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.
The epitaph of a mathematician
Some mathematicians devoted themselves to mathematics before their death, and after their death, they carved symbols representing their life achievements on tombstones.
Archimedes, an ancient Greek scholar, died at the hands of Roman enemy soldiers who attacked Sicily. ), people carved the figure of the ball in the cylinder on his tombstone to commemorate his discovery that the volume and surface area of the ball are two-thirds of that of the circumscribed cylinder. After discovering the regular practice of regular heptagon, German mathematician Gauss gave up the original intention of studying literature, devoted himself to mathematics, and even made many great contributions to mathematics. Even in his will, he suggested building a tombstone with a regular 17 prism as the base.
/kloc-Rudolph, a German mathematician in the 6th century, spent his whole life calculating pi to 35 decimal places, which was later called Rudolph number. After his death, someone else 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 carved on the tombstone, and the inscription also read: "Although I have changed, I am the same as before." This is a pun, which not only describes the spiral nature, but also symbolizes his love for mathematics.
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 used "the diameter of three weeks a week" as pi, which was called "Gubi". Later, it was found that the error of Gubi was too large, and the pi should be "the diameter of a circle is greater than the diameter of three weeks". However, 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" which approximated the circumference of a circle with the circumference inscribed by a regular polygon. Liu Hui calculated the circle inscribed with a 96-sided polygon and got π=3. 14, and pointed out that the more sides inscribed with a regular polygon, the more accurate the π value obtained. On the basis of predecessors' achievements, Zu Chongzhi devoted himself to research and repeated calculations. It is found that π is between 3. 14 15926 and 3. 14 15927, and 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. There's no way to check now. If he tries to find it according to Liu Hui's secant method, he must work out 16384 polygons inscribed in the circle. How much time and labor it takes! It is obvious that his perseverance and wisdom in academic research are admirable. It has been more than 1000 years since foreign mathematicians obtained the same result in the secrecy rate calculated by Zu Chongzhi. In order to commemorate Zu Chongzhi's outstanding contribution, some mathematicians abroad 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. They adopted a principle at that time: "If the power supply potential is the same, the products should 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 based on the following points. However, it was discovered by Karl Marx more than 1000 years ago. In order to commemorate the great contribution of grandfather and son in discovering this principle, everyone also called this principle "the ancestor principle".
Interesting math problems in junior high school
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 runs at a constant speed of 10 miles per hour and flies fly at a constant speed of 15 miles per hour, how many miles will flies fly?
answer
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 in 1 hour, it always flies 15 miles.
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 will interact with the flow rate of the river, 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?
answer
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 bank remains motionless, we can imagine that the river is completely static and the bank 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 rivers, he always paddles 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 2 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 motion has the same effect on all objects on its surface, so most problems about speed and distance can be completely ignored.
3. An airplane flies from City A to City B, and then returns to City A. 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?
answer
Mr. White said that the wind increases the speed of the plane in one direction by the same amount as it decreases the speed of the plane in the other direction. 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 exceeds the speed of the plane, 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 has three volumes. The first volume describes the system of counting, 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 the pheasant number and y be the rabbit number, then there is
x+y=b，2x+4y=a
Get a solution
y=b/2-a，
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. Daily expenses for services, maintenance, etc. Each occupied room is calculated in 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.
6 Mathematician Weiner's age, the whole question is as follows: The cube of my age this year is four digits, and the fourth power of my age is six digits. These two numbers only use all ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. How old is Weiner? Answer: this question is difficult at first glance, but it is not. Let Wiener's age be X. First, the cube of age is four digits, which defines a range. The cube of 10 is 1000, the cube of 20 is 8000, and the cube of 2 1 is 926 1, which is a four-digit number; The cube of 22 is10648; So 10 =
Uniformly arranged 1, 2,3,4 1987 natural numbers ... 1986, 1987 form a big circle, counting from 1: every 1 crosses 2 and 3; Cross out 5 and 6 every 4, so that two numbers are crossed out every other number, and then circle. Q: How many numbers are left in the end?
Answer: 663