The benefits of mathematics are numerous, and scientists from ancient to modern times have also pointed them out. The 19th century mathematician J.J. Sylvester pointed out: "Continuous exploration and pursuit in the field of mathematics can sublimate human thinking activities to a pure and harmonious realm." Mr. Wang Hao, a contemporary mathematical logician, also said, Mathematics has a pure beauty. J. Arbuthnot said: "Mathematical knowledge adds vitality to thinking and frees it from the shackles of prejudice, credulity and superstition." W.E. Serauer said: "Just as literature induces people's emotions, mathematics inspires people's imagination. and reasoning. ”
In short, mathematics can make your thinking pure and harmonious, and will add vitality to your thinking. It gives you the wings of imagination and opens channels for your reasoning. Mathematics is used by us in real life. It teaches us to identify something and teaches us how to obtain benefits. Sometimes mathematics can help us recognize deception or even create deception.
Many students may have tried computer fortune telling, and may have even believed it to be true. "Computer fortune telling" seems quite mysterious. As long as you state the year, month, day and gender of your birth, and press a button, sentences about your personality and destiny will appear on the screen. It is said that this is your "fate".
In fact, this is just a computer game at best. We can easily illustrate its absurdity using the mathematical drawer principle.
The drawer principle, also known as the pigeonhole principle or Dirichlet's principle, is a special method of proving existence in mathematics. To give the simplest example, if you put 3 apples into two drawers in any way, then there must be two or more apples in one drawer. Using the same reasoning, you can get:
Principle 1 If more than n objects are placed in n drawers, then at least one drawer contains 2 or more objects.
Principle 2 If more than mn objects are placed in n drawers, then at least one drawer contains m+1 or more than m+l objects.
If calculated based on 70 years, the number of different combinations of year, month, day and gender of birth should be 70×365×2=51100, which we regard as the "drawer" number. Our country's current population is 1.1 billion, which we regard as an "object" number. Since 1.1× =21526×511021400, according to principle 2, there are more than 21526 people. Although their origins, experiences, talents, and opportunities are different, they have exactly the same "fate". This is really ridiculous. !
In ancient my country, some people have long known how to use the drawer principle to expose the fallacies of birth dates. For example, Chen Qiyuan of the Qing Dynasty wrote in "Notes of Yongxianzhai": "I don't believe in the theory of star destiny. I think that one person is born in one hour (note: refers to one hour, two hours in total), and twelve people are born in one day. In terms of age, there are 4,320 people. Calculated in one year (note: refers to sixty years), there are only 259,200 people. Now it is only calculated in one county. Their household registration The number is no less than hundreds of thousands (for example, 800,000 people in the city of Hangzhou in the 10th year of Xianfeng). If you look at the size of the world, from the princes to the common people, there are hundreds of millions of people. There must be many of them who were born at the same time. That's right. When princes and great men are born, there must be common people born at the same time. How can there be any difference between the rich and the poor? "Here, a year is calculated as 360 days, and one day is divided into twelve hours. The number of drawers is 60×360×12=259200.
The so-called "computer fortune-telling" is nothing more than storing the artificially compiled fortune-telling sentences in their own cabinets one by one like a traditional Chinese medicine cabinet. Different combinations are mechanically put into various "cabinets" of the computer according to different codes to take out the so-called sentences of fate. This kind of activity of casting a halo of modern science on the superstitious souls of ancient times is a blasphemy against science.
Deception in business is also inseparable from mathematics. Afanti gave us the best explanation.
The Eid al-Adha festival is coming soon, and the north and south of the Tianshan Mountains are full of festive atmosphere. The market town was bustling with traffic and extremely lively. Shops, roadsides, and street stalls are all filled with goods, with everything you need. The fruit merchants moved out the stored apples, grapes, pears, petroleum, and cantaloupe, hoping to sell them at a good price.
At noon that day, Afanti finished his work for a long time and came to the market on his donkey. Afanti is famous for his intelligence, ability, integrity and justice. Who doesn't know him? Along the way, he kept saying hello to acquaintances and friends. Suddenly, he heard someone shouting his name. Afanti looked back and saw that it was Ai Shan, the owner of the fruit shop. This person is treacherous and greedy. He not only often uses fake and shoddy goods to defraud customers, but also specializes in exploiting people with usury. He is a villain that everyone hates. Affan had long wanted to teach this guy a lesson, but he just didn't get the chance. At this time, Ai Shan was sitting in front of two large baskets of grapes with a scale beam in his hand, dazed. One basket contains purple grapes, priced at 2 yuan per catty; one basket contains green grapes, priced at 1 yuan per catty. It’s just that more people ask and fewer people buy.
“Brother Afanti, it’s not easy to do business nowadays. You see, I’ve been here all morning and haven’t sold a few kilograms of grapes. Now I still have purple grapes and green grapes left. It’s 60 pounds, I don’t know how long it will take to sell it!” Ai Shan actually wanted to ask Afanti to help him with an idea to sell grapes, but he was too embarrassed to say it.
Afanti heard the implication and thought: This guy just happened to come to my door. Let’s find a way to make him lose some money and let everyone vent their anger. He came to the fruit stall and said to Aishan: "Ah, brother Aishan, you are so stupid! Although purple grapes are sweet, they are expensive, and green grapes are cheap, but they taste sour. Why not mix the two grapes together, Sold at 3 yuan per catty, that is, 1 yuan per catty. Isn’t it easy to sell and save trouble?"
Ai Shan immediately smiled when he heard this, and quickly gave a thumbs up and praised: "Afanti? Brother is really smart and deserves his reputation!" So Aishan followed Afanti's method to sell the grapes, and as expected, more and more people bought the grapes. After a while, all the grapes were sold out.
However, when Ai Shan counted the money from the sale, he couldn't help but frowned: If sold at the original price, the purple grapes should be sold for 2 yuan × 60 = yuan, and the green grapes should be sold for 1 yuan. × (60÷2) = 30 yuan. One *** should be sold for 100 yuan + 30 yuan = 150 yuan, but now it only sells for 100 yuan. Why is it 30 yuan less? He walked around in front of the grape stall with crouched eyes, looking for the missing 30 yuan in every corner. Finally, I realized that I had let Afanti play a trick on me. When he wanted to catch up with Afanti and ask for clarification, Afanti had already disappeared without a trace on his donkey.
Answer: Uncle Wujiu - Trainee Magician Level 2 2-26 22:38
You should write about the application of mathematics in life, so that it is easier to start. < /p>
Answer: Listening to Dreams and Moaning - Apprentice Magician Level 2 3-1 17:51
Mathematics Essay
Mathematics on the Basketball Court
One Sunday morning, I went to play basketball with my friends.
After a while, we both got tired and went to the auditorium to rest. Suddenly, a question came to my mind, and I couldn't help but say it: "Xiao Ming shoots 8 balls in one minute, and Xiao Hong shoots 6 balls in one minute. After they shoot together for 8 minutes, Xiao Hong improves his shooting rate and shoots 8 balls in one minute." Xiao Ming only counted 6 balls in one minute due to lack of physical strength. How many minutes later did Xiao Hong and Xiao Ming only score the same number? ”
Maybe it’s because my friend is too tired. He couldn't answer simple questions. He thought about it for a while and still couldn't figure it out after a long time. Time passed by minute by second, and he really couldn't think of it, so he had to say embarrassedly: "Without the draft book, I can't do it." I knew that even if he had the draft, he might not be able to do it.
I said proudly: "It turns out that Xiao Ming made 2 more shots than Xiao Hong, and he shot for 8 minutes, that is, 8×2=16 (shots). Later, Xiao Hong did the reverse. There are 4 more shots per point than Xiao Ming, so how many more minutes does it take to shoot 16 balls? 16÷4=4 (points), it takes 4 minutes to catch up. "He said, "You are so good!" "I am a genius! Well!" I joked. We both laughed.
Through this incident, I discovered that mathematics is everywhere in life, in life, in study, and in work. From then on, I liked mathematics even more
By the way, I don’t agree with your attitude towards children. You should be good at inducing children, rather than doing anything for them. The following is about how to write a mathematics essay Essay, I hope it will be helpful to you and your children.
How to learn to write a short essay on mathematics
"What to write? How to write?" This is what everyone learns to write a short essay on This is a problem that all students will encounter. The production of a good paper is a creative labor for its author. Creative labor has high demands on workers. The materials, level, and even creative inspiration... are by no means easily obtained. They require long-term accumulation and thinking by the author in his own study and life practice. Judging from the papers collected by our school, some of the authors pay great attention to summarizing and extending textbook knowledge, and have many unexpected gains in their studies; some have gained inspiration and gained inspiration from extracurricular readings. Topic selection;... What's more, some authors pay attention to observation and exploration when they find problems in life, and connect them with their own mathematics learning. They think, summarize and summarize the results of observation and exploration, and sublimate them into theories. Wrote an amazing paper. Looking at the young authors of the award-winning papers, most of them are dedicated people in mathematics learning. The author of a good paper must not only have a good mathematical understanding, but also have good literary accomplishment and comprehensive literacy.
(1) What to write
The key to writing a short essay is to choose a topic first. When choosing a topic, everyone should start with the content that they are most familiar with and want to write about.
Now I will conduct a simple topic analysis based on the topics selected by some of the award-winning papers of our school students.
Papers are classified according to content, and they are roughly as follows:
① Be diligent in practice, apply what you have learned, establish mathematical models for practical problems, and then use the models to analyze and predict problems. ;
For example: exploring the thermal expansion and contraction of the bridge
② For the common and annoying little things in life, ingenious mathematical methods are proposed to solve them; < /p>
For example: Unexpected benefits created by a water dispenser
③Study the mathematical problem itself, explore the rules, and come up with a general method to solve the problem
For example: Exploration of kinship in the "family" of fractions
For example: Mathematics in paper airplanes
④Experience and understanding of a certain chapter or content of your own mathematics study Reflection
For example: "No conditions" reasoning
For example: A small discussion on the "golden section"
For example: The wonderful five-pointed star
< p>(2) How to write① The topic should be small, focused, and targeted;
② The insights should be true, unique, insightful, and innovative;
② p>
③ Use your own language to express what you want to express
(4) Criteria for evaluating small mathematics papers
What kind of small mathematics paper is considered a good paper? Woolen cloth? There are many standards, but I think a good mathematics paper must have the following three characteristics - novelty, truth and beauty. "New" means that the topic selection should have a unique perspective, and the content should not simply repeat others' stuff or simply download a paragraph. It is best for the text to be original. At least it must have its own creation, its own point of view, and its own thoughts; "true" means that the content must be realistic and reasonable, and it must not be empty or boring, nor be lengthy and protracted. The article should stick closely to the topic, strive to be accurate and concise, and reflect the rigor and scientific nature of mathematics as much as possible; "beauty" refers to smooth language and smooth writing, and the article should give people the enjoyment of beauty. Of course, judging from the name of the second Era Mathematics Learning "Era Star" Practice and Innovation Paper Contest, papers that are both practical and innovative are definitely more likely to be favored by the judges. Therefore, I hope that students will get closer Live, pay attention to observation, search, and discover, connect life with mathematics, learn to write papers, and strive to write good papers as an evaluation, a supplement, and an improvement of your own mathematics learning, so that you The purpose of learning to write short essays is right, and you will write better and better math essays.
“The fragrance of plum blossoms comes from the bitter cold.” As long as you are willing to work hard, bear the hardships, and keep thinking, guessing, and learning, good mathematics papers will definitely be in your hands. Birth. In short, learning to write papers and striving to write good papers is always an excellent way for each of our students to exercise themselves and improve their abilities. I believe that the students in the first and second grades of our school will actively participate in the activities and exchanges of the second "Times Mathematics Learning" and "Times Star" Practice and Innovation Paper Competition under the organization and guidance of their teachers, and achieve good results. . I wish that more and better mathematics essays will be born in the hands of students in the future; I hope that more students will take off from learning to write mathematics essays and write more high-level and high-quality essays in the future. thesis.
Example: "Answers that are easy to ignore"
The world is full of wonders, and there are also many interesting things in our mathematical kingdom. For example, in my current exercise book for Volume 9, there is a question that goes like this: "A passenger bus drove from the East City to the West City, traveling 45 kilometers per hour, and stopped after 2.5 hours. At this time It is exactly 18 kilometers away from the midpoint of the east and west cities. How many kilometers are there between the east and west cities? When Wang Xing and Xiaoying solved the above question, their calculation methods and results were different. The number of kilometers calculated by Xiaoying is small, but Teacher Xu said that the results of both of them are correct. Have you figured out why? You can also calculate the results of the two of them. "Actually, this question is. We can quickly make a method, which is: 45×2.5=112.5 (kilometers), 112.5+18=130.5 (kilometers), 130.5×2=261 (kilometers), but after careful consideration, it is Something doesn't feel right. In fact, we have overlooked a very important condition here, which is the word "li" mentioned in the condition "At this time, it is exactly 18 kilometers away from the midpoint of East and West City". It does not say whether it has not reached the midpoint or has exceeded it. The midpoint. If it is less than 18 kilometers from the midpoint, the column formula is the previous one. If it is 18 kilometers beyond the midpoint, the column formula should be 45×2.5=112.5 (kilometers), 112.5-18 =94.5 (kilometer), 94.5×2=189 (kilometer). So the correct answer should be: 45×2.5=112.5 (kilometers), 112.5+18=130.5 (kilometers), 130.5×2=261 (kilometers) and 45×2.5=112.5 (kilometers), 112.5-18= 94.5 (kilometer), 94.5×2=189 (kilometer). Two answers, that is to say, Wang Xing's answer plus Xiaoying's answer is comprehensive.
In daily study, there are often multiple answers to many mathematics questions, which are easily overlooked in exercises or exams. This requires us to carefully review the questions, awaken life experience, carefully consider them, and fully and correctly understand them. The meaning of the question. Otherwise, it is easy to ignore other answers and make the mistake of generalizing.
The benefits of mathematics are numerous, and scientists from ancient to modern times have also pointed them out. The 19th century mathematician J.J. Sylvester pointed out: "Continuous exploration and pursuit in the field of mathematics can sublimate human thinking activities to a pure and harmonious realm." Mr. Wang Hao, a contemporary mathematical logician, also said, Mathematics has a pure beauty. J. Arbuthnot said: "Mathematical knowledge adds vitality to thinking and frees it from the shackles of prejudice, credulity and superstition." W.E. Serauer said: "Just as literature induces people's emotions, mathematics inspires people's imagination. and reasoning. ”
In short, mathematics can make your thinking pure and harmonious, and will add vitality to your thinking. It gives you the wings of imagination and opens channels for your reasoning. Mathematics is used by us in real life. It teaches us to identify something and teaches us how to obtain benefits. Sometimes mathematics can help us recognize deception or even create it.
Many students may have tried computer fortune telling, and may have even believed it to be true. "Computer fortune telling" seems quite mysterious. As long as you state the year, month, day and gender of your birth, and press a button, sentences about your personality and destiny will appear on the screen. It is said that this is your "fate".
In fact, this is just a computer game at best. We can easily illustrate its absurdity using the mathematical drawer principle.
The drawer principle, also known as the pigeonhole principle or Dirichlet's principle, is a special method of proving existence in mathematics. To give the simplest example, if you put 3 apples into two drawers in any way, then there must be two or more apples in one drawer. Using the same reasoning, you can get:
Principle 1 If more than n objects are placed in n drawers, then at least one drawer contains 2 or more objects.
Principle 2 If more than mn objects are placed in n drawers, then at least one drawer contains m+1 or more than m+l objects.
If calculated based on 70 years, the number of different combinations of year, month, day and gender of birth should be 70×365×2=51100, which we regard as the "drawer" number. Our country's current population is 1.1 billion, which we regard as an "object" number. Since 1.1× =21526×511021400, according to principle 2, there are more than 21526 people. Although their origins, experiences, talents, and opportunities are different, they have exactly the same "fate". This is really ridiculous. !
In ancient my country, some people have long known how to use the drawer principle to expose the fallacies of birth dates. For example, Chen Qiyuan of the Qing Dynasty wrote in "Notes of Yongxianzhai": "I don't believe in the theory of star destiny. I think that one person is born in one hour (note: refers to one hour, two hours in total), and twelve people are born in one day. In terms of age, there are 4,320 people. Calculated in one year (note: refers to sixty years), there are only 259,200 people. Now it is only calculated in one county. Their household registration The number is no less than hundreds of thousands (for example, 800,000 people in the city of Hangzhou in the 10th year of Xianfeng). If you look at the size of the world, from the princes to the common people, there are hundreds of millions of people. There must be many of them who were born at the same time. When princes and great men are born, there must be common people born at the same time. How can there be any difference between the rich and the poor? "Here, a year is calculated as 360 days, and one day is divided into twelve hours. The number of drawers is 60×360×12=259200.
The so-called "computer fortune-telling" is nothing more than storing the artificially compiled fortune-telling sentences in their respective cabinets one by one like a traditional Chinese medicine cabinet. Different combinations are mechanically put into various "cabinets" of the computer according to different codes to take out the so-called sentences of fate. This kind of activity of casting a halo of modern science on the superstitious souls of ancient times is a blasphemy against science.
Deception in business is also inseparable from mathematics. Afanti gave us the best explanation.
The Eid al-Adha festival is coming soon, and the north and south of the Tianshan Mountains are full of festive atmosphere. The market town was bustling with traffic and extremely lively. Shops, roadsides, and street stalls are all filled with goods, with everything you need. The fruit merchants moved out the stored apples, grapes, pears, petroleum, and cantaloupe, hoping to sell them at a good price.
At noon that day, Afanti finished his work for a long time and came to the market on his donkey. Afanti is famous for his intelligence, ability, integrity and justice. Who doesn't know him? Along the way, he kept saying hello to acquaintances and friends. Suddenly, he heard someone shouting his name. Afanti looked back and saw that it was Ai Shan, the owner of the fruit shop. This person is treacherous and greedy. Not only does he often use fake and shoddy goods to defraud customers, but he also specializes in exploiting people with loan sharks. He is a villain that everyone hates. Affan had long wanted to teach this guy a lesson, but he just didn't get the chance. At this time, Ai Shan was sitting in front of two large baskets of grapes with a scale beam in his hand, dazed. One basket contains purple grapes, priced at 2 yuan per catty; one basket contains green grapes, priced at 1 yuan per catty. It’s just that more people ask and fewer people buy.
“Brother Afanti, it’s not easy to do business nowadays.
You see, I've been here all morning and haven't sold a few kilograms of grapes. Now I still have 60 kilograms of purple grapes and green grapes left. I don't know when they will be sold! "Ai Shan actually wanted to beg Afanti to help him come up with an idea to sell grapes, but he was embarrassed to say it.
Afanti heard the implication and thought: This guy just came to his door to make a Let's make him lose some money and let everyone vent his anger. He came to the fruit stall and said to Ai Shan: "Ah, brother Ai Shan, you are so stupid! Purple grapes are sweet but expensive, while green grapes are cheap but sour. Why not mix the two kinds of grapes together and sell them at 3 yuan per catty, which is 1 yuan per catty. Wouldn't it be easier to sell and save trouble?
Ai Shan immediately beamed when he heard this, and quickly gave a thumbs up and praised: "Brother Afanti is really smart, and his reputation is well-deserved!" "So Ai Shan sold the grapes according to Afanti's method, and as expected, more and more people bought the grapes. After a while, all the pounds of grapes were sold out.
However, when Ai Shan counted the money sold, I couldn't help but frown: If sold at the original price, the purple grapes should be sold for 2 yuan × 60 = yuan, the green grapes should be sold for 1 yuan × (60÷2) = 30 yuan, and a *** should be sold for 1 yuan + 30 yuan Yuan = 150 Yuan, but the money sold now is only Yuan. Why is there 30 Yuan missing? He walked around in front of the grape stall with his eyes wide open, looking for the missing 30 Yuan in every corner. Finally, he realized that Afanti was playing a trick on him. When he wanted to catch up with Afanti and ask for clarification, Afanti had already disappeared without a trace on his donkey.