The benefits of mathematics are too numerous to mention, and scientists at all times and all over the world have also pointed out it. /kloc-J.J. Sylvester, a mathematician in the 0/9th century, pointed out: "Constant exploration and pursuit in the field of mathematics can sublimate human thinking activities to a pure and harmonious realm." Wang Hao, a contemporary mathematical logician, also said that mathematics has pure beauty. J. Abbas Nott said: "Mathematical knowledge makes thinking more energetic and frees thinking from prejudice, credulity and superstition." W.E. Cerraul said, "Just as literature induces people's emotions, mathematics stimulates people's imagination and reasoning ability."

In a word, mathematics can make your thinking pure and harmonious, and it will add vitality to your thinking. It gives you wings of imagination and opens the channel of reasoning for you. Mathematics is used by us in real life. It teaches us something and how to gain benefits. Sometimes mathematics can help us identify deception and even create deception.

Many students may have tried computer fortune telling, or they may believe it. "Computer fortune telling" looks mysterious. As long as you report the year, month, day and sex of your birth, a so-called character and destiny will appear on the screen when you press the button. It is said that this is your "destiny".

In fact, this is just a computer game at best. We can easily use the pigeon hole principle in mathematics to illustrate its absurdity.

Pigeon hole principle, also known as pigeon cage principle or Dirichlet principle, is a special method to prove the existence in mathematics. For the simplest example, if you put three apples in two drawers in any way, there must be two or more apples in one drawer. The same reasoning can be obtained:

Principle 1 If more than n objects are put into n drawers, at least one drawer has more than two objects.

Principle 2 If there are more than mn objects in N drawers, at least one drawer has more than m+ 1 or m+l objects.

If calculated in 70 years, the number of combinations with different sexes according to the date of birth should be 70× 365× 2 = 5 1 100, and we regard it as the number of drawers. The current population of China is 1 1 100 million, and we regard this figure as the number of "things". Because1.1× = 2 1526× 51/kloc-0+21400, according to principle 2, it is more than 21526, although

In ancient China, people knew how to use the pigeon hole principle to expose the fallacy of birth. For example, in Qing Dynasty, Chen Qiyuan wrote in Notes on Leisure Zhai: "I don't believe in the theory of pushing the stars, thinking that one person is born at a time (note: one hour, two hours), and twelve people are born in one day, which is 4,320 people in terms of age. Counting a Jia (note: 60 years), there are only 259,200 people. Today, only one county is counted. During this period, when the princes were born, there must be people born at the same time. What is the difference between the rich and the poor? " Here, a year is calculated as 360 days, and a day is divided into 12 hours, and the number of drawers obtained is 60× 360× 12 = 259200.

The so-called "computer fortune-telling" is nothing more than storing the manually compiled fortune-telling sentences in their respective cabinets in advance like Chinese medicine cabinets. Who wants to tell fortune, that is, according to the different combinations of birth date, date and gender, according to different codes, mechanically take out the so-called fate sentence from the computer cabinet. It is blasphemy to put the aura of modern science on the dead who were superstitious in ancient times.

Cheating in business is also inseparable from mathematics. Two generations of love give us the best explanation.

The Eid al-Adha Festival is coming, and the atmosphere of the festival is everywhere in the north and south of Tianshan Mountain. In the market town, the traffic is busy and lively. Shops, roadsides, and stalls are full of goods everywhere, with a dazzling array of things. Fruit merchants have moved out the fresh apples, grapes, Sydney, oil and cantaloupe, hoping to sell them at a good price.

At noon that day, Afandi finished half a day's work and rode a donkey to the market. Two generations of love are famous for their intelligence, ability, integrity and integrity. Who doesn't know him? Along the way, he kept greeting his acquaintances and friends. Suddenly, I heard someone calling his name. Looking back, I found Ai Shan, the owner of the fruit shop. This man is treacherous and greedy. He not only uses fake and shoddy goods to harm customers, but also specializes in usury to exploit the people. He is a bad guy that everyone hates. Two generations of love have long wanted to teach this guy a lesson, but he didn't have a chance. At this time, Aishan is sitting in front of two baskets of grapes with a balance beam. A basket is purple grapes, the price is 2 yuan 1 kg; A basket is green grapes, the price is 1 yuan 2 Jin. It's just that many people ask and few people buy.

"Any lift eldest brother, it is not easy to do some business now. You see, I've been here all morning, and I haven't sold a few Jin of grapes. Now there are 60 kilograms of purple grapes and green grapes. I don't know when to sell! " Ai Shan really wanted to ask Avanti to help him come up with an idea to sell grapes, but he was embarrassed to say it.

Afandi heard the implication and thought: This guy just came to the door, so let him pay some money and make everyone angry. He came to the fruit stand and said to Ai Shan, "Oh, Ai Shan, you are so stupid! Purple grapes are sweet, but expensive. Green grapes are cheap, but they taste sour. Why not mix the two kinds of grapes and sell them at the price of 3 kg of 3 yuan, that is, per kg 1 yuan, which is not only easy to sell but also convenient? "

When Ai Shan heard this, he suddenly smiled and quickly gave a thumbs-up and praised: "The two generations of big brothers are really smart, and they really deserve their reputation!" So Ai Shan sold grapes according to the method of two generations of love, and sure enough, more people bought them. Soon, a catty of grapes was sold out.

However, after calculating the amount of money sold, Ai Shan could not help but frown: if sold at the original price, purple grapes should be sold at 2 yuan × 60 = yuan, green grapes should be sold at 1 yuan × (60 ÷ 2) = 30 yuan, and a * * * should be able to sell at yuan +30 yuan = 150 yuan, but now the money can. He wandered around in front of the grape stall, looking for it everywhere, but he couldn't find the lost 30 yuan money. Finally, I realized that two generations of love had played a trick on me. When he wanted to catch up with the two generations of love and ask him, the two generations of love had gone without a trace on a donkey.

Responder: Uncle Wu Jiu-Trainee Magician Level 2 2-26 22:38

You should write about the application of mathematics in life, which makes it easier to start.

Responder: Listening to Dreams and Groaning-Trainee Magician Level 2 3- 1 17:5 1

Mathematical paper

Mathematics on the basketball court

One Sunday morning, my friends and I went to play basketball.

After a while, we were tired of playing and went to the audience to have a rest. Suddenly I thought of a question and couldn't help but say it: "Xiaoming throws 8 balls a minute, Xiaohong throws 6 balls a minute. After they throw together for 8 minutes, Xiaohong improves the hit rate and throws 8 balls a minute. Xiao Ming only throws six balls a minute because of physical exhaustion. How many minutes later, Xiaohong and Xiaoming threw the same number? "

Probably because my friend is too tired to answer such a simple question. He thought for a while, but didn't come up with it. After a long time, he still didn't figure it out. As time went by, he really couldn't think of it, so he had to say shyly, "It can't be done without a draft." I know that even if he has a draft, he may not be able to do it.

I proudly said, "It turns out that Xiao Ming scored two more goals than Xiao Hong, and one scored eight minutes, which is 8×2= 16 (1). Later, Xiaohong scored four more goals than Xiaoming, so how many minutes does it take 16? " 16÷4=4 (minutes), it takes 4 minutes to catch up. "He said," You are amazing! " "I am a genius!" I joked. We all laughed.

Through this incident, I found that mathematics is everywhere in life, in life, study and work. Since then, I like math even more.

By the way, I don't agree with your attitude towards children. You should be good at inducing children, not doing anything for them. The following is about how to write a math paper. I hope it will help you and your children.

How to learn to write a math paper?

"What to write? How to write? " This is a problem that every student who learns to write small papers will encounter. The production of a good paper is a creative work for its author. Creative labor needs a large number of workers. The material, level and inspiration of his creation are by no means easy to get. They need the author to accumulate and think for a long time in his own study and life practice. Judging from the papers collected in our school, some authors usually pay great attention to summarizing and expanding the knowledge of textbooks, and have many unexpected gains in their study; Some are inspired by extracurricular reading and can choose topics; ..... What's more, some authors pay attention to observation and exploration when they find problems in their lives, and link them with their own mathematics learning, and think, summarize and summarize the results of observation and exploration, sublimate them into theories and write amazing good papers. Most of the small authors who read the award-winning papers are concerned about mathematics learning. The author of a good paper should not only have good mathematical knowledge, but also have good literary literacy and comprehensive literacy.

(1) What to write?

The key to writing a small paper is to choose a topic first. Everyone should start with what they are most familiar with and want to write.

Below I combine the topics of some award-winning papers of my classmates to make a simple analysis of the topics.

Papers are classified by content, and there are probably the following:

① Be diligent in practice, apply what you have learned, establish a mathematical model for practical problems, and then use the model to analyze and predict the problems;

Probe into thermal expansion and cold contraction of bridges

(2) Put forward clever mathematical methods to solve common and annoying little things in life;

Such as: unexpected benefits created by drinking fountains

(3) Study the mathematical problem itself, explore the law, and get the general method to solve the problem.

For example, the study of kinship in the score "family"

Mathematics in paper airplane

④ Experience and reflection on a chapter or content of one's own mathematics study.

Such as "unconditional" reasoning

For example, a brief discussion on the "golden section"

For example, the wonderful positive five-pointed star

(2) How to write

(1) The topic should be small, focused and targeted;

② Views should be true, unique, emotional and innovative;

3 express what you want to express in your own language.

(4) Evaluation criteria of mathematical papers.

What kind of math paper is a good one? There are many standards, but I think a good math paper must have the following three characteristics-novelty, truth and beauty. "New" means that the topic should have a unique perspective, and the content written is not simply repeating other people's things or simply downloading a paragraph. Words, it is best to be original, at least to have their own creation, their own views, their own ideas; "Truth" means that the content should be true and reasonable, not empty and tasteless, nor lengthy. The article should stick to the theme, strive to be accurate and concise, and embody the rigor and scientificity of mathematics as much as possible; "Beauty" refers to the fluency of language and writing, and articles should give people the enjoyment of beauty. Of course, judging from the name of the second Mathematics Learning "Star of the Times" Practice and Innovation Thesis Competition, papers with both practice and innovation are definitely more likely to win the favor of the judges. Therefore, I hope that students will be closer to life, pay attention to observation, discovery and discovery, connect life with mathematics, and take writing papers and trying to write them well as evaluation, supplement and innovation for their mathematics learning.

"Plum blossoms come from bitter cold". As long as you are willing to make great efforts, as long as you are willing to endure hardships, keep thinking, guessing and learning, good math papers will be born in your hands. In a word, learning to write papers and trying to write good papers will always be an excellent way for each of our students to exercise themselves and improve their abilities. I believe that the students of Grade One and Grade Two in our school will actively participate in the activities and exchanges of the second "Time Mathematics Learning" and "Time Star" practical innovation thesis competition under the organization and guidance of teachers, and get good results. I wish more and better math papers will be born in the hands of students in the future. I hope that more students will take off from learning to write math papers in the future and write more high-level and high-quality papers.

Example: An easily overlooked answer

The world is full of wonders, and there are many interesting things in our mathematics kingdom. For example, in my ninth exercise book, there is a thinking question that reads: "A bus goes from Dongcheng to Xicheng at a speed of 45 kilometers per hour and stops after 2.5 hours. At this time, it is just 18 km away from the center of the east and west cities. How many kilometers is it between East and West? When Wang Xing and Xiaoying solve the above problems, their calculation methods and results are different. Wang Xing's mileage is less than Xiao Ying's, but xu teacher said that both of them were right. Why is this? Have you figured it out? You can also calculate the calculation results of both of them. " In fact, we can quickly work out a method for this problem, which is: 45× 2.5 = 1 12.5 (km),112.5+18 =130.5 (. In fact, we have neglected a very important condition here, that is, the word "Li" mentioned in the condition is "just 18 km from the center of the east and west cities", and it does not say whether it has not yet reached the midpoint or exceeded the midpoint. If the distance from the midpoint is less than 18km, the formula is the previous one; If it is greater than 18km, the formula should be 45× 2.5 = 1 12.5 (km), 1 12.5-65448. Therefore, the correct answer should be: 45 × 2.5 = 1 12.5 (km),12.5+18 =130.5 (km),/kloc-. Two answers, that is to say, Wang Xing's answer and Xiaoying's answer are comprehensive.

In daily study, there are often many math problems with multiple solutions, which are easily overlooked in practice or examination. This requires us to carefully examine the problem, awaken our own life experience, scrutinize it carefully, and fully and correctly understand the meaning of the problem. Otherwise, it is easy to ignore other answers and make a mistake of generalizing.

The benefits of mathematics are too numerous to mention, and scientists at all times and all over the world have also pointed out it. /kloc-J.J. Sylvester, a mathematician in the 0/9th century, pointed out: "Constant exploration and pursuit in the field of mathematics can sublimate human thinking activities to a pure and harmonious realm." Wang Hao, a contemporary mathematical logician, also said that mathematics has pure beauty. J. Abbas Nott said: "Mathematical knowledge makes thinking more energetic and frees thinking from prejudice, credulity and superstition." W.E. Cerraul said, "Just like literature induces people's emotions, mathematics stimulates people's imagination and reasoning ability."

In a word, mathematics can make your thinking pure and harmonious, and it will add vitality to your thinking. It gives you wings of imagination and opens the channel of reasoning for you. Mathematics is used by us in real life. It teaches us something and how to gain benefits. Sometimes mathematics can help us identify deception and even create deception.

Many students may have tried computer fortune telling, or they may believe it. "Computer fortune telling" looks mysterious. As long as you report the year, month, day and sex of your birth, a so-called character and destiny will appear on the screen when you press the button. It is said that this is your "destiny".

In fact, this is just a computer game at best. We can easily use the pigeon hole principle in mathematics to illustrate its absurdity.

Pigeon hole principle, also known as pigeon cage principle or Dirichlet principle, is a special method to prove the existence in mathematics. For the simplest example, if you put three apples in two drawers in any way, there must be two or more apples in one drawer. The same reasoning can be obtained:

Principle 1 If more than n objects are put into n drawers, at least one drawer has more than two objects.

Principle 2 If there are more than mn objects in N drawers, at least one drawer has more than m+ 1 or m+l objects.

If calculated in 70 years, the number of combinations with different sexes according to the date of birth should be 70× 365× 2 = 5 1 100, and we regard it as the number of drawers. The current population of China is 1 1 100 million, and we regard this figure as the number of "things". Because1.1× = 2 1526× 51/kloc-0+21400, according to principle 2, it is more than 21526, although

In ancient China, people knew how to use the pigeon hole principle to expose the fallacy of birth. For example, in Qing Dynasty, Chen Qiyuan wrote in Notes on Leisure Zhai: "I don't believe in the theory of pushing the stars, thinking that one person is born at a time (note: one hour, two hours), and twelve people are born in one day, which is 4,320 people in terms of age. Counting a Jia (note: 60 years), there are only 259,200 people. Today, only one county is counted. During this period, when the princes were born, there must be people born at the same time. What is the difference between the rich and the poor? " Here, a year is calculated as 360 days, and a day is divided into 12 hours, and the number of drawers obtained is 60× 360× 12 = 259200.

The so-called "computer fortune-telling" is nothing more than storing the manually compiled fortune-telling sentences in their respective cabinets in advance like Chinese medicine cabinets. Who wants to tell fortune, that is, according to the different combinations of birth date, date and gender, according to different codes, mechanically take out the so-called fate sentence from the computer cabinet. It is blasphemy to put the aura of modern science on the dead who were superstitious in ancient times.

Cheating in business is also inseparable from mathematics. Two generations of love give us the best explanation.

The Eid al-Adha Festival is coming, and the atmosphere of the festival is everywhere in the north and south of Tianshan Mountain. In the market town, the traffic is busy and lively. Shops, roadsides, and stalls are full of goods everywhere, with a dazzling array of things. Fruit merchants have moved out the fresh apples, grapes, Sydney, oil and cantaloupe, hoping to sell them at a good price.

At noon that day, Afandi finished half a day's work and rode a donkey to the market. Two generations of love are famous for their intelligence, ability, integrity and integrity. Who doesn't know him? Along the way, he kept greeting his acquaintances and friends. Suddenly, I heard someone calling his name. Two generations of love turned around and saw Ai Shan, the owner of the fruit shop. This man is treacherous and greedy. He not only uses fake and shoddy goods to harm customers, but also specializes in usury to exploit the people. He is a bad guy that everyone hates. Two generations of love have long wanted to teach this guy a lesson, but he didn't have a chance. At this time, Aishan is sitting in front of two baskets of grapes with a balance beam. A basket is purple grapes, the price is 2 yuan 1 kg; A basket is green grapes, the price is 1 yuan 2 Jin. It's just that many people ask and few people buy.

"Any lift eldest brother, it is not easy to do some business now. You see, I've been here all morning, and I haven't sold a few Jin of grapes. Now there are 60 kilograms of purple grapes and green grapes. I don't know when to sell! " Ai Shan really wanted to ask Avanti to help him come up with an idea to sell grapes, but he was embarrassed to say it.

Afandi heard the implication and thought: This guy just came to the door, so let him pay some money and make everyone angry. He came to the fruit stand and said to Ai Shan, "Oh, Ai Shan, you are so stupid! Purple grapes are sweet, but expensive. Green grapes are cheap, but they taste sour. Why not mix the two kinds of grapes and sell them at the price of 3 kg of 3 yuan, that is, per kg 1 yuan, which is not only easy to sell but also convenient? "

When Ai Shan heard this, he suddenly smiled and quickly gave a thumbs-up and praised: "The two generations of big brothers are really smart, and they really deserve their reputation!" So Ai Shan sold grapes according to the method of two generations of love, and sure enough, more people bought them. Soon, a catty of grapes was sold out.

However, after calculating the amount of money sold, Ai Shan could not help but frown: if sold at the original price, purple grapes should be sold at 2 yuan × 60 = yuan, green grapes should be sold at 1 yuan × (60 ÷ 2) = 30 yuan, and a * * * should be able to sell at yuan +30 yuan = 150 yuan, but now the money can. He wandered around in front of the grape stall, looking for it everywhere, but he couldn't find the lost 30 yuan money. Finally, I realized that two generations of love had played a trick on me. When he wanted to catch up with the two generations of love and ask him, the two generations of love had gone without a trace on a donkey.