From one to one hundred

Gauss has many interesting stories, and the first-hand information of these stories often comes from Gauss himself, because he always likes to talk about his childhood in his later years. We may doubt the truth of these stories, but many people have confirmed what he said.

Gauss's father works as a foreman in a tile factory. He always pays his workers every Saturday. When Gauss was three years old in the summer, when he was about to get paid, Little Gauss stood up and said, "Dad, you are mistaken." Then he said another number. It turned out that three-year-old Gauss was lying on the floor, secretly following his father to calculate who to pay. The results of recalculation proved that little Gauss was right, which made the adults standing there dumbfounded.

Gauss often joked that he had learned to calculate before he learned to speak, and often said that he learned to read by himself only after consulting adults about the pronunciation of letters.

At the age of seven, Goss entered St. Catherine's Primary School. When I was about ten years old, my teacher had a difficult problem in arithmetic class: "Write down the integers from 1 to 100 and add them up! Whenever there is an exam, they have this habit: the first person who finishes it puts the slate face down on the teacher's desk, and the second person puts the slate on the first slate, thus falling one by one. Of course, this question is not difficult for people who have studied arithmetic progression, but these children are just beginning to learn arithmetic! The teacher thinks he can have a rest. But he was wrong, because in less than a few seconds, Gauss had put the slate on the lecture table and said, "Here's the answer! Other students added up the numbers one by one, sweating on their foreheads, but Gauss sat quietly, ignoring the contemptuous and suspicious eyes cast by the teacher. After the exam, the teacher checked the slate one by one. Most of them were wrong, so the students were whipped. Finally, Gauss's slate was turned over and there was only one number on it: 5050 (needless to say, this is the correct answer. The teacher was taken aback, and Gauss explained how he found the answer:1+100 =1,2+99 =10/,3+98 =/kloc-. A * * * has 50 pairs, and the sum is 10 1, so the answer is 50 × 10 1 = 5050. It can be seen that Gauss found the symmetry of arithmetic progression, and then put the numbers together in pairs, just like the general arithmetic progression summation process.

Chungchi Tsu

Zu Chongzhi (AD 429-500) was born in Laiyuan County, Hebei Province during the Northern and Southern Dynasties. He read many books on astronomy and mathematics since childhood, studied hard and practiced hard, and finally made him an outstanding mathematician and astronomer in ancient China.

Zu Chongzhi's outstanding achievement in mathematics is about the calculation of pi. Before the Qin and Han Dynasties, people took "the diameter of three weeks a week" as pi, that is, "the ancient rate". Later, it was found that the error of ancient rate was too big, and pi should be "the diameter of the circle is one and greater than Wednesday", but there are different opinions on how much is left. Until the Three Kingdoms period, Liu Hui put forward a scientific method to calculate pi-"secant method", that is, to approximate the circumference of a circle with the circumference of inscribed regular polygons. Liu Hui calculated a polygon with 96 sides inscribed in a circle and got π=3. 14, and pointed out that the more sides inscribed in a regular polygon, the more accurate the π value obtained. On the basis of predecessors' achievements, Zu Chongzhi worked hard and calculated repeatedly, and found that π was between 3. 14 15926 and 3. 14 15927. The approximate value in the form of π fraction is obtained as the reduction rate and density rate, where the six decimal places are 3. 14 1929, which is the closest fraction to π value in 1000. How did Zu Chongzhi achieve this result? There's no way to check now. If you imagine that he will solve the problem according to Liu Hui's secant method, you must work out 16384 polygons inscribed in the circle. How much time and labor it takes! This shows that his perseverance and intelligence in academic research are admirable. It has been more than 1000 years since Zu Chongzhi calculated the secret rate and foreign mathematicians got the same result. In order to commemorate Zu Chongzhi's outstanding contribution, some foreign mathematicians suggested that π = be called "ancestral rate".

Zu Chongzhi exhibited famous works at that time and insisted on seeking truth from facts. He compared and analyzed a large number of materials calculated by himself, found serious mistakes in the past calendars, and dared to improve them. At the age of 33, he successfully compiled the Daming Calendar, which opened a new era in calendar history.

Zu Chongzhi and his son Zuxuan (also a famous mathematician in China) solved the calculation of the volume of a sphere with ingenious methods. One principle they adopted at that time was: "If the power supply potential is the same, the products will not be different." That is to say, two solids located between two parallel planes are cut by any plane parallel to these two planes. If the areas of two sections are always equal, then the volumes of two solids are equal. This principle is called cavalieri principle in western languages, but it was discovered by Karl Marx more than 1000 years after the ancestor. In order to commemorate the great contribution of grandfather and son in discovering this principle, everyone also called this principle "the ancestor principle".

The story of mathematician gauss

Gauss 1777~ 1855 was born in Brunswick, north-central Germany. His grandfather is a farmer, his father is a mason, his mother is a mason's daughter, and he has a very clever brother, Uncle Gauss. He takes good care of Gauss and occasionally gives him some guidance, while his father can be said to be a "lout" who thinks that only strength can make money, and learning this kind of work is useless to the poor.

Gauss showed great talent very early, and at the age of three, he could point out the mistakes in his father's book. At the age of seven, I entered a primary school and took classes in a dilapidated classroom. Teachers are not good to students and often think that teaching in the backcountry is a talent. When Gauss was ten years old, his teacher took the famous "from one to one hundred" exam and finally discovered Gauss's talent. Knowing that his ability was not enough to teach Gauss, he bought a deep math book from Hamburg and showed it to Gauss. At the same time, Gauss is familiar with bartels, a teaching assistant who is almost ten years older than him. bartels's ability is much higher than that of the teacher. Later, he became a university professor, giving Professor Gauss more and deeper mathematics.

Teachers and teaching assistants went to visit Gauss's father and asked him to let Gauss receive higher education. But Gauss's father thought that his son should be a plasterer like him, and there was no money for Gauss to continue his studies. The final conclusion is-find a rich and powerful person to be his backer, although I don't know where to find it. After this visit, Gauss got rid of weaving every night and discussed mathematics with Bater every day, but soon there was nothing to teach Gauss in Bater.

1788, Gauss entered higher education institutions despite his father's opposition. After reading Gauss's homework, the math teacher told him not to take any more math classes, and his Latin soon surpassed the whole class.

Interesting stories of mathematician Hua when he was a child

Hua (1910-1982) is a native of Jintan County, Jiangsu Province. He was named Luo Geng because his father, Hua fellow villager, put him on the laundry list of a lucky birth.

Hua was fond of playing since he was a child and liked to join in the fun, but his lessons were mediocre and sometimes he failed. I barely finished primary school and entered Jintan Middle School in my hometown, but I was still playful and my handwriting was crooked. When I do my math homework, I draw it carefully, but it's like graffiti. Therefore, Hua in junior high school is still disliked by teachers and often ruled.

Wang Weike, a middle school teacher in Jintan, has a unique vision. He studied Hua's graffiti book and found that these altered places reflected various methods he explored when solving problems. On one occasion, Teacher Wang Weike told his students that Sun Tzu's Calculation of the Art of War had such a problem: "This matter is unknown, and the number of three and three is the second, the number of five and five is the third, and the number of seven and seven is the second. What is the geometry of things? " When everyone was silent, a student stood up. As you can see, flowers have always been looked down upon. At that time, he was only fourteen. Can you guess how much Hua said?

The story of mathematicians-Sue

Su Yu 1902 was born in a mountain village in Pingyang County, Zhejiang Province in September. Although the family is poor, his parents scrimp and save, and they have to work hard to pay for his education. When he was in junior high school, he was not interested in mathematics. He thinks mathematics is too simple, and he will understand it as soon as he learns it. It can be measured that a later math class influenced his life.

That was when Su was in the third grade. He was studying in No.60 Middle School in Zhejiang Province. Teacher Yang teaches mathematics. He has just returned from studying in Tokyo. In the first class, Mr. Yang didn't talk about math, but told stories. He said: "In today's world, the law of the jungle, the world powers rely on their ships to build guns and gain benefits, and all want to eat and carve up China. The danger of China's national subjugation and extinction is imminent, so we must revitalize science, develop industry and save the nation. Every student here has a responsibility to' rise and fall in the world'. " He quoted and described the great role of mathematics in the development of modern science and technology. The last sentence of this class is: "In order to save the country and survive, we must revitalize science. Mathematics is the pioneer of science. In order to develop science, we must learn math well. "I don't know how many lessons Sue took in her life, but this lesson will never be forgotten.

Teacher Yang's class deeply touched him and injected new stimulants into his mind. Reading is not only to get rid of personal difficulties, but to save the suffering people in China; Reading is not only to find a way out for individuals, but to seek a new life for the Chinese nation. That night, Sue tossed and turned and stayed up all night. Under the influence of Teacher Yang, Su's interest shifted from literature to mathematics, and since then, she has set the motto "Never forget to save the country when reading, and never forget to save the country when reading". I am fascinated by mathematics. No matter it is the heat of winter or the snowy night in first frost, Sue only knows reading, thinking, solving problems and calculating, and has worked out tens of thousands of math exercises in four years. Now Wenzhou No.1 Middle School (that is, the provincial No.10 Middle School at that time) still treasures a Su's geometry exercise book, which is written with a brush and has fine workmanship. When I graduated from high school, my grades in all subjects were above 90.

/kloc-At the age of 0/7, Su went to Japan to study, and won the first place in Tokyo Technical School, where she studied eagerly. The belief of winning glory for our country drove Su to enter the field of mathematics research earlier. At the same time, he has written more than 30 papers, and made great achievements in differential geometry, and obtained the doctor of science degree in 193 1. Before receiving her doctorate, Su was a lecturer in the Department of Mathematics of Imperial University of Japan. Just as a Japanese university was preparing to hire him as an associate professor with a high salary, Su decided to return to China to teach with his ancestors. After the professor of Zhejiang University returned to Suzhou, his life was very hard. In the face of difficulties, Su's answer is, "Suffering is nothing, I am willing, because I have chosen the right road, which is a patriotic and bright road!" "

This is the patriotism of the older generation of mathematicians.

Chen Jingrun: When I was a child, my professor gave me a pearl.

More than 20 years ago, a reportage "Goldbach Conjecture", which caused a sensation in China, made a mathematical wizard a household name overnight. The deeds of this man even promoted the early arrival of a great era of respecting science, knowledge and talents to a certain extent. His name is Chen Jingrun.

Not talkative, he used to be an "ugly duckling". Usually, a person who is born deaf will have a particularly keen eye, a person who is born blind will have a very keen hearing, and an "ugly duckling" who has been neglected and unpopular since childhood will often meditate involuntarily or in all kinds of helplessness, explore things, learn from things, and find a suitable position in the world to develop his potential. You can say that this is forced out, but such "forced" will often "force" many great people. Like Chen Jingrun in childhood. Chen Jingrun was born in 1933, the family of a post office clerk. He just turned 4 when War of Resistance against Japanese Aggression started. Soon, the wolf smoke of the Japanese invaders burned to his hometown of Fujian, and the whole family fled into the mountains, and the children entered the mountain school. Fathers are too busy making a living to take care of their children's education; My mother is an old housewife and has worked hard all her life. She had 65,438+02 children, but only six survived. Chen Jingrun is the third, with brothers and sisters, and younger brothers and sisters. There is an old saying in China that "the little boy in the middle has a flat head". He is thin and weak. It is conceivable that he is dissatisfied with his parents and is not good for his brothers and sisters. At school, he is no better, because he is silent and doesn't like to talk. Unpopular, bullied, and often beaten and scolded for no reason. It happened that he was stubborn by nature and never begged for forgiveness in order to improve his situation. Unconsciously, he formed a self-enclosed introverted personality. People always need to communicate, especially children. A gifted child, faced with this dilemma, may become a perverse Woodenhead, but Chen Jingrun didn't. His natural passion for numbers and symbols made him forget the hardships and troubles of life and concentrate on the pagoda of knowledge. He wants to find a breakthrough and find happiness in life there. Teaching students in accordance with their aptitude is to create a space for each student to fully develop according to their own characteristics through certain educational and teaching methods and means.

Chen Jingrun Jr. teaches students in accordance with their aptitude.

Fortunately, this pupil has met a professor all his life, but he is still a child. In addition to burying your head in reading, you need face-to-face and hands-on guidance. After all, what can bring the greatest, most direct and vivid inspiration and joy to children is the kind of communication and contact between people, which can make people's hearts glow with brilliant sparks. Fortunately, when the family returned to Fuzhou, Chen Jingrun met Shen Yuan, a famous teacher who claimed to be a lifelong beneficiary.

Shen Yuan is a famous aerodynamicist, an aviation engineering educator and a leading figure in China's aviation industry. He graduated from the University of London, Imperial College London, and was the head of the aviation department in Tsinghua University. He went back to Fuzhou from 1948 to take care of his family. During the war, he had to stay in his alma mater Huaying Middle School to teach temporarily, and Chen Jingrun was the student in his class.

Professors in famous universities have their own unique skills in teaching young children. According to the age and psychological characteristics of the teaching object, Shen Yuan often introduces the explanation of the topic in a simple way by telling stories, which can easily lure those young children into the superb scientific world and arouse their great enthusiasm for science and learning. For example, on this day, Professor Shen Yuan told the students a story about Goldbach's conjecture with great interest.

The "pearl" left by the teacher illuminates the future of juvenile struggle.

"We all know that in positive integers, 2, 4, 6, 8, 10 ... these numbers that can be divisible by 2 are called even numbers; 1, 3,5,7,9, etc. It is called odd number. There is also a number that can only be divisible by 1 and itself, but not by other integers. This number is called a prime number. "

As usual, the whole classroom can even hear the sound of an embroidery needle falling to the ground in silence, only Professor Shen's calm and rich voice echoes.

"More than two hundred years ago, a German middle school teacher named Goldbach found that every even number not less than 6 is the sum of two prime numbers. For example, 6 = 3+3, 12 = 5+7,18 = 7+1,24 = 1 1+ 13 ...

"However, guess is guess after all. Without rigorous scientific argumentation, it can only be a guess forever. " Now it's Chen Jingrun Jr.' s turn to make a commotion. But in my heart.

How to scientifically demonstrate? Can I grow up? He thought. Later, Goldbach wrote a letter to the famous mathematician Euler at that time. Euler received this letter with great enthusiasm and threw himself into this interesting debate almost immediately. Unfortunately, however, despite Euler's painstaking efforts, he failed to prove this conjecture until his death. Since then, Goldbach conjecture has become a world-famous mathematical problem. For more than 200 years, it has made many talented scholars and heroes in the field of mathematics advance wave after wave and compete with each other. The classroom is boiling, and the children's curiosity and imagination are mobilized.

"Mathematics is the queen of natural science, and the crown on the queen's head is number theory. The Goldbach conjecture I just mentioned is a dazzling pearl in the queen's crown! "

Shen Yuan finished the story about Goldbach's conjecture in one go. The students talked about it in succession, and it was very lively, but the introverted Chen Jingrun didn't say a word, and the whole person was "crazy". This quiet, quiet and thoughtful child was completely brought into a colorful magical world by Shen Yuan's story. Although other students are amazed, when this admiration is over, it will be over, but he secretly tells himself over and over again:

"Are you okay? Can you take off this jewel in the crown of mathematics? "

One is a university professor and the other is a child with yellow mouth. Although there is no communication or even conversation between them in the strict sense, this class is really a heart-to-heart meeting, because it laid the foundation for Chen Jingrun Jr.' s beautiful ideal, a goal to work hard for, and made him willing to fight for it all his life! Many years later, Chen Jingrun graduated from Xiamen University. A few years later, he was appreciated by the famous mathematician Hua and transferred to the Institute of Mathematics of China Academy of Sciences. Since then, under the leadership of China, Chen Jingrun devoted himself to the long-term and outstanding demonstration of Goldbach's conjecture day and night.

1966, a dazzling new star rose in the field of mathematics in China. Chen Jingrun told the world in the China Science Bulletin that he proved it (1+2)!

1In February, 973, Chen Jingrun, who rose from the catastrophe of the Cultural Revolution, revised (1+2) the certificate again. A theorem it proved shocked the international mathematics community and was named "Chen Theorem". I don't know if Professor Shen Yuan can still remember what he said to these children in those years, but Chen Jingrun always remembers that he has been so clear all his life.

Celebrity zhangcheng road

Chen Jingrun (1933- 1996) is a famous mathematician. 1950 was admitted to the sophomore year of Xiamen university, and 1953 graduated to teach there. 65438-0957, transferred to Institute of Mathematics, Chinese Academy of Sciences, and later became a researcher. 1973 published the paper "The big even table is the product of a prime number and the product of no more than two prime numbers". 1979 "The Minimum Prime Number in arithmetic progression" was published. 1980 was elected academician of China Academy of Sciences (academician of China Academy of Sciences).

Descartes

The Cartesian coordinate system we use now is usually called Cartesian coordinate system. Cartesian coordinate system was introduced from Descartes R. (1596.3.31~1650.2.11), and then people can study geometric problems by algebraic methods, establish and improve analytic geometry and establish calculus.

The French mathematician Lagrange (1736.1.25 ~1813.4.10) once said: "As long as algebra and geometry part ways, their progress will be slow and their application will be narrow. However, when these two kinds of science are combined into partners, they absorb fresh vitality from each other. Since then, it has been making rapid progress. "

China mathematician Hua (1910.1.12 ~1985.6.12) once said: "Numbers and shapes are interdependent. Without numbers, it is not so intuitive, and without numbers, it is difficult to be nuanced. The combination of form and number is good in all aspects, but everything is wrong without it. Don't forget, the unity of geometry and algebra is always connected and never separated! "

The words of these great men are actually comments on Descartes' contribution.

Cartesian coordinate system is different from general theorems and general mathematical theories. It is a kind of thinking method and skill, which has completely changed the whole mathematics and made Descartes one of the founders of modern mathematics.

Descartes was an outstanding French philosopher in the17th century, the founder of modern biology, and a first-rate physicist at that time, not a professional mathematician.

Descartes' father is a lawyer. When he was eight years old, his father sent him to a missionary school. He left school at the age of sixteen, then went to study at the University of Poitiers, and went to Paris as a lawyer after graduation at the age of twenty. 16 17 joined the army. During his nine years in the army, he has been studying mathematics in his spare time. Later, he returned to Paris and was excited about the power of the telescope. He studied the theory and structure of optical instruments behind closed doors, and at the same time studied philosophical problems. 1682 moved to the Netherlands and got a relatively quiet and free academic environment. He lived there for 20 years and completed many important works, such as Guiding Principles of Thought, World System, Methodology for Better Guiding Reasoning and Seeking Scientific Truth (including three famous appendices: Geometry, Refraction and Meteor) and so on. Among them, Appendix Geometry is the only mathematical book written by Descartes, which clearly reflects his thoughts on coordinate geometry and algebra. Descartes was invited to Sweden as the queen's teacher in 1649. The severe winter in Stockholm had a very bad influence on Descartes' weak body. Descartes suffered from pneumonia in February 1650 and died ten days later. He died in February 1650, 1 1, one month and three weeks before he was 54 years old.

Descartes liked mathematics since he was a child, but it was an accidental opportunity to really believe that he had a talent for mathematics and began to study it seriously.

Yes161811. Descartes served in the army and was stationed in a small city in the Netherlands to fill Boleda. One day, when he was walking in the street, he saw a group of people gathered near a sign posting a notice. They were talking excitedly. He approached curiously. But because he couldn't understand Dutch and the Dutch characters on the notice, he asked the people next to him in French. A passer-by who can understand French looked disapprovingly at the young soldier and told him that there was a prize contest to solve mathematical problems. If you want him to translate all the contents of the notice, you need one condition, that is, the soldiers should send him the answers to all the questions in the notice. The Dutch claimed that he was a teacher of physics, medicine and mathematics. Unexpectedly, the next day, Descartes really came to him with the answers to all the questions; What surprised Beckman in particular was that all the answers of the young French soldier were not wrong at all. As a result, the two became good friends, and Descartes became a frequent visitor to Beckman's house.

Descartes began to study mathematics seriously under the guidance of Beckman, who also taught Descartes to learn Dutch. This situation lasted for more than two years, which laid a good foundation for Descartes to create analytic geometry later. Moreover, it is said that the Dutch words that Buick taught Descartes also saved Descartes' life:

Descartes once sailed to France with his servant on a small merchant ship, and the fare was not very expensive. I didn't realize this was a pirate ship. The captain and his deputy thought that Descartes' master and servant were French and didn't understand Dutch, so they negotiated to kill them in Dutch and robbed them of their money. Descartes understood the words of the captain and his deputy, made preparations quietly, finally subdued the captain and returned to France safely.

After living in France for several years, in order to express his views on things in words, he left France with religious prejudice and secular autocracy and returned to the lovely and hospitable Netherlands. Even the conflict with pirates can't erase his fond memories of Holland. Descartes completed his geometry in Holland. This book is not long, but it is a treasure in geometry works.

Descartes died in Stockholm 16 years later, his ashes were sent back to Paris. Originally placed in Barville Abbey, 1667 moved to the French cemetery of great men-the sacred cemetery of Parisian defenders and celebrities. Many outstanding French scholars found their final destination there.

Thales, the father of mathematics

Thales, born in 624 BC, was the first great mathematician in ancient Greece who enjoyed a world-renowned reputation. He used to be a shrewd businessman. After he accumulated considerable wealth by selling olive oil, Thales devoted himself to scientific research and travel. He is diligent and studious, at the same time, he is not superstitious about the ancients, and he is brave in exploration, creation and positive thinking. His hometown is not too far from Egypt, so he often travels to Egypt. There, Thales learned about the rich mathematical knowledge accumulated by ancient Egyptians for thousands of years. When he traveled in Egypt, he calculated the height of the pyramids in a clever way, which made the ancient Egyptian king Amerasis admire him very much.

Thales's method is ingenious and simple: choose a sunny day, erect a small stick at the edge of the pyramid, and then observe the change of the shadow length of the stick. When the shadow length is exactly equal to the length of the stick, quickly measure the length of the pyramid shadow, because at this time, the height of the pyramid is exactly equal to the length of the tower shadow. It is also said that Thales calculated the height of the pyramid with the ratio of the length of the rod shadow to the tower shadow equal to the ratio of the rod height to the tower height. If this is the case, it is necessary to use the mathematical theorem that the corresponding sides of a triangle are proportional. Thales boasted that he taught this method to the ancient Egyptians, but the fact may be just the opposite. It should be that the Egyptians knew a similar method a long time ago, but they were only satisfied with knowing how to calculate, without thinking about why they could get the correct answer.

Before Thales, people were only satisfied with how to explain all kinds of things when they knew nature, and Thales' greatness was that he not only could explain, but also added a scientific question mark on why. The mathematical knowledge accumulated by ancient orientals is mainly some calculation formulas summarized from experience. Thales believes that the formula thus obtained may be correct in one problem, but it may not be correct in another. Only when they are proved to be universally correct in theory can they be widely used to solve practical problems. In the early stage of the development of human culture, Thales consciously put forward such a view, which is commendable. It endows mathematics with special scientific significance and is a great leap in the history of mathematics development. So Thales is known as the father of mathematics, and that's why.

Thales first proved the following theorem:

1. The circle is divided into two by any diameter.

2. The two base angles of an isosceles triangle are equal.

3. Two straight lines intersect and the vertex angles are equal.

4. The inscribed triangle of a semicircle must be a right triangle.

5. If two triangles have one side and the two angles on this side are equal, then the two triangles are congruent.

This theorem was first discovered and proved by Cyrus, and later generations usually call it Cyrus theorem. According to legend, Thales was very happy after he proved this theorem and slaughtered a bull to worship the gods. Later, he also used this theorem to calculate the distance between the ship at sea and the land.

Thales also made pioneering contributions to ancient Greek philosophy and astronomy. Historians affirm that Thales should be considered as the first astronomer. He often lies on his back to observe the constellations in the sky and explore the mysteries of the universe. His maid often joked that Thales wanted to know the distant sky, but ignored the beautiful scenery in front of him. According to the research of Herodotus, a historian of mathematics, it is known that the day suddenly turned into night (actually a solar eclipse) after hals War, and Thales had predicted this before the war. There is an inscription on Thales' tombstone: "The tomb of the king of astronomers is a little small, but his glory in the field of stars is quite great. 」