Complete works of humorous stories about mathematics

Interesting mathematical story 1, butterfly effect meteorologist Lorenz put forward a paper entitled "Will butterflies flap their wings to cause tornadoes in taxonomic groups?" This paper discusses that if the initial condition of a system is a little worse, its result will be very unstable. He called this phenomenon "the butterfly effect". Just like we roll the dice twice, no matter how deliberately we roll, the physical phenomena and points thrown twice are not necessarily the same. Why did Lorenz write this paper? This story happened in the winter of 196 1 2008. He operated the meteorological computer in the office as usual. Usually, he only needs to input meteorological data such as temperature, humidity and air pressure, and the computer will calculate the possible meteorological data at the next moment according to the built-in three differential equations, thus simulating the meteorological change map. On this day, Lorenz wanted to know more about the subsequent changes of a record. He re-entered the meteorological data at a certain moment into the computer, so that the computer could calculate more subsequent results. At that time, the speed of computer processing data was not fast enough, so he had time to have a cup of coffee and chat with his friends for a while before the results came out. An hour later, the result came out, but he was dumbfounded. Compared with the original information, the original data is similar, and the later data is more different, just like two different pieces of information. The problem is not the computer, but the data he entered is 0.0005438+027. These subtle differences make a world of difference. So it is impossible to accurately predict the weather for a long time. References:

Cao Cao's Gourd (Volume II)-Yuan Zhe Science Education Foundation II. The mathematical "genius" hive in animals is a strict hexagonal cylinder with a flat hexagonal opening at one end and a closed hexagonal diamond bottom at the other end, which consists of three identical diamonds. The rhombic obtuse angle of the chassis is 109 degrees 28 minutes, and all acute angles are 70 degrees 32 minutes, which is both firm and material-saving. The honeycomb wall thickness is 0.073 mm, and the error is very small. Red-crowned cranes always move in groups, forming a "human" shape. The angle of the herringbone is 1 10 degrees. More accurate calculation also shows that half the angle of the herringbone-that is, the angle between each side and the direction of the crane group is 54 degrees, 44 minutes and 8 seconds! And the angle of diamond crystal is exactly 54 degrees, 44 minutes and 8 seconds! Is it a coincidence or some "tacit understanding" of nature? The spider's "gossip" net is a complex and beautiful octagonal geometric pattern, and it is difficult for people to draw a symmetrical pattern similar to a spider's net even with the compass of a ruler. In winter, when a cat sleeps, it always hugs its body into a ball. There is also mathematics in it, because the shape of the ball minimizes the surface area of the body, so it emits the least heat. The real "genius" of mathematics is coral. Coral writes a "calendar" on its body, and "draws" 365 stripes on its wall every year, apparently one a day. Strangely, paleontologists found that corals 350 million years ago "painted" 400 watercolors every year. Astronomers tell us that at that time, the earth only had 2 1.9 hours a day, not 365 days a year, but 400 days. (Life Times) 3. Every piece of paper in Mobius tape has two sides and a closed curved edge. If there is a piece of paper with one side and only one side, is it possible for an ant to reach another point from any point on the paper without crossing the edge? In fact, it is possible. Just twist a piece of paper tape in half and stick both ends on it. This is the German mathematician Mobius (M? Beus. A.F 1790- 1868) was found in 1858. Since then, that kind of belt has been named after him, called Mobius belt. With this toy, a branch of mathematical topology can flourish. 4. Mathematician's Will The will of Arab mathematician Hua Razmi, when his wife was pregnant with their first child. "If my dear wife gives birth to a son for me, my son will inherit two thirds of the inheritance and my wife will get one third; If it is a girl, my wife will inherit two-thirds of the inheritance and my daughter will get one-third. " . Unfortunately, the mathematician died before the child was born. What happened after that made everyone more troubled. His wife gave birth to twins, and the problem happened in his will. How to follow the mathematician's will and divide the inheritance among wife, son and daughter? 5. Matching Games One of the most common matching games is that two people play together. Put some matches on the table first, and two people take turns to take them. Each time, there can be some restrictions on the number of competitions, stipulating that the person who wins the final competition wins. Rule 1: How can we win if the number of competitions we participate in at one time is limited to at least one and at most three? For example, there are n= 15 matches on the table. Party A and Party B take turns to take it, and Party A takes it first. How should Party A lead them to win? In order to get the last one, A must leave zero matches for B at the end, so A can't leave 1 or 2 or 3 in the round before the last step, otherwise B can win all of them. If there are four games left, then B can't win them all, so no matter how many games B wins (1 or 2 or 3), A can win all the remaining games. Similarly, if there are eight matches left on the table for B to take, no matter how B takes them, A can leave four matches after this round, and finally A must win. It can be seen from the above analysis that as long as the matching numbers on the table are 4, 8, 12, 16, etc. Party A will be a shoo-in. Therefore, if the original number of matches on the table is 15, A should take three matches. (∫ 15-3 = 12) What if the original matching number on the table is 18? Then A should take 2 pieces first (∵ 18-2= 16). Rule 2: If the number of matches taken at one time is limited to 1 4, how can we win? Principle: If Party A takes it first, then every time Party A takes it, it must leave a multiple of 5 matches for Party B.. General rule: There are n matches, and you can take 1 to k matches at a time, so the number of matches left after each take of A must be a multiple of k+ 1. Rule 3: How to limit the number of matches taken at one time to some discontinuous numbers, such as 1, 3, 7? Analysis: 1, 3, 7 are all odd numbers. Since the target is 0 and 0 is even, the number of matches on the table must be even, because B can't get 0 after taking 1, 3 or 7 matches, but if so, there is no guarantee that A will win, because A is also odd or even about the number of matches. Because [even-odd = odd, odd-odd = even], after each fetch, the matching numbers on the table are even and odd. If it is an odd number at first, such as 17, and A takes it first, then no matter how much A takes (1 or 3 or 7), the rest are even numbers, then B turns even numbers into odd numbers, A turns odd numbers into even numbers, and finally A is destined to be the winner; On the other hand, if it is an even number from the beginning, A is doomed to lose. General rule: the first one wins if the opening is odd; On the other hand, if you start with an even number, the first one will lose. Rule 4: Limit the number of matches taken at one time to 1 or 4 (odd and even numbers). Analysis: Like the previous rule 2, if A takes it first, then A will leave five matches for B to take, and then A will win. In addition, if the remaining matching number of A to B is a multiple of 5 plus 2, A can also win this game, because the matching number of each conjunction can be controlled at 5 (if B takes 1, A takes 4; If B takes 4, A takes 1), and finally there is 2 left. B can only get 1, and A can win the last one. General rule: If A takes it first, the number of matches A leaves each time is a multiple of 5 or a multiple of 5 plus 2. Interesting Mathematics-Intelligent Counting Tanks [2008-12-1515: 28: 00 | Author: Li Shaogang] One night in the Northern Song Dynasty, the owner of a small hotel was making jars with his buddies. Because business has been particularly good recently, there are naturally many jars. The boss is happy and thinking about how to make more money. He wants to stack the cans neatly and beautifully to attract more customers to the hotel. The jars are piled beautifully, layer by layer neatly. The wave in front of the hotel fluttered with the wind, making people stop and want to have a few drinks in the store. When the hotel owner is in high spirits, he wants to count how many cans there are. However, it is not easy to count cans. The boss went from front to back, and then from back to front. The freshly dried sweat came out again, and the guys laughed the next day. This pile of jars really attracted many customers, and the boss was overjoyed when he looked at the jars. At this time, a well-dressed young scholar came over and faced the jars thoughtfully. The boss thought, I spent a lot of time counting this pile of cans yesterday. This young man is extraordinary in appearance, and I will test him. "Young man, do you know how many cans there are in this pile?" The boss asked half jokingly. "It's very simple, as long as you tell me how many rows there are on the top layer of this pile of cans, and how many rows there are in each row, a total of several layers. I don't need to count. I know the number of cans in this pile at once. " Young people obviously have answers when they talk like this. "Oh!" The boss thought, this young man really talks big. Let's tell him his conditions and see what he can do. So the boss said cheerfully, "There are four rows of jars on the top floor, eight in each row, and five rows of jars on the second floor, nine in each row ..." "Well, there are seven floors altogether," the young man interrupted the boss and reported the answer without thinking. "There are 567 jars altogether. Right? " The boss was so surprised that he forgot to shut his open mouth. So soon! The boss immediately invited the young people into the hotel, served tea and toasted them, and treated them well. The boss really admired the young man, asked his name and asked his advice on how to count the altar. The young man's name is Shen Kuo. Superior family life conditions gave him the opportunity to study, and he was curious and willing to study, so he became a very talented person. Shen Kuo replied to the boss: "My method of counting jars is actually very simple, because there are 77 jars in the middle, with seven floors in total. Just multiply it by 7 and finally add a constant of 28. " Shen Kuo was interested in calculation since he was a child, and read many famous mathematical books. Later, I wrote a mathematical monograph, Gap Product, which was devoted to the summation of higher-order arithmetic progression. Shen Kuo's method of counting altars is the summation of higher-order arithmetic progression, which is much more convenient than simple counting. In mathematics, you may encounter problems with large numbers and items, which can be solved at one time by this method.

1. Two boys each ride a bicycle, starting from two places 20 miles apart (1 mile +0.6093 km) and riding in a straight line. At the moment they set off, a fly on the handlebar of one bicycle began to fly straight to another bicycle. As soon as it touched the handlebar of another bicycle, it immediately turned around and flew back. The fly flew back and forth, between the handlebars of two bicycles, until the two bicycles met. If every bicycle travels at a constant speed of 10 miles per hour and flies fly at a constant speed of 15 miles per hour, how many miles have flies flown? The speed of each bicycle is 10 miles per hour, and the two will meet at the midpoint of the distance of 2O miles after 1 hour. The speed of a fly is 15 miles per hour, so it flies 1 5 miles in total in1hour. Many people try to solve this problem in a complicated way. They calculate the first distance between the handlebars of two bicycles, then return the distance, and so on, and calculate those shorter and shorter distances. But this will involve the so-called infinite series summation, which is very complicated advanced mathematics. It is said that at a cocktail party, someone asked John? John von neumann (1903 ~ 1957) is one of the greatest mathematicians in the 20th century. ) Put forward this question, he thought for a moment, and then gave the correct answer. The questioner seems a little depressed. He explained that most mathematicians always ignore the simple method to solve this problem and adopt the complex method of summation of infinite series. Von Neumann had a surprised look on his face. "However, I use the method of summation of infinite series," he explained. 2. A fisherman, wearing a big straw hat, sat in a rowboat and fished in the river. The speed of the river is 3 miles per hour, and so is his rowing boat. "I must row a few miles upstream," he said to himself. "The fish here don't want to take the bait!" Just as he started rowing upstream, a gust of wind blew his straw hat into the water beside the boat. However, our fisherman didn't notice that his straw hat was lost and rowed upstream. He didn't realize this until he rowed the boat five miles away from the straw hat. So he immediately turned around and rowed downstream, and finally caught up with his straw hat drifting in the water. In calm water, fishermen always row at a speed of 5 miles per hour. When he rowed upstream or downstream, he kept the speed constant. Of course, this is not his speed relative to the river bank. For example, when he paddles upstream at a speed of 5 miles per hour, the river will drag him downstream at a speed of 3 miles per hour, so his speed relative to the river bank is only 2 miles per hour; When he paddles downstream, his paddle speed and the flow rate of the river will work together, making his speed relative to the river bank 8 miles per hour. If the fisherman lost his straw hat at 2 pm, when did he get it back? Because the velocity of the river has the same influence on rowing boats and straw hats, we can completely ignore the velocity of the river when solving this interesting problem. Although the river is flowing and the embankment remains motionless, we can imagine that the river is completely still and the embankment is moving. As far as rowing boats and straw hats are concerned, this assumption is no different from the above situation. Since the fisherman rowed five miles after leaving the straw hat, he certainly rowed five miles back to the straw hat. Therefore, compared with the river, he rowed a total of 10 miles. The fisherman rowed at a speed of 5 miles per hour relative to the river, so he must have rowed 65,438+00 miles in two hours. So he found the straw hat that fell into the water at 4 pm. This situation is similar to the calculation of the speed and distance of objects on the earth's surface. Although the earth rotates in space, this movement has the same effect on all objects on its surface, so for most problems of speed and distance, this movement of the earth can be completely ignored. In the absence of wind, the average ground speed (relative ground speed) of the whole round-trip flight is 100 mph. Suppose there is a persistent strong wind blowing from city A to city B. If the engine speed is exactly the same as usual during the whole round-trip flight, what effect will this wind have on the average ground speed of the round-trip flight? Mr. White argued, "This wind will not affect the average ground speed at all. In the process of flying from City A to City B, strong winds will accelerate the plane, but in the process of returning, strong winds will slow down the speed of the plane by the same amount. " "That seems reasonable," Mr. Brown agreed, "but if the wind speed is 100 miles per hour. The plane will fly from city A to city B at a speed of 200 miles per hour, but the speed will be zero when it returns! The plane can't fly back at all! " Can you explain this seemingly contradictory phenomenon? Mr. White said that the wind increased the speed of the plane in one direction and slowed it down in the other. That's right. But he said that the wind had no effect on the average ground speed of the whole round-trip flight, which was wrong. Mr. White's mistake is that he didn't consider the time taken by the plane at these two speeds. It takes much longer to return against the wind than with the wind. In this way, it takes more time to fly when the ground speed is slow, so the average ground speed of round-trip flight is lower than when there is no wind. The stronger the wind, the more the average ground speed drops. When the wind speed is equal to or higher than the plane speed, the average ground speed of the round-trip flight becomes zero, because the plane cannot fly back. 4. Sunzi Suanjing is one of the top ten famous arithmetical classics in the early Tang Dynasty, and it is an arithmetic textbook. It consists of three volumes. The first volume describes the counting system, the rules of multiplication and division, and the middle volume illustrates the method of calculating scores and Kaiping with examples, which are all important materials for understanding the ancient calculation in China. The second book collects some arithmetic problems, and the problem of "chickens and rabbits in the same cage" is one of them. The original question is as follows: let pheasant (chicken) rabbits be locked together, with 35 heads above and 94 feet below. Male rabbit geometry? The solution of the original book is; Let the number of heads be a and the number of feet be b, then b/2-a is the number of rabbits and a-(b/2-a) is the number of pheasants. This solution is really great. When solving this problem, the original book probably adopted the method of equation. Let x be pheasant number and y be rabbit number, then X+Y = B, 2x+4Y = A, and X = A-(B/2-A). According to this set of formulas, it is easy to get the answer to the original question: 12 rabbits, 22 pheasants. Let's try to run a hotel with 80 suites and see how knowledge becomes wealth. According to the survey, if we set the daily rent as 160 yuan, we can be full; And every time the rent goes up in 20 yuan, three guests will be lost. The daily service and maintenance cost of each occupied room totals 40 yuan. Question: How can we set the price to be the most profitable? A: The daily rent is 360 yuan. Although 200 yuan was higher than the full price, we lost 30 guests, but the remaining 50 guests still brought us 360*50= 18000 yuan. After deducting 40*50=2000 yuan for 50 rooms, the daily net profit is 16000 yuan. When the customer is full, the net profit is only 160*80-40*80=9600 yuan. Of course, the so-called "learned through investigation" market was actually invented by myself, so I entered the market at my own risk. When Su Dongpo, a great poet in Song Dynasty, was young, he went to Beijing with several schoolmates to take the exam. When they arrived at the examination center, it was too late. The examiner said that I made a couplet, and if you are right, I will let you into the examination room. The examiner's team is two or three people alone, with four oars and five sails. After six beaches and seven bays, it was very late. Su Dongpo's couplets have been cold for ten years. Today, the examiner and Su Dongpo both embedded ten numbers from one to ten in the couplets, vividly describing the hardships and assiduousness of the literati. When learning mathematics, we should not only solve problems correctly, but also make no mistakes in the specific problem-solving process. The difference is often thousands of miles away. An old woman living on a pension in Chicago, USA, went home after a minor operation in the hospital. Two weeks later, she received the bill from the hospital. The amount is $63,440. When she saw such a huge number, she couldn't help being surprised. She had a heart attack and fell to the ground dead. Later, someone checked with the hospital, and it turned out that the computer had misplaced the decimal point. In fact, she only needs to pay $63.44. A wrong decimal point actually killed a person. As Newton said, in mathematics, the smallest error can't be ignored. The century is the unit for counting years. A hundred years is a century. The start year and end year of the first century are 1 and 100 respectively. The common mistake is that some people regard the starting year as the year zero, which obviously does not conform to logic and our habits, because in general, the calculation of ordinal number starts from 1, not from 0. It is this misunderstanding that led to the misunderstanding that the year at the end of the century was 99 AD, which is why 1999 was wrongly considered as the year at the end of the twentieth century and the year 2000 was the year at the beginning of the twenty-first century. Because the AD count is ordinal, it should start from 1, and the first year of 2 1 century is 200 1. French mathematician Buffon invited many friends to his home and did an experiment. Buffon spread a big piece of white paper on the table, which was covered with parallel lines with equal distance. He also took out many small needles of equal length, the length of which was half that of parallel lines. Buffon said, please feel free to put these small needles on this piece of white paper. The guests did as he said. Buffon's statistics show that everyone throws 22 12 times, in which the small needle intersects the parallel line on the paper 704 times, and 22 10÷704≈3. 142. Buffon said that this number is an approximation of π. You will get an approximate value of pi every time. The more times you throw it, the more accurate the approximate value of pi will be. This is the famous Buffon test. 198 1 One day in summer, India held a mental arithmetic competition. The performer is a 37-year-old woman from India. Her name is Shagongtana. On that day, she will compete with an advanced electronic computer with amazing mental arithmetic ability. The staff wrote a long list of 20/kloc-0 bits, asking to find the 23rd root of this number. As a result, it took Shagongtana only 50 seconds to report the correct answer to the audience. In order to get the same answer, the computer must input 20,000 instructions, and then calculate, which takes much more time than Shagongtana. This anecdote caused a sensation in the world, and Shagongtana was called a mathematical magician. Watson was born in Jiangsu. He likes math since he was a child, and he is very clever. 1930, 19-year-old Hua went to Tsinghua University to study. During his four years in Tsinghua, under the guidance of Professor Xiong Qinglai, Hua studied hard and published more than a dozen papers in succession. Later, he was sent to study in Britain and got a doctorate. He studied number theory deeply and got the famous Fahrenheit theorem. He paid special attention to integrating theory with practice and traveled to more than 20 provinces, municipalities and autonomous regions to mobilize the masses to apply the optimization method to agricultural production. In an interview, the reporter asked him what is your greatest wish? It was not until the last day of work that he answered without thinking. On the last day of working hard for science, he really fulfilled his promise. When Su Dongpo, a great poet in the Song Dynasty, was young, he went to Beijing with several schoolmates to catch the exam. When they arrived at the examination center, it was too late. The examiner said, "I made a couplet. If I get it right, I'll let you into the examination room." The examiner's couplet is: a single leaf in a boat, two or three students, four oars and five sails, crossing six beaches and seven bays, it is very late. Su Dongpo is right. I have studied hard for the Five Classics and Four Books, and I have to do well in the exam today. Examiners and Su Dongpo both embedded ten numbers from one to ten in the couplets, which vividly described the hardships and assiduousness of the scholars. Wrong decimal point is not only the correct way to solve mathematical problems, but also the specific problem-solving process can not be wrong. An old woman living on a pension in Chicago, USA, went home after a minor operation in the hospital. Two weeks later, she received a bill from the hospital for $63,440. When she saw such a huge number, she couldn't help being surprised. She had a heart attack and fell to the ground dead. Later, someone checked with the hospital, and it turned out that the computer misplaced the decimal point, but in fact she only had to pay $63.44. A wrong decimal point actually killed a person. As Newton said, "in mathematics, even the smallest error can't be made." Century is the unit for calculating age, and a hundred years is a century. The start year and end year of the first century are 1 and 100 respectively. The common mistake is that some people regard the starting year as the year zero, which obviously does not conform to logic and our habits, because in general, the calculation of ordinal number begins with "1" instead of "1". It is this misunderstanding that led to the misunderstanding that the year at the end of the century was 99 AD, which is why 1999 was wrongly considered as the year at the end of the twentieth century and the year 2000 was the year at the beginning of the twenty-first century. Because the AD count is ordinal, it should start with "1", and the first year of 2 1 century is 20065433. French mathematician Buffon invited many friends to his home and did an experiment. Buffon spread a big piece of white paper on the table, which was covered with parallel lines with equal distance. He also took out many small needles of equal length, the length of which was half that of parallel lines. Buffon said, "Please feel free to leave these small needles on this piece of white paper!" " The guests did as he said. Buffon's statistics show that everyone throws 22 12 times, in which the small needle intersects the parallel line on the paper 704 times, and 2210 ≈ 704 ≈ 3.142. Buffon said, "This number is an approximation of π. Every time you get an approximation of pi, the more times you throw it, the more accurate the approximation of pi is. " This is the famous Buffon Experiment. 198 1 One day in summer, a math magician held a mental arithmetic competition in India. The performer is a 37-year-old woman from India. Her name is Shagongtana. On that day, she will compete with an advanced electronic computer with amazing mental arithmetic ability. The staff wrote a long list of 20/kloc-0 bits, asking to find the 23rd root of this number. As a result, it took Shagongtana only 50 seconds to report the correct answer to the audience. In order to get the same answer, the computer must input 20,000 instructions, and then calculate, which takes much more time than Shagongtana. This anecdote caused a sensation in the world, and Shagongtana was called a "mathematical magician". Hua, who worked until the last day, is from Jiangsu. He likes math since he was a child and is very clever. 1930, 19-year-old Hua went to Tsinghua University to study. During his four years in Tsinghua, under the guidance of Professor Xiong Qinglai, Hua studied hard and published more than a dozen papers in succession. Later, he was sent to study in Britain and got a doctorate. He studied number theory deeply and got the famous Fahrenheit theorem. He paid special attention to integrating theory with practice and traveled to more than 20 provinces, municipalities and autonomous regions to mobilize the masses to apply the optimization method to agricultural production. The reporter asked him in the interview: "What is your greatest wish?" Without thinking, he replied, "Work until the last day." On the last day of working hard for science, he really fulfilled his promise.