What exactly is mathematics? We say that mathematics is a science that studies the relationship between spatial form and quantity in the real world. It is widely used in modern life and production, and is an essential basic tool for studying and studying modern science and technology.
Like other sciences, mathematics has its past, present and future. We know its past in order to understand its present and future. The development of modern mathematics is extremely rapid. In recent 30 years, the new mathematical theory has surpassed the sum of 18 and 19 th century theories. It is estimated that it will take less than 10 years for each "doubling" of future mathematical achievements.
An obvious trend in the development of modern mathematics is that all sciences are going through the process of mathematization.
For example, physics has long been regarded as inseparable from mathematics. In colleges and universities, it is also a well-known fact that students of mathematics department should study general physics and students of physics department should study advanced mathematics.
Another example is chemistry. We should use mathematics to quantitatively study chemical reactions. We should take the concentration and temperature of the substances involved in the reaction as variables, express their changing laws with equations, and study the chemical reaction through the "stable solution" of the equations. Not only basic mathematics should be applied here, but also "frontier" and "developing" mathematics should be applied.
For example, biology should study the periodic movement of heartbeat, blood circulation and pulse. This movement can be expressed by an equation. By finding the "periodic solution" of the equation and studying the appearance and maintenance of this solution, we can grasp the above biological phenomena. This shows that biology has developed from qualitative research to quantitative research in recent years, and it is also necessary to apply "developing" mathematics, which has made great achievements in biology.
When it comes to demography, it is not enough just to add, subtract, multiply and divide. When we talk about population growth, we often say what the birth rate is and what the death rate is. So the birth rate minus the death rate is the annual population growth rate? No, in fact, people are constantly born, and the number of births is related to the original base. So is death. This situation is called "dynamic" in modern mathematics. It can't be simply treated by addition, subtraction, multiplication and division, but described by complex "differential equations". Study such problems, equations, data, function curves, computers, etc. Both are indispensable. Finally, it can be clear how each family can have only one child, how to have only two children, and so on.
As for water conservancy, we should consider the storm at sea, water pollution and port design. We also use equations to describe these problems, and then input the data into the computer to find out their solutions, and then compare them with the actual observation results to serve the actual situation. Very advanced mathematics is needed here.
When it comes to exams, students often think that exams are used to check students' learning quality. In fact, the examination methods (oral examination, written examination, etc. ) and the quality of the test paper itself is not the same. Modern educational statistics and educational metrology test the examination quality through quantitative indicators such as validity, difficulty, discrimination and reliability. Only qualified exams can effectively test students' learning quality.
As for literature, art and sports, mathematics is essential. We can see from CCTV's literary and art grand prix program that when an actor is graded, it is often "to remove a highest score" and then "to remove a lowest score". Then, the average score of the remaining scores is calculated as the actor's score. Statistically speaking, "the highest score" and "the lowest score" have the lowest credibility, so they are removed.
Mr. Guan, a famous mathematician in China, said: "There are various inventions in mathematics, and I think there are at least three: one is to solve classic problems, which is a great job; First, put forward new concepts, new methods and new theories. In fact, it is this kind of person who has played a greater role in history and is famous in history; Another is to apply the original theory to a brand-new field, which is a great invention from the perspective of application. " This is the third invention. "There are a hundred flowers here, and the prospects for the development of mathematics and other sciences to comprehensive science are infinitely bright."
As Mr. Hua said in May 1959, mathematics has developed by leaps and bounds in the past 100 years. It is no exaggeration to summarize the wide application of mathematics with "the vastness of the universe, the smallness of particles, the speed of rockets, the cleverness of chemical industry, the change of the earth, the mystery of biology, the complexity of daily life, etc." The greater the scope of applied mathematics, all scientific research can solve related problems with mathematics in principle. It can be asserted that there are only departments that can't apply mathematics now, and they will never find areas where mathematics can't be applied in principle.
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 its 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".
golden section
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. The architect found that designing the hall according to this ratio,