Stories for n very short mathematicians are shorter. Ha, the more Doha you want, the more points you give. One story is 5 points.

Lu Yu Nezha: Bajie was walking forward when he heard someone calling him from behind: "Old pig, how comfortable!" Looking back, Bajie saw that it was Nezha, the third prince of King Tota.

Pig shook his head and said, "Isn't this the demon with three heads and six arms?"

When Nezha heard Pig call him a demon, he flew into a rage and shouted, "Change!" Then he turned into a three-headed and six-armed man, with six weapons in his six hands: demon-cutting sword, demon-cutting knife, demon-binding rope, demon-lowering pestle, hydrangea and fireball, and made a vicious attack on Bajie.

Pig didn't dare to neglect him. He waved his rake and greeted him. The two of them "tinkled" and fought. After a while, Nezha saw that he didn't take advantage, and shouted: "Change!" The weapons in six hands immediately exchanged positions. In this way, Nezha kept changing the method of holding weapons, which knocked Bajie out.

Pig waved his hand again and again and said, "Stop fighting, stop fighting. How many different ways do you hold these six hands?"

"72 kinds!" Nezha is swaggering.

"brag!" Pig curled his mouth and said, "I still believe in twenty or thirty kinds, 72 kinds?" Don't lie to me! "

Nezha asked five hands to hold a demon-chopping sword, a demon-chopping knife, a demon-binding rope, a demon-lowering pestle and an embroidered ball in turn, and said to Bajie, "Look, the weapons in my five hands are fixed. At this time, my sixth hand can only hold a fire wheel."

Bajie nodded and said, "Well, yes, just one way to hold it."

Nezha asked four hands to hold the demon-chopping sword, the demon-chopping knife, the demon-tying rope and the demon-lowering pestle in turn. At this time, the fifth and sixth hands can alternately hold the hydrangea and the fire wheel, and there are two ways to hold it.

Nezha asked three hands to hold the demon-chopping sword, the demon-chopping knife and the demon-tying rope in turn, while the other three hands transformed into the following six holding methods:

Demon-dropping pestle, hydrangea and fire wheel;

Demon pestle, fire wheel, hydrangea;

hydrangea, demon pestle and fire wheel;

hydrangea, fire wheel, demon pestle;

fire wheels, hydrangeas, and demon-killing pestle;

firebricks, pestle, hydrangea.

Pig touched his head and said, "How can you arrange this if you take all six hands casually? Still not dizzy! "

Nezha criticised: "What a fool! Look at the following three numbers: 1 = 1, 2=1×2, 6 = 1× 2× 3. It can be inferred that if two hands are fixed and the remaining four hands are held at will, there are 1× 2× 3× 4× = 24 holding methods. And all six hands are free to take it? There are 1× 2× 3× 4× 5× 6 = 72 different methods. "

Bajie gave Nezha a hand: "You've changed so much, I'm impressed."

Countermeasures to win

During the Warring States Period, Qi Weiwang and the general Tian Ji raced horses, and Qi Weiwang and Tian Ji each had three good horses: getting on, winning and dismounting. The race is divided into three times, and each horse race is bet on thousands of dollars. Because the horsepower of the two horses is almost the same, and the horses in Qi Weiwang are better than those in Tian Ji, so most people think that Tian Ji will lose. However, Tian Ji adopted the advice of his protege Sun Bin (a famous strategist), dismounted Qi Weiwang's horse, dismounted Qi Weiwang's Zhongma, and dismounted Qi Weiwang. As a result, Tian Ji won a daughter by winning Qi Weiwang 2-1. This is an example of using game theory to solve problems in ancient China.

Here is a game played by two people: take turns to report the number, and the number reported cannot exceed 8 (nor can it be ). Add up the numbers reported by two-faced individuals, and whoever reports the number and makes the sum 88 will win. If you were asked to count first, how many times should you count first to win?

analysis: because everyone reports at least 1 and at most 8 at a time, when someone reports, another person will find a number, so that the sum of this number and a reported number is 9. According to the rules, whoever counts off and makes the sum 88 wins, so it can be inferred that whoever counts off and makes the sum 79 (= 88-9) wins. 88 = 9× 9+7, and so on. Whoever counts off and makes the sum 16 will win. Further, whoever reports 7 first will win. Therefore, it is concluded that the winning strategy of the first reporter is: first report 7, and then if the other party reports K(1≤K≤8), you report (9-K). In this way, when you report the tenth number, you will win.

when does the snail climb the well?

A snail accidentally fell into a dry well. It lay down at the bottom of the well and began to cry. A toad (

lai) crawled over and said to the snail in a low voice, "Don't cry, little brother! It's no use crying. The shaft wall is too high. If you fall here, you can only live here. I have been here for many years, and I haven't seen the sun for a long time, let alone want to eat swan meat! " The snail looked at the old and ugly toad and thought to himself, "What a beautiful world outside the well! I can never live in a dark and cold well like it!" " The snail said to Toad, "Uncle Toad, I can't live here. I must climb up!"! How deep is this well? " "Ha ha ha ....., what a joke! This well is 1 meters deep. How can you climb it at your young age and with such a heavy shell? " "I'm not afraid of hardship and fatigue. I can always climb out after climbing for a while every day!" The next day, the snail ate enough and drank enough water, and began to climb up the wall. It kept climbing, and finally climbed 5 meters in the evening. The snail was very happy and thought, "At this rate, I can climb up tomorrow evening." Thinking about it, it fell asleep unconsciously. In the morning, the snail was awakened by a purr. At first glance, it turned out that Uncle Tu was still sleeping. It was surprised: "How come I am so close to the bottom of the well?" It turned out that the snail slipped down 4 meters from the well wall after falling asleep. The snail sighed, gritted his teeth and began to climb again. In the evening, it climbed another 5 meters, but at night the snail slipped another 4 meters. Climb and climb, and finally the strong snail finally climbed up the well platform. Can you guess that it takes a few days for a snail to climb the well platform?

The story of a mathematician-Su Buqing

Su Buqing was born in a mountain village in Pingyang County, Zhejiang Province in September 192. Although his family is poor, his parents scrimp and save, and they have to work hard for him to go to school. When he was in junior high school, he was not interested in mathematics. He thought mathematics was too simple and would understand it as soon as he learned it. It can be measured that a later math class influenced his life.

That was when Su Buqing was in the third grade, and he was studying in Zhejiang No.6 Middle School. A teacher, Yang, who had just returned from studying in Tokyo, taught math. 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 prevails, and the world powers rely on their ships to build their guns and gain profits, all of which want to nibble and carve up China. The danger of China's national subjugation and extinction is imminent, so it is necessary to revitalize science, develop industry and save the nation from extinction. Every man is responsible for the rise and fall of the world,' and every student here is responsible. " He quoted extensively 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 nation and survive, we must revitalize science. Mathematics is the pioneer of science. In order to develop science, we must learn mathematics well. " I don't know how many lessons Su Buqing has attended in his life, but this lesson will never be forgotten.

Mr. 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 for individuals, but to seek new life for the Chinese nation. That night, Su Buqing tossed and turned, sleepless all night. Under the influence of Teacher Yang, Su Buqing's interest shifted from literature to mathematics, and from then on, he set the motto "Never forget to save the country by reading, and never forget to study by saving the country". Being fascinated by mathematics, whether it's hot summer in the middle of winter or frosty morning and snowy night, Su Buqing only knows reading, thinking, solving problems and calculating, and has calculated tens of thousands of mathematical exercises in four years. Now Wenzhou No.1 Middle School (that is, the provincial No.1 Middle School at that time) still treasures a geometry exercise book of Su Buqing, which is written with a brush and is well-crafted. When he graduated from high school, Su Buqing scored above 9 in all subjects.

at the age of p>17, Su Buqing went to Japan to study, and won the first place in Tokyo Higher Institute of Technology, where he studied eagerly. The belief of winning glory for our country drove Su Buqing to enter the research field of mathematics earlier. While completing his studies, he wrote more than 3 papers, made remarkable achievements in differential geometry, and obtained a doctorate in science in 1931. Before receiving his Ph.D., Su Buqing had been a lecturer in the Department of Mathematics of Imperial University of Japan. Just as a Japanese university was preparing to hire him as a well-paid associate professor, Su Buqing decided to return to China to teach at his ancestors who raised him. Back in Su Buqing, a professor at Zhejiang University, life was very hard. In the face of difficulties, Su Buqing's answer is, "Suffering is nothing, I am willing, because I have chosen a correct road, which is a patriotic and bright road!"

This is the patriotic heart of the older generation of mathematicians.

The epitaph of mathematicians

Some mathematicians devoted themselves to mathematics during their lifetime, and after their death, their tombstones are engraved with symbols representing their life achievements.

Archimedes, an ancient Greek scholar, died at the hands of Roman enemy soldiers who attacked Sicily (he was still in the Lord before his death: "Don't break my circle". ), people carved the figure of the ball inscribed in the cylinder on his tombstone to commemorate his discovery that the volume and surface area of the ball are two-thirds of the volume and surface area of the circumscribed cylinder. German mathematician Gauss gave up his original intention to study literature and devoted himself to mathematics after he discovered the rule practice of regular heptagon, and even made many great contributions to mathematics. Even in his will, he suggested to build a tombstone with a regular 17-sided prism as the base.

Rudolph, a 16th century German mathematician, spent his whole life calculating pi to 35 decimal places, which was later called Rudolph number. After his death, others carved this number on his tombstone. Jacques Bernoulli, a Swiss mathematician, studied the spiral (known as the thread of life) before his death. After his death, a logarithmic spiral was engraved on the tombstone, and the inscription also said: "Although I have changed, I am the same as before." This is a pun that not only depicts the spiral nature, but also symbolizes his love for mathematics.

Zu Chongzhi (429-5 AD) was born in Laiyuan County, Hebei Province during the Northern and Southern Dynasties. He read many books on astronomy and mathematics since he was a child, studied hard and practiced hard, and finally made him an outstanding mathematician and astronomer in ancient China.

Zu Chongzhi's outstanding achievements in mathematics are People take "diameter of one week and three weeks" as pi, which is called "ancient ratio". Later, it was found that the error of ancient ratio was too big, and pi should be "diameter of one circle was more than that of three weeks", but opinions were divided on how much was left. Until the Three Kingdoms period, Liu Hui put forward a scientific method to calculate pi-"secant technique", which approximated the circumference of a circle by the circumference of a regular polygon. Liu Hui calculated it into a circle. The more accurate the π value is. On the basis of predecessors' achievements, Zu Chongzhi worked hard and calculated repeatedly, and found that π was between 3.1415926 and 3.1415927. He also obtained the approximate value of π fraction, which was taken as the reduction rate and the secret rate, in which the six decimal places were 3.141929, which was the closest fraction to π value within 1. What method did Zu Chongzhi use to get this? There is no way to examine it now. If he tries to find it according to Liu Hui's "secant" method, he will have to calculate that the circle is inscribed with 16,384 polygons. How much time and labor it takes! It can be seen that his perseverance and intelligence in academic research are admirable. It has been more than 1 years since Zu Chongzhi calculated the secret rate, and foreign mathematicians obtained the same result. In order to commemorate Zu Chongzhi's outstanding contribution, some foreign mathematicians suggested that π = be called "ancestral rate".

Zu Chongzhi Expo was famous classics at that time, and he insisted on seeking truth from facts. He compared and analyzed a large number of materials measured and calculated by himself and found serious errors in the past calendars. He was brave enough to improve, and when he was thirty-three, he successfully compiled Da Ming Calendar, which opened up a new era in calendar history.

Zu Chongzhi, together with his son Zu Xuan (also a famous mathematician in China), solved the calculation of the volume of a sphere with ingenious methods. They adopted a principle at that time: "If the powers and potentials are the same, the products cannot be different." That is, two solids located between two parallel planes are parallel. If the areas of two sections are always equal, the volumes of the two solids are equal. This principle is called Cavalieri's principle in western languages, but it was discovered by Karl Marx more than 1 years after Zu's father. In order to commemorate the great contribution of Zu's father and son in discovering this principle, everyone also calls it Zu's principle.

The vitality of mathematics lies in its interest. Mathematics is interesting because of its enlightenment to thinking.

The following is a story about the origin of probability theory.

Earlier, there were two great French mathematicians, one named bhaskar and the other named Fermat.

bhaskar knew two gamblers who asked him a question. They said that after they made a bet, it was agreed that whoever won the first five games would get all the bets. After gambling for a long time, A won four games and B won three games. It was late and they didn't want to gamble any more. So, how should this money be divided?

is it right to divide the money into seven parts, with four parts for those who win four games and three parts for those who win three games? Or, because the first time it was said to be full of five innings, and no one reached it, so one person divided it into half?

neither of these two methods is correct. The correct answer is: those who win four games get 3/4 of this money, and those who win three games get 1/4 of this money.

why? Suppose the two of them bet another game, either A wins or B wins. If A wins five games, all the money should go to him. If A loses, that is, A and B win four games each, the money should be divided in half. Now, the probability of A winning or losing is 1/2, so the money he takes should be 1/2× 1+1/2× 1/2 = 3/4, and of course, B should get 1/4.

Through this discussion, an important concept in probability theory-mathematical expectation is formed.

In the above problems, the mathematical expectation is an average value, that is, how to calculate the uncertain money in the future today. This requires multiplying the money that A may get by 1/2 of the probability of winning or losing, and then adding them up.

probability theory has developed since then, and it has become a very widely used subject today.