One day, the barber in Saville village hung a sign: "I cut all the men in the village who don't cut their hair. I only cut my own hair." So someone asked him, "Who will cut your hair?" The barber was speechless at once.
Because if he cuts his own hair, then he belongs to the kind of person who cuts his own hair. However, the sign says that he doesn't cut such people's hair, so he can't cut it himself. If another person cuts his hair, he is the one who doesn't cut his own hair. The sign clearly says that he will cut all men who don't cut their own hair, so he should cut his own hair. It can be seen that no matter what the inference is, what the barber says is always contradictory.
This is a famous paradox called "Russell Paradox". This was put forward by the British philosopher Russell, who expressed a famous paradox about set theory in a popular way.
1874, the German mathematician Cantor founded the set theory, which soon penetrated into most branches and became their foundation. By the end of 19, almost all mathematics was based on set theory. At this time, some contradictory results appeared in set theory, especially the paradox reflected in the barber's story put forward by Russell in 1902, which is extremely simple and easy to understand. In this way, the foundation of mathematics has been shaken passively, which is the so-called third "mathematical crisis".
Since then, in order to overcome these paradoxes, mathematicians have done a lot of research work, produced a lot of new achievements and brought a revolution in mathematical concepts.
Neumann
Neumann (1903~ 1957) is a Hungarian-born American mathematician and a member of the American Academy of Sciences.
Neumann was born in the family of a Jewish banker, and he was a rare child prodigy. He mastered calculus at the age of 8, and read function theory at the age of 12. On his growing up, there is an interesting story: in the summer of 19 13, Mr. Max, a banker, gave a revelation that he was willing to hire a tutor for his eldest son Neumann, who was 1 1 years old, and his salary was 10 times that of ordinary teachers. Although this seductive revelation made many people feel heartbroken, no one dared to teach such a well-known child prodigy ... After he received his Ph.D. in physics-mathematics at the age of 2 1, he began multidisciplinary research, first mathematics, mechanics, physics, then economics, meteorology, then atomic bomb engineering, and finally, he devoted himself to the research of electronic computers. All these make him a complete scientific generalist. His main achievement is mathematical research. He has made great contributions to many branches of higher mathematics, and the most outstanding work is to open up a new branch of mathematics-game theory. 1944 published his excellent book Game Theory and Economic Behavior. During the Second World War, he made an important contribution to the development of the first atomic bomb. After the war, he used his mathematical ability to guide the manufacture of large electronic computers and was known as the father of electronic computers.
Gauss
Gauss (C.F. Gauss,1777.4.30-1855.2.23) is a German mathematician, physicist and astronomer, who was born in a poor family in Zwick, Germany. His father, Gerhard Di Drich, worked as a berm, bricklayer and gardener. His first wife lived with him for more than 65,438+00 years and died of illness, leaving him no children. Diderich later married Luo Jieya, and the next year their child Gauss was born, which was their only child. My father is extremely strict with Gauss, even a little too strict. He often likes to plan his life for the young Gauss according to his own experience. Gauss respected his father and inherited his honest and cautious character. De Derrick died in 1806, when Gauss had made many epoch-making achievements.
In the process of growing up, young Gauss mainly paid attention to his mother and uncle. Gauss's grandfather was a stonemason who died of tuberculosis at the age of 30, leaving two children: Gauss's mother Luo Jieya and his uncle Flier. Flier Ritchie is smart, enthusiastic, intelligent and capable, and has made great achievements in textile trade. He found his sister's son clever, so he spent part of his energy on this little genius and developed Gauss's intelligence in a lively way. A few years later, Gauss, who was an adult and achieved great success, recalled what his uncle had done for him and felt that it was crucial to his success. He remembered his prolific thoughts and said sadly, "We lost a genius because of the death of our uncle". It is precisely because Flier Ritchie has an eye for talents and often persuades her brother-in-law to let her children develop into scholars that Gauss didn't become a gardener or a mason.
In the history of mathematics, few people are as lucky as Gauss to have a mother who strongly supports his success. Luo Jieya got married at the age of 34 and was 35 when she gave birth to Gauss. He has a strong personality, wisdom and sense of humor. Since his birth, Gauss has been very curious about all phenomena and things, and he is determined to get to the bottom of it, which is beyond the scope allowed by a child. When the husband reprimands the child for this, he always supports Gauss and resolutely opposes the stubborn husband who wants his son to be as ignorant as he is.
Luo Jieya sincerely hopes that his son can do something great and cherish Gauss's talent. However, he was afraid to put his son into mathematics research that could not support his family at that time. /kloc-when she was 0/9 years old, although Gauss had made many great achievements in mathematics, she still asked her friend W. Bolyai (the father of J. Bolyai, one of the founders of non-Euclidean geometry): Will Gauss have a future? W Bolyai said that her son would become "the greatest mathematician in Europe", and her eyes were filled with tears.
At the age of seven, Gauss went to school for the first time. Nothing special happened in the first two years. 1787 years old, Gauss 10. He entered the first mathematics class. Children have never heard of such a course as arithmetic before. The math teacher is Buttner, who also played a certain role in the growth of Gauss.
A story that is widely circulated all over the world says that when Gauss was at 10, by adding all the integers from 1 to 100, he worked out the arithmetic problem that Butner gave to the students. As soon as Butner described the question, Gauss got the correct answer. However, this is probably an untrue legend. According to the research of E·T· Bell, a famous mathematical historian who has studied Gauss, Butner gave the children a more difficult addition problem: 81297+81495+81693+…+100899.
Of course, this is also a summation problem of arithmetic progression (the tolerance is 198 and the number of items is 100). As soon as Butner finished writing, Gauss finished the calculation and handed in the small tablet with the answers written on it. E. T. Bell wrote that in his later years, Gauss often liked to talk about this matter with people, saying that only his answer was correct at that time, and all the other children were wrong. Gauss didn't specify how he solved the problem so quickly. Mathematical historians tend to think that Gauss had mastered arithmetic progression's summation method at that time. For a child as young as 10, it is unusual to discover this mathematical method independently. The historical facts described by Bell according to Gauss's own account in his later years should be more credible. Moreover, it can better reflect the characteristics that Gauss paid attention to mastering more essential mathematical methods since he was a child.
Gauss's computing ability, mainly his unique mathematical methods and extraordinary creativity, made Butner sit up and take notice of him. He specially bought Gauss the best arithmetic book from Hamburg and said, "You have surpassed me, and I have nothing to teach you." Then Gauss and Bater's assistant Bater established a sincere friendship until Bater died. They studied together and helped each other, and Gauss began real mathematics research.
1788, 1 1 year-old gauss entered a liberal arts school. In his new school, all his classes are excellent, especially classical literature and mathematics. On the recommendation of Bater and others, the Duke of zwick summoned Gauss, who was 14 years old. This simple, clever but poor child won the sympathy of the Duke, who generously offered to be Gauss' patron and let him continue his studies.
Duke Brunswick played an important role in Gauss's success. Moreover, this function actually reflects a model of scientific development in modern Europe, indicating that private funding was one of the important driving factors for scientific development before the socialization of scientific research. Gauss is in the transition period of privately funded scientific research and socialization of scientific research.
1792, Gauss entered Caroline College in Brunswick for further study. 1795, the duke paid various expenses for him and sent him to the famous German family in G? ttingen, which made Gauss study hard and started creative research according to his own ideals. 1799, Gauss finished his doctoral thesis and returned to his hometown of Bren-Zwick. Just when he fell ill because he was worried about his future and livelihood-although his doctoral thesis was successfully passed, he was awarded a doctorate and obtained a lecturer position, but he failed to attract students and had to return to his hometown-the duke extended a helping hand. The Duke paid for the printing of Gauss's long doctoral thesis, gave him an apartment, and printed Arithmetic Research for him, so that the book could be published in 180 1. Also bear all the living expenses of Gauss. All this moved Gauss very much. In his doctoral thesis and arithmetic research, he wrote a sincere dedication: "To Dagong" and "Your kindness relieved me of all troubles and enabled me to engage in this unique research".
1806, the duke was killed while resisting the French army commanded by Napoleon, which dealt a heavy blow to Gauss. He is heartbroken and has long been deeply hostile to the French. The death of Dagong brought economic difficulties to Gauss, the misfortune that Germany was enslaved by the French army, and the death of his first wife, all of which made Gauss somewhat disheartened, but he was a strong man and never revealed his predicament to others, nor did he let his friends comfort his misfortune. It was not until19th century that people knew his state of mind at that time when sorting out his unpublished mathematical manuscripts. In a discussion of elliptic functions, a subtle pencil word was suddenly inserted: "For me, it is better to die than to live like this."
The generous and kind benefactor died, and Gauss had to find a suitable job to support his family. Because of Gauss's outstanding work in astronomy and mathematics, his fame spread all over Europe from 1802. The Academy of Sciences in Petersburg has continuously hinted that since Euler's death in 1783, Euler's position in the Academy of Sciences in Petersburg has been waiting for a genius like Gauss. When the Duke was alive, he strongly discouraged Gauss from going to Russia. He is even willing to raise his salary and set up an observatory for him. Now, Gauss is facing a new choice in life.
In order not to lose Germany's greatest genius, B.A. von von humboldt, a famous German scholar, joined other scholars and politicians to win Gauss the privileged positions of professor of mathematics and astronomy at the University of G? ttingen and director of the G? ttingen Observatory. 1807, Gauss went to Kottingen to take office, and his family moved here. Since then, he has lived in G? ttingen except for attending a scientific conference in Berlin. The efforts of Humboldt and others not only made the Gauss family have a comfortable living environment, but also enabled Gauss himself to give full play to his genius, and created conditions for the establishment of Gottingen Mathematics School and Germany to become a world science center and mathematics center. At the same time, it also marks a good beginning of scientific research socialization.
Gauss's academic position has always been highly respected by people. He has the reputation of "prince of mathematics" and "king of mathematicians" and is considered as "one of the three (or four) greatest mathematicians in human history" (Archimedes, Newton, Gauss or Euler). People also praised Gauss as "the pride of mankind". Genius, precocity, high yield, persistent creativity, ..., almost all the praises in the field of human intelligence are not too much for Gauss.
Gauss's research field covers all fields of pure mathematics and applied mathematics, and has opened up many new fields of mathematics, from the most abstract algebraic number theory to intrinsic geometry, leaving his footprints. Judging from the research style, methods and even concrete achievements, he is the backbone of 18- 19 century. If we imagine mathematicians in the18th century as a series of high mountains, the last awe-inspiring peak is Gauss; If mathematicians in the19th century are imagined as rivers, then their source is Gauss.
Although mathematical research and scientific work did not become an enviable career at the end of 18, Gauss was born at the right time, because the development of European capitalism made governments around the world pay attention to scientific research when he was close to 30 years old. With Napoleon's emphasis on French scientists and scientific research, Russian czars and many European monarchs began to look at scientists and scientific research with new eyes. The socialization process of scientific research is accelerating and the status of science is improving. As the greatest scientist at that time, Gauss won many honors, and many world-famous scientists regarded Gauss as their teacher.
1802, Gauss was elected as an academician of communication and a professor of Kazan University by the Academy of Sciences in Petersburg, Russia. 1877, the Danish government appointed him as a scientific adviser, and this year, the government of Hanover, Germany also hired him as a government scientific adviser.
Gauss's life is a typical scholar's life. He has always maintained the frugality of a farmer, making it hard to imagine that he is a great professor and the greatest mathematician in the world. He was married twice, and several children annoyed him. However, these have little influence on his scientific creation. After gaining a high reputation and German mathematics began to dominate the world, a generation of Tianjiao completed the journey of life.
Descartes
Generation of analytic geometry
/kloc-After the 6th century, due to the development of production and science and technology, astronomy, mechanics and navigation put forward new demands for geometry. For example, the German astronomer Kepler found that the planet runs around the sun along an ellipse, and the sun is at a focus of this ellipse; Italian scientist Galileo discovered that throwing objects tested parabolic motion. These findings all involve conic curves. In order to study these complex curves, the original set of methods is obviously not applicable, which leads to the emergence of analytic geometry.
1637, Descartes, a French philosopher and mathematician, published Methodology. There are three appendices at the back of this book, one is called refractive optics, the other is called meteorology, and the other is called geometry. At that time, this "geometry" actually referred to mathematics, just like "arithmetic" and "mathematics" in ancient China.
Cartesian geometry is divided into three volumes. The first volume discusses the rule drawing method. The second volume is the nature of the curve; The third volume is the drawing method of three-dimensional and "super-three-dimensional", which is actually an algebraic problem and discusses the properties of the roots of equations. Mathematicians and historians of mathematics in later generations regard Descartes' geometry as the starting point of analytic geometry.
It can be seen from Descartes' Geometry that Descartes' central idea is to establish a "universal" mathematics and unify arithmetic, algebra and geometry. He imagined that transforming any mathematical problem into an algebraic problem is to simplify any algebraic problem into solving an equation.
In order to realize the above hypothesis, Descartes pointed out the corresponding relationship between points on the plane and real number pairs (x, y) from the latitude and longitude system of astronomical geography. Different values of x and y can determine many different points on the plane, so we can study the properties of curves by algebraic method. This is the basic idea of analytic geometry.
Specifically, the basic idea of plane analytic geometry has two main points: one is to establish a coordinate system on the plane, and the coordinates of a point correspond to a set of ordered real number pairs; Secondly, after the coordinate system is established on the plane, a curve on the plane can be expressed by a binary algebraic equation. It can be seen that the application of coordinate method can not only solve geometric problems through algebraic methods, but also closely relate important concepts such as variables, functions, numbers and shapes.
The appearance of analytic geometry is not accidental. Before Descartes wrote geometry, many scholars used two intersecting straight lines as coordinate systems to study it. While studying astronomical geography, some people put forward that a position can be determined by two "coordinates" (longitude and latitude). All these have a great influence on the establishment of analytic geometry.
In the history of mathematics, it is generally believed that Fermat, a contemporary French amateur mathematician with Descartes, is also one of the founders of analytic geometry and should share the honor of the establishment of this discipline.
Fermat is an amateur scholar engaged in mathematical research and has made important contributions to number theory, analytic geometry and probability theory. He is modest and quiet, and has no intention of publishing his book. But from his correspondence, we know that Descartes had written a short article about analytic geometry long before he published Geometry, and he already had the idea of analytic geometry. It was not until 1679 that Fermat's thoughts and works were published in Letters to Friends.
Descartes' Geometry, as a work of analytic geometry, is incomplete, but it is important to bring forth the old and bring forth the new and make contributions to opening up a new garden of mathematics.
The Basic Content of Analytic Geometry
In analytic geometry, coordinate system is first established. As shown above, two mutually perpendicular straight lines with a certain direction and measurement unit on the plane are called rectangular coordinate system oxy. Using the coordinate system, a one-to-one relationship can be established between a point on a plane and a pair of real numbers (x, y). In addition to rectangular coordinate system, there are oblique coordinate system, polar coordinate system, spatial rectangular coordinate system and so on. There are also spherical coordinates and cylindrical coordinates in the spatial coordinate system.
The coordinate system establishes the close relationship between geometric objects and numbers, geometric relations and functions, which simplifies the study of spatial morphology into a relatively mature and easy-to-control quantitative relationship. Learning geometry in this way is usually called analytic method. This analysis method is not only important for analytic geometry, but also for studying various branches of geometry.
The establishment of analytic geometry introduced a series of new mathematical concepts, especially the introduction of variables into mathematics, which made mathematics enter a new development period, which is the variable mathematics period. Analytic geometry promotes the development of mathematics. Engels once commented: "The turning point in mathematics is Descartes' variable. With the change of books, sports entered mathematics; With variables, dialectics enters mathematics; With variables, differentiation and integration will become necessary immediately, ... "
Application of analytic geometry
Analytic geometry is divided into plane analytic geometry and space analytic geometry.
In plane analytic geometry, besides the properties of straight lines, the properties of conic curves (circle, ellipse, parabola and hyperbola) are mainly studied.
In spatial analytic geometry, besides the properties of plane and straight line, cylinders, cones and rotating surfaces are mainly studied.
Some properties of ellipse, hyperbola and parabola are widely used in production or life. For example, the reflector of the spotlight bulb of a movie projector is oval, the filament is in one focus and the movie door is in another focus; Searchlights, spotlights, solar cookers, radar antennas, satellite antennas and radio telescopes are all made by using the principle of parabola.
Generally speaking, analytic geometry can solve two basic problems by using coordinate method: one is to satisfy the trajectory of a given point and establish its equation through coordinate system; The other is to study the curve properties expressed by the equation through the discussion of the equation.
The steps of solving problems by coordinate method are as follows: firstly, establish a coordinate system on the plane and "translate" the geometric conditions of known point trajectories into algebraic equations; Then use algebraic tools to study the equation; Finally, the properties of algebraic equations are described in geometric language, and the answers to the original geometric problems are obtained.
The idea of coordinate method urges people to use various algebraic methods to solve geometric problems. It used to be regarded as a difficult problem in geometry, but once algebraic methods are used, it becomes bland. The coordinate method also provides a powerful tool for the mechanization proof of modern mathematics.
Lee Liu
(born around 250 AD) is a very great mathematician in the history of Chinese mathematics, and also occupies a prominent position in the history of world mathematics. His representative works "Nine Arithmetic Notes" and "Arithmetic on the Island" are China's most precious mathematical heritage.
Nine Chapters of Arithmetic was written in the early Eastern Han Dynasty. * * * There are solutions to 246 problems. In solving simultaneous equations, calculating four fractions, calculating positive and negative numbers, calculating the volume and area of geometric figures and many other aspects, it is among the advanced in the world. However, due to the primitive solution and the lack of necessary proof, Liu Hui made supplementary proof for it. These proofs show his creative contributions in many aspects. The solution of linear equations is improved. In geometry, the secant method is put forward, that is, the method of finding the area and perimeter of a circle by using inscribed or circumscribed regular polygons. He scientifically obtained the result that pi = 3. 14 by using secant technology. Liu Hui put forward in the secant technique that "if you cut it carefully, the loss is not great, and then you can't cut it."
In the book Island Calculation, Liu Hui carefully selected nine surveying problems, which were creative, complex and representative and attracted the attention of the West at that time.
Liu Hui has quick thinking and flexible methods, and advocates both reasoning and intuition. He is the first person who China explicitly advocated to demonstrate mathematical propositions by logical reasoning.
Liu Hui's life is a life of hard work for mathematics. Although the status is low, but the personality is noble. He is not a mediocre man who seeks fame and fame, but a great man who never tires of learning. He left a precious wealth to our Chinese nation.
Leibniz
Leibniz is the most important mathematician, physicist and philosopher in Germany at the turn of 17 and 18 centuries, and a rare scientific genius in the world. He read widely and dabbled in encyclopedias, making indelible contributions to enriching the treasure house of human scientific knowledge.
biography
Leibniz was born in a scholarly family in Leipzig, eastern Germany. He had extensive contact with ancient Greek and Roman cultures and read the works of many famous scholars, thus gaining a solid cultural foundation and clear academic goals. 15 years old, he entered the University of Leipzig to study law, and also extensively read the works of Bacon, Kepler and Galileo, and deeply thought and evaluated their works. After listening to Euclid's "Elements of Geometry", Leibniz became interested in mathematics. /kloc-at the age of 0/7, he studied mathematics for a short time at the University of Jena and obtained a master's degree in philosophy.
At the age of 20, he published his first mathematical paper on combinatorial art. This is an article about mathematical logic, and its basic idea is to reduce the theoretical truth argument to a calculation result. Although this paper is not mature enough, it shines with innovative wisdom and mathematical talent.
Leibniz joined the diplomatic community after receiving his Ph.D. from Altdorf University. During his visit to Paris, Leibniz was deeply inspired by Pascal's deeds and determined to study advanced mathematics, and studied the works of Descartes, Fermat, Pascal and others. His interest obviously turned to mathematics and natural science, and he began to study infinitesimal algorithms, independently established the basic concepts and algorithms of calculus, and laid the foundation of calculus together with Newton. 1700 was elected as an academician of the Paris Academy of Sciences, which contributed to the establishment of the Berlin Academy of Sciences and served as the first president.
Primitive calculus
/kloc-in the second half of the 0/7th century, European science and technology developed rapidly. Due to the improvement of productivity and the urgent needs of all aspects of society, through the efforts of scientists from all over the world and the accumulation of history, calculus theory based on function and limit concept came into being. The idea of calculus can be traced back to the method of calculating area and volume proposed by Archimedes and others in Greece. Newton founded calculus in 1665, and Leibniz also published his works on calculus in 1673- 1676. In the past, differential and integral were studied as two mathematical operations and two mathematical problems respectively. Cavalieri, Barrow, Wallis and others have obtained a series of important results of finding area (integral) and tangent slope (derivative), but these results are isolated and incoherent.
Only Leibniz and Newton really communicated integral and differential, and clearly found the internal direct relationship between them: differential and integral are two reciprocal operations. And this is the key to the establishment of calculus. Only by establishing this basic relationship can we establish systematic calculus. And from the differential and quadrature formulas of various functions, the algorithm program of * * * is summarized, which makes the calculus method universal and develops into a symbolic calculus algorithm.
However, there has been a heated debate in the field of mathematics about the order of the creation of calculus. In fact, Newton's research on calculus was earlier than Leibniz's, but Leibniz's results were published earlier than Newton's. Leibniz's paper "Finding a Wonderful Computing Type of Minimax" published in Teacher's Magazine on June 1684+00 is considered as the earliest published calculus document in the history of mathematics. Newton also wrote in the first and second editions of Mathematical Principles of Natural Philosophy published in 1687: "Ten years ago, I and the most outstanding geometer G.
△ jules verne, a French science fiction writer, carefully read more than 500 kinds of books and materials in order to write his adventures on the moon. He wrote 104 science fiction novels in his life. There are 25,000 reading notes.
△ Darwin, British naturalist and founder of evolution, traveled around the world with the research ship Beagle. He traveled overseas, studied biological remains, recorded 500,000 words of precious materials, and finally wrote the book Origin of Species, which caused a sensation in the world, and founded the theory of evolution.
△ Chekhov, a great Russian writer, pays great attention to accumulating life materials and writes down some things he hears, sees or thinks in his notebook at any time, which is called "life handbook". Once, Chekhov heard a friend tell a joke, and he burst into tears. He smiled and took out his Life Handbook, pleading, "Please say it again and let me write it down."
△ In the room of American writer Jack London, strings of small pieces of paper are hung everywhere, whether on curtains, clothes hangers, cabinets, bedside or mirrors. Looking carefully, it turns out that wonderful words, vivid metaphors and useful information are written on the paper. He hung pieces of paper in different parts of the room. That is, whenever and wherever you sleep, dress, shave and walk, you can see and remember. He also took a lot of pieces of paper in his pocket when he went out. He studied hard and accumulated information, and finally wrote such fascinating works as Love Life, Iron Shoes and Waves.
(1) Edison had more than 1000 inventions in his life. Where did the time for these countless experiments come from? From often even
Out of the extreme tension of working for two days and three days. Later, he constantly squeezed out time, so he was never exhausted.
Experimental time. Became a scientist.
(2) Lu Xun disciplined himself with the motto "Time is life" and engaged in proletarian literature and art for 30 years, relying on time.
Just like life, writing never stops.
(3) Balzac works hard every day 16 or 17 hours, although his arm hurts from fatigue.
Pain, tears, not willing to waste a moment.
(4) Edison seized every "today" for scientific invention and worked for more than ten hours every day, except
In order to eat, sleep and exercise, I have almost never been idle. Prolonging working hours every day is equivalent to prolonging life. Therefore,
When the local people celebrated their 79th birthday, they called themselves 135 years old. Edison lived to be 85 years old before he published it in the US Patent Office.
There are 1328 invention patents, and there is an invention every 15 days on average.
(5) Qi Baishi, a master of Chinese painting, insists on painting every day and never stops except for physical discomfort. 85 years old
Now, one day, after painting four pictures in a row, he painted another one specially for yesterday and wrote an inscription: "It was stormy yesterday, and I was in a bad mood."
Restless, never draw, make up now, don't teach for a day. "
(6), "Don't teach a day off", anyone who has achieved something will do it. Please read Lu Xun's The Last Year (1936
Years),1-1October (65438+1October 26th), stayed in bed for 8 months, and wrote essays and other articles.
In chapter 54, I translated three chapters of the second part of Dead Soul, made two notes, replied to more than 270 letters and gave a lot of information.
In 2000, the author read the manuscript and kept a diary when he was ill. Three days before his death, he wrote a preface for a translated novel. Six years before his death
Lu Xun has always lived near Hongkou Park in Shanghai, only a few minutes' walk from his residence to the park, but
Never played in the park. This is Lu Xun who "spends all other people's coffee time at work".
Celebrity case-tolerance
In the Spring and Autumn Period, Chu Zhuangwang won the championship.
One night, I held a candlelight party with my beloved princess and held a grand banquet for the ministers. Halfway through the wine, suddenly a strong wind blew out the candle. A military commander wanted to flirt with Princess Ai in the dark, and Princess Ai tore off the red tassel on his helmet. Princess Ai suggested that the King of Chu light a lamp at once to see which guy lost the red tassel on his helmet and severely punish him. A friend's wife should not be bullied, let alone a leader's wife. Unexpectedly, King Zhuang was magnanimous and ordered all the generals to take off the red tassels on their helmets before lighting the lamps. Soon, the king of Chu made a personal expedition, engaged the enemy, and fell into a tight encirclement. His soldiers will flee everywhere, and the life of the king of Chu is at stake. Suddenly, a desperate battle appeared to protect deus ex, the king of Chu, and get back a life. The king of Chu said excitedly, "Everyone else is running for their lives. Only Ai Qing is willing to lay down his life to save the driver. What's your name? Which unit is it? " The general should answer: "I was the one who molested your wife at the candlelight party that day!" " "
(Legend, because I can't tell the source! Edison invented the first light bulb. He asked one of his disciples to have it tested, and he broke it! Disciples are ashamed. But when Edison made the second light bulb, he ignored other people's objections and gave it to his disciples for experiments. Edison said, "The greatest tolerance is to give him another chance!" " "
On the day of the report, Lincoln came to the report office to take the exam. When he came to the report office, he found that the people in the prison were the ones he offended, and he finished the exam with a heavy burden. When he asked about offending him, the man said, "Really? I don't remember. "