Everyone should be familiar with the "golden section"!
Since the Pythagorean school in ancient Greece studied the drawing methods of regular pentagons and regular decagons in the 6th century BC, modern mathematicians have come to the conclusion that Pythagoras school had touched and even mastered the golden section at that time. In the 4th century BC, eudoxus, an ancient Greek mathematician, first studied this problem systematically and established the theory of proportion.
When Euclid wrote The Elements of Geometry around 300 BC, he absorbed eudoxus's research results and further systematically discussed the golden section, which became the earliest treatise on the golden section. After the Middle Ages, the golden section was cloaked in mystery. Several Italians, pacioli, called the ratio between China and the destination sacred and wrote books on it. German astronomer Kepler called the golden section sacred. It was not until the19th century that the name golden section gradually became popular. The golden section number 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 first proposed by American mathematician Kiefer in 1953 and popularized in China in 1970s.
Perhaps, we have learned a lot about the performance of 0.6 18 in science and art, but have you ever heard that 0.6 18 has an indissoluble bond with the fierce and cruel battlefield of gunfire and bloodshed, and also shows its great and mysterious power in the military? Napoleon the Great, a lean man, never thought that his fate would be closely linked with 0. 18. June, 18 12, is 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.
The Parthenon in ancient Greece is a world-famous perfect building with an aspect ratio of 0.6 18. Architects found that the palace designed according to this ratio is more magnificent and beautiful; If you design a villa, it will be more comfortable and beautiful. Even doors and windows designed as golden rectangles will be more harmonious and pleasing to the eye.
Interestingly, this number can be seen everywhere in nature and people's lives: the navel is the golden section of the whole human body, and the knee is the golden section from the navel to the heel. The aspect ratio of most doors and windows is also 0.618. On some plants, the included angle between two adjacent petioles is 137 degrees 28', which is exactly the included angle between two radii that divide the circumference into 1: 0.6 18. According to research, this angle has the best effect on ventilation and lighting of the factory building. The golden section is closely related to people. The latitude range of the earth's surface is 0-90 degrees. If divided into the golden section, 34.38-55.62 is the golden zone of the earth. No matter from the aspects of average temperature, annual sunshine hours, annual precipitation and relative humidity, it is the most suitable area for human life. Coincidentally, this region covers almost all the developed countries in the world.
Observe life more, and you will find the wonderful mathematics in life!
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China has an idiom-"as the name implies". Many things can be as the name implies, but there are exceptions. Such as Arabic numerals. When many people hear Arabic numerals, they think they were invented by Arabs. But it turns out that this is not the case. Arabic numerals 1, 2, 3, 4, 5, 6, 7, 8, 9. 0 is a common number in the world. This figure was not created by Arabs, but it can't erase the credit of Arabs. In fact, Arabic numerals originated from Indians and were gradually created by their ancestors in production practice.
In 3000 BC, the number of residents in the Indus Valley was advanced, and the decimal system was adopted. By the Vedic era (65438 BC+0400 BC-543 BC), Aryans had realized the role of numbers in production activities and daily life, and created some simple and incomplete numbers. In the 3rd century BC, a complete set of numbers appeared in India, but there were different writing styles in different places, among which Brahmanism was the typical one. Its uniqueness lies in that each number has a special symbol from 1 ~ 9, from which modern numbers are born. At that time, "0" had not appeared. It was not until the Gupta era (300-500 years) that there was a "0", which was called "Shunya", expressing a black dot "●" and later evolved into "0". This produces a complete set of figures. This is the great contribution of the ancient Indian people to world culture.
Indian figures first spread to Sri Lanka, Myanmar, Cambodia and other countries. In the 7th and 8th centuries, with the rise of the Arab Empire across Asia, Africa and Europe, Arabs eagerly absorbed the advanced cultures of ancient Greece, Rome, India and other countries and translated a large number of their scientific works. In 77 1 year, Indian astronomer and traveler Maoka visited Baghdad, the capital of the Abbasid Dynasty of the Arab Empire (750- 1258), and presented an Indian astronomical work Sidan Tower to the then caliph Mansour (757-775), who translated it into Arabic and named it Sindh. There are many numbers in this book, so it is called "Indian Numbers", which means "from India".
Arabian mathematicians Hua Lazimi (about 780-850) and Haibosh first accepted Indian numerals and used them in astronomical tables. They gave up their 28 letters, revised and perfected them in practice, and introduced them to the west without reservation. At the beginning of the 9th century, Hua Lazimi published "India Counting Algorithm", and expounded Indian numbers and their application methods.
Indian numerals replaced the long and clumsy Roman numerals, which spread in Europe and were opposed by some Christians, but proved to be better than Roman numerals in practice. 1202 The Calculation Book published by Leonardo in Italy marked the beginning of the use of Indian numerals in Europe. Chapter *** 15 of the book says: "The nine numbers in India are' 9, 8, 7, 6, 5, 4, 3, 2, 1', and any number can be represented by these nine numbers and the symbol' 0' called sifr (zero) by Arabs."
/kloc-In the 4th century, printing in China spread to Europe, which accelerated the popularization and application of Indian numerals in Europe and was gradually adopted by Europeans.
Westerners accepted the Indian numerals sent by Arabs, but forgot their founders and called them Arabic numerals.
About "0"
0, can be said to be the earliest human contact number. Our ancestors only knew nothing and existence at first, and none of them was 0, so 0 isn't it? I remember the primary school teacher once said, "Any number minus itself is equal to 0, and 0 means there is no number." This statement is obviously incorrect. As we all know, 0 degrees Celsius on the thermometer indicates the freezing point of water (that is, the temperature of ice-water mixture at standard atmospheric pressure), where 0 is the distinguishing point between solid and liquid water. Moreover, in Chinese characters, 0 means more as zero, such as: 1) fragmentary; A small part. 2) The quantity is not enough for a certain unit ... At this point, we know that "no quantity is 0, but 0 not only means no quantity, but also means the difference between solid and liquid water, and so on."
"Any number divided by 0 is meaningless." This is a "conclusion" about 0 that teachers from primary school to middle school are still talking about. At that time, division (primary school) was to divide a copy into several parts and figure out how many there were in each part. A whole cannot be divided into 0 parts, which is "meaningless". Later, I learned that 0 in a/0 can represent a variable with zero as the limit (the absolute value of a variable is always smaller than an arbitrarily small positive number in the process of change) and should be equal to infinity (the absolute value of a variable is always larger than an arbitrarily large positive number in the process of change). From this, another theorem about 0 is obtained: "A variable whose limit is zero is called infinitesimal".
"Room 203 105 in 2003", although all of them are zeros, they are roughly similar in appearance; They have different meanings. 0 indicator vacancy of 105 and 2003 cannot be deleted. 0 in Room 203 separates "Building (2)" from "House Number". (3) "(that is, Room 8 on the second floor) can be deleted. 0 also means that ...
Einstein once said: "I always think it is absurd to explore the meaning and purpose of a person or all living things." I want to study all the numbers of "existence", so I'd better know the number of "non-existence" first, so as not to become what Einstein called "absurd".
As a middle school student, my ability is limited after all, and my understanding of 0 is not thorough enough. In the future, I hope (including action) to find "my new continent" in the "ocean of knowledge".
Math is very useful.
Learning mathematics should be used in real life. Mathematics is used by people to solve practical problems. In fact, there will be math problems in life. For example, when you go shopping, you will naturally use addition and subtraction, and you always have to draw pictures when you build a house. There are countless problems like this, and this knowledge comes from life and is finally summed up as mathematical knowledge, which solves more practical problems.
I once saw a report that a professor asked a group of foreign students, "How many times will the minute hand and the hour hand overlap between 12 and 1?" Those students all took off their watches from their wrists and began to set hands; When the professor tells the same question to the students in China, the students will use mathematical formulas to make calculations. The commentary said that it can be seen that China students' mathematical knowledge is transferred from books to their brains, so they can't use it flexibly. They seldom think of learning and mastering mathematics knowledge in real life.
From then on, I began to consciously connect mathematics with daily life. Once, my mother baked a cake, and two cakes could be put in the pot. I thought, isn't this a math problem? It takes two minutes to bake a cake, one minute in front and one minute in the back. At most, two cakes are put in the pot at the same time. How many minutes does it take to bake three cakes at most? I thought about it and came to the conclusion that it takes 3 minutes: first, put the first cake and the second cake into the pot at the same time, 1 minute later, take out the second cake, put the third cake and turn the first cake over; Bake again 1 min, so that the first cake is ready. Take it out. Then put the reverse side of the second cake on it, and turn the third cake upside down at the same time, so it will be all done in 3 minutes.
I told my mother about this idea, and she said, actually, it won't be so coincidental. There must be an error, but the algorithm is correct. It seems that we must apply what we have learned in order to make mathematics serve our lives better.
Mathematics should be studied in life. Some people say that the knowledge in books has little to do with reality now. This shows that their knowledge transfer ability has not been fully exercised. It is precisely because learning cannot be well understood and applied in daily life that many people do not attach importance to mathematics. I hope that students can learn mathematics in their lives and use mathematics in their lives. Mathematics is inseparable from life. If they study thoroughly, they will naturally find that mathematics is actually very useful.