. The Golden Section and the people are closely related. Latitude range of the Earth's surface is 0 - 90 °, its golden section, the 34.38 ° - 55.
62 ° is the Earth's Golden Mile. In terms of average temperature, annual sunshine hours, annual precipitation, relative humidity, etc. are available for the best areas of human life. To say it Coincidentally, this region covers almost all the world's developed countries.
To observe more than life, you will find wonderful life math!
Digital
China has a saying - "As the name suggests." As the name suggests can be many things, but there are exceptions. For example, the Arabic numerals. Many people heard Arabic numerals, the Arabs will be considered to be invented. But the fact is not. Arabic numerals 1,2,3,4,5,6,7,8,9. 0 is internationally digital. The creation of this figure is not the Arabs, but Arabs can not erase credit. In fact, the Arabic numerals from the first hands of the Indians, the ancestors of their practice in the production gradually created.
3000 BC, the Indus Valley the number of residents have been more progressive, using the decimal system of calculation. To the Vedic period (BC 1400 - BC 543), the Aryans have been aware of the digital in the production activities and the role of everyday life, creating a number of simple figures incomplete. 3rd century BC, India had a full set of figures, but all over the different wording, which is a typical Brahmin style, it is unique from 1 ~ 9 each have a dedicated number of symbols, is the modern digital in from their originated from. At that time, the "0" has not yet appeared.
To the Gupta era (300-500 years) have a "0", called "If the sun" (shunya), that is a black "●", then spread into a "0." In this way, a complete set of figures produced. This is the ancient Indian people's great contributions to world culture.
India reached the number of the first Sri Lanka, Myanmar, Cambodia and other countries. 7-8 century, as across Asia, Africa, Europe Sanzhou the rise of the Arab Empire, the Arabs hungry to learn from ancient Greece, Rome, India and other countries of advanced culture, a large number of translation of its scientific work. 771 years, the Indian astronomers, travel home to visit Mao card Abbas Arab Empire Dynasty (750-1258) is the capital of Baghdad, will carry a book of astronomy in India, "西德罕塔" dedicated to the man at the time of Caliph suhr (757-775), translated into Arabic to make Mansour, named "德欣德letter."
This book a large number of figures, so called "Indian figures", the original intent of which is "come from India."
Arab mathematicians spent close Shiraz (about 780-850) and first of all to accept海伯什such as the Indian figures, and the use of astronomical tables. They gave up their 28 letters, modified to improve in practice and to introduce it without reservation to the West. 9 the beginning of the century and spent close Shiraz published "Counting Algorithm of India", the figures of India and applications.
India replaced the long clumsy figures of Roman numerals, the spread in Europe, opposed by some Christians, but the practice has proved superior to Roman numerals. Lei Russia in 1202, Italy issued a number of the "Book of Calculation", marked in Europe the beginning of the use of the Indian figures. The book has 15 chapters, the chapter said: "The nine Indian figures are: 9, 8,7,6,5,4,3,2,1 ', using the nine figures and the Arabs called sifr (zero ) mark'0 ', any number can be expressed. "
The 14th century when printing in China spread to Europe, India, but also speeded up the number of application in Europe, gradually adopted by the Europeans.
Westerners accepted by the Arabs from India, but its creators forgotten ancestor, known as Arabic numerals.
Useful mathematical
Learn mathematics is to be applied in real life, mathematics is used to solve practical problems, in fact, mathematical problems arise in life. For example, the natural use to buy things to take to the streets to add and subtract, repair houses built drawings must be painted. Just to name a few issues like this, the knowledge generated from the life, the last was to summarize the mathematical knowledge to solve more practical problems.
I have seen such a report: A professor asked a group of foreign students: "1:00 to 12:00 between the minute hand and the clock will overlap several times?" Those students watch from his wrist, hands began to allocate; and this professors to the Chinese students mentioned the same issue, the students will apply mathematical formulas to calculate. Commented that we can see that the mathematical knowledge of Chinese students are moved from the books in mind, can not be applied with flexibility, very little thought in real life learning, master of mathematical knowledge.
From this, I began to have awareness of the link mathematics and everyday life. On one occasion, her mother烙饼, 2 cake pan can be put. I thought, this is not a mathematical problem? Bake a cake with two minutes, is branded, the opposite of the one-minute at the same time take up to two pot pie, then baked with a maximum of three minutes this cake? I thought, come to the conclusion: take 3 minutes: the first first, the second cake into the pan at the same time, 1 minute, remove the second cake, Add the third cake, the first over cake surface; one minutes and then baked, this cake is like the first, and check out. The second cake and then put the opposite, at the same time to turn over the third cake,
3 minutes to do all get on.
I told my mother the idea, she said, in fact, will not be a coincidence, there is always some error, but the algorithm is correct. It appears that we must apply what they have learned in order to better enable mathematics to serve our lives.
Mathematics should be learning in life. It was said that the knowledge in books and not the actual link. This shows that knowledge of their migration has not been sufficient training. It is precisely because the school can not be well understood and applied in daily life, that makes a lot of people do not attach importance to mathematics. Hope into the lives of secondary school students in mathematics, mathematics used in daily life, mathematics and life are inseparable, studying the deep, and thoroughly, and not surprising to find that very useful mathematical fact.
The mathematical science of
Mathematics what is it? We say that mathematics is to study the real world of space and quantity of the relationship between the form of a science. In modern life and modern production of a very wide range of learning and research of modern science and technology essential to the basic tools.
As with other science, mathematics has its past, present and future. We recognize that it's past, is to understand its present and future. The development of modern mathematics very rapidly, almost 30 years, the mathematical theory of the new century, 18,19 more than the sum of the theory. Mathematical achievements of the future is expected for each "double" or 10 years. Therefore, understanding of the mathematics in the past, the general taste of what the present and the future of mathematics is very good.
The development of modern mathematics a clear trend, that is, the science are undergoing the process of mathematics.
Such as physics, know that it has long been inextricably linked with mathematics. In colleges and universities, the Department of Mathematics ordinary students to learn Physics, Department of Physics students to learn advanced mathematics, this is a well known fact.
Another example is the chemical, to use mathematics to the quantitative study of chemical reactions. To participate in response to the concentration of the material, temperature, etc., as variables, the equation changes in the law that they, through the equation of a "stable solution" to study the chemical reaction. Here the basis of not only the application of mathematics, but also to the application of "cutting-edge on", "developing" Mathematics.
Another example is biology, it is necessary to study the heart beat, blood circulation, pulse, such as a cyclical movement. This movement can be expressed by equations, equations by seeking a "cycle solution" to study the emergence of such a solution and to maintain, to control the above-mentioned phenomenon of living nature. This shows that in recent years, biological research and development from qualitative to quantitative research, but also to the application of "development" of mathematics. This allows access to a biology major achievement.
黄金分割
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第1个回答 2009-05-27
去Google上搜学术论文就可以，然后再用Google整篇翻译就可以了。
Google上也可以搜到有中英对照网页的那种论文。你连复制粘贴都可以省了。
Google上也可以搜到有中英对照网页的那种论文。你连复制粘贴都可以省了。
第2个回答 2009-05-27
LS得有病啊 。。。 GOOGLE翻译语法全错
如果要交得话 ， 很容易穿帮 ， 找死啊
你还是自己努力吧 ， 学习靠自己啊
如果要交得话 ， 很容易穿帮 ， 找死啊
你还是自己努力吧 ， 学习靠自己啊
第3个回答 2009-05-27
上学校图书馆，登陆 知网 查论文
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