Application of small mathematical knowledge in life

1. Urgent

Mathematics is everywhere in people’s daily lives, and the correct use of mathematical knowledge can improve life.

Although mathematics is a great contributor to us humans, if we humans do not know how to use it, it will still be "unhelpful to the world". Therefore, we must use smart brains and use mathematics to make our lives more beneficial. More convenient. Magical mathematics is actually around us. Let us start from every little thing around us. You will definitely find that this magical mathematics affects us and helps us all the time. Mathematical knowledge and mathematical thinking are in It is widely used in industrial and agricultural production and people's daily life. For example, people need to keep accounts after shopping for year-end statistical inquiries; go to the bank to handle savings; check the water and electricity bills of each household, etc. These make use of arithmetic and statistical knowledge.

In addition, the "sliding automatic retractable door" at the entrance of the community and government compound; the smooth connection of the straight track and the curve of the sports field runway; the calculation of the height of the building whose bottom cannot be approached; the determination of the starting point of the two-way operation of the tunnel ; The design of folding fans and the golden section are the application of knowledge about the properties of straight lines in plane geometry and the solution of Rt triangles. Mathematics is also widely used in sociology, especially in statistics.

It could even be used to stave off epidemics or lessen their impact. When we are unable to immunize the entire population, mathematics can help us determine who must be vaccinated to reduce risk.

In the arts, mathematics is still everywhere. Music, painting, sculpture... all categories of art are helped by mathematics in one way or another.

Japanese sculptor Shio Keizo likes to use geometry and topology to create his works, using mathematical calculations to divide the granite used for sculptures. Chao Keizan said: "Mathematics is the language of the universe."

"Mathematics is the invisible culture of our time." It affects our lifestyle and work style in many fields to varying degrees. Of course, ordinary people and scientists understand mathematics from different angles and levels. Ordinary people generally only understand the connection between mathematics and one aspect of life, but do not realize its connection with all aspects of life.

People always think that mathematics is relatively abstract and has no direct help for practical work. There is no need to study and research mathematics in depth. In fact, this is not the case. Mathematics, like other sciences, is closely related to our lives.

The famous mathematician Mr. Hua Luogeng once said: "The universe is huge, the particles are tiny, the speed of rockets, the ingenuity of chemical engineering, the changes of the earth, and the complexity of daily life. Mathematics is used everywhere." It is a brilliant description of the relationship between mathematics and life by a wise scientist.

Contemporary mathematics is much more than arithmetic and geometry. It is a rich and colorful subject, a creative combination of calculation and deduction, rooted in data and presented in abstract forms, by revealing hidden phenomena. model to help people understand and understand the world around them. It deals with data, measurement and observation data in science, inference, deduction and proof, mathematical models of natural phenomena, human behavior and social systems, numbers, chances, shapes, algorithms and changes.

Here is an example to let everyone experience the application of mathematics in real life. Example: During World War II, the military, production, and transportation faced a series of problems: how should aircraft detect the activities of submarines, how should limited forces be deployed, how should production be organized more rationally, etc. wait.

In the middle of World War II, Nazi Germany under Hitler's rule was very rampant and submarine activities were frequent. Based on the suggestions of some mathematicians, a plan for systematic patrolling by aircraft was adopted.

According to this plan, a certain range of waters can be controlled with as few aircraft as possible. After the implementation of this plan, the possibility of German submarines being detected increased greatly.

In February 1943, the U.S. military learned that a Japanese fleet was assembled on New Britain Island in the South Pacific, intending to cross the Bismarck Sea and head for New Guinea. The U.S. Southwest Pacific Air Force was ordered to intercept and sink the Japanese fleet.

There are two routes from New Britain to New Guinea, the north and the south, both taking three days. The weather forecast obtained by the US military showed that it would be rainy on the northern route in the next three days, while the weather on the southern route was better.

In this case, will the Japanese fleet take the north route or the south route? This is something the US military must analyze and judge. Because in order to complete the bombing mission, a small number of aircraft must first be dispatched for reconnaissance and search, requiring the Japanese fleet to be discovered as soon as possible, and then a large number of aircraft must be dispatched for bombing.

The Air Force Commander considered the strategy of dispatching a small number of aircraft to conduct searches in two routes. There are several strategies: First, the search focused on the north route, and the Japanese ships also took the north route. Although the weather was very bad and the visibility was very low at this time, because the search force was concentrated, the Japanese ship was expected to be discovered within one day, so there were two days of bombing time.

Second, the focus was on the northern route, but the Japanese ship took the southern route. Although the weather was better on the South Road at this time, because the search efforts were concentrated on the North Road, there were only a few aircraft on the South Road, so it would take a day to discover the Japanese ships.

So the bombing time was only two days.

Third, the search focused on the southern route, while the Japanese ship took the northern route.

At this time, there were only a few aircraft on the North Road, and the weather was very bad. It would take two days to discover the Japanese warships, leaving only one day for bombing. Fourth, the search focused on the southern route, and the Japanese ships also took the southern route.

At this time, there are more planes searching and the weather is good. You can expect to find the Japanese warships soon. The bombing time is basically three days. From the American point of view, the fourth situation is of course the most advantageous. . However, fighting a war cannot be based on "wishful thinking".

From the Japanese point of view, of course it is much more advantageous to take the northern route. So the chances of the second and fourth scenarios possibly happening are slim.

Therefore, the Air Force Commander resolutely decided to focus the search on the North Road. As expected, the Japanese chose this route, and the naval battle basically took place at the location expected by the United States. As a result, the Japanese suffered a disastrous defeat.

Some people say: Mathematics is the queen of science. I think the status of mathematics is very similar to that of philosophy.

Throughout the ages, philosophers of all ages have attached great importance to mathematics. The great philosopher Plato once wrote a sentence on the door of his home: "Those who do not understand mathematics should not enter." This shows how important mathematics is in the minds of philosophers.

Mathematics, like philosophy, comes from life.

2. What are the applications of mathematics in life?

What are the applications of mathematics in life 1. Enter life and use mathematical eyes to observe and understand the things around you: The world So big, there are important contributions to mathematics everywhere.

Cultivating students' mathematical awareness and the ability to use mathematical knowledge to solve practical problems is not only one of the goals of mathematics teaching, but also a need to improve students' mathematical quality. In teaching, students should be exposed to reality, understand life, and understand that life is full of mathematics and mathematics is around you.

For example, in the introduction of "The Meaning and Basic Properties of Proportion", I designed this paragraph: Do you know the many interesting proportions in our human body? Roll your fist over in a circle. The ratio of its length to the length of the sole of your foot is about 1:1. The ratio of the length of your sole to your height is about 1:7... Knowing these interesting ratios has many uses. When you go to the store to buy socks, just put the socks on If you circle your fist, you will know whether this pair of socks is suitable for you; if you are a detective, you can estimate the height of the criminal as long as you find the footprints of the criminal... These are all composed of body ratios. It is an interesting proportion. Today we will study the "meaning and basic properties of proportion"; In addition, teachers can also design some highly practical assignments such as "investigation", "experience" and "operation" based on the age characteristics of students, so that students can Consolidate the knowledge learned during the activities and improve abilities in various aspects: For example, before teaching the application of the relationship between "unit price, quantity, and total price", students can be assigned to be small investigators and complete the following table: Product Name: Cucumber, Cabbage, Radish, Pork Unit price (yuan) Quantity (kilogram) Total price (yuan) In this way, students will have a perceptual understanding of the knowledge they have learned, slow down their learning curve, and give them a deep understanding of the relationship between unit price, quantity, and total price. It helps a lot. For another example, after learning the stability of triangles, students can observe where the stability of triangles is used in life; after learning the knowledge of circles, students can explain from a mathematical perspective why the shape of the wheel is round and the rows of triangles. no? Students can also be asked to find ways to find the center of the circle of pot lids and washbasins;... This greatly enriches the knowledge students learn and allows students to truly realize that mathematics is everywhere around them. Mathematics is in the middle of our lives and is not a mystery. , and at the same time, they also unknowingly understand the true meaning of mathematics, which in turn arouses the emotion of loving, learning, and using mathematics since childhood, promotes the development of students' thinking towards scientific thinking, and cultivates students to consciously apply the knowledge they have learned. Awareness of practical life.

2. Understand life and build a bridge between mathematics and life: "Everyone learns useful mathematics, and useful mathematics should be learned by everyone" has become the slogan of the mathematics teaching reform experiment. In teaching, I connect with the reality of life, shorten the distance between students and mathematical knowledge, and explain mathematical problems with concrete, vivid and vivid life examples.

1. Use life experience to solve mathematical problems. When taking the lesson "Using Letters to Represent Numbers", I used the CAI courseware to demonstrate the scene of Li Lei picking up gold, and then broadcast a "Lost and Found" "Notice": Lost and Found: Li Lei, a student, found RMB A near the flag-raising platform on campus. Please come to the Young Pioneers Brigade Headquarters to claim the lost property. School Young Pioneers Brigade 2002.3 Students were surprised that the teacher talked about lost and found things in math class? My students and I analyzed and discussed the meaning of A dollar. Teacher: Can A dollar be 1 yuan? Student 1: A yuan can be 1 yuan, which means that 1 yuan was picked up.

Teacher: Can Yuan A be 5 Yuan? Student 2: Yes! It means picking up 5 yuan. Teacher: How much more can A dollar be? Student 3: It can also be 85 yuan, which means that 85 yuan was found.

Teacher: How much more can A dollar be? Student 4: It can also be 0.5 yuan, which means that you picked up 5 cents.

... Teacher: Then can A yuan be 0 yuan? Student 5: Absolutely not. If it is 0 yuan, then this lost and found notice is a big joke! Teacher: Why not just say how many yuan you picked up, but express it in A yuan? ... Since students can easily recognize specific and definite objects, but the numbers represented by letters are uncertain and variable, it is often difficult for students to understand them at the beginning of learning.

The "Lost and Found Notice" in this question is an activity familiar to students, which stimulates students' desire to learn new knowledge, and students can involuntarily participate in the problem-solving process. During discussions and exchanges, brainstorming enabled students to understand new knowledge in a pleasant atmosphere, and have a better understanding and firmer grasp of the knowledge they have learned; on the other hand, it also improved their interpersonal skills and enhanced their awareness of mutual help and cooperation. Receiving good ideological education also exercises students' insight into society.

2. Use mathematical knowledge to solve practical problems. For example, after learning the calculation of the area of ??rectangles and squares and the calculation of combined figures, I try to let students use the knowledge they have learned to solve practical problems in life. For example: The teacher’s house has a house with two bedrooms and one living room, as shown in the picture: Can you help him calculate how big the living area is for these two bedrooms and one living room? To calculate the area, what lengths do we need to measure the area first? After giving certain data, let the students calculate; then I also asked the students to go home and calculate the actual living area of ??their homes.

In such a practical calculation process, it not only increases interest, but also cultivates the ability of actual measurement and calculation, allowing students to learn and use it in life. For example, after learning addition and subtraction within 100, a teaching situation of "buying a car" was created: there was a big price cut on mini-cars. How many cars did Xiao Lin buy for 100 yuan? How many cars did he buy, and which ones were they? Through observation, thinking, discussion, and with my encouragement and guidance, the students used formulas to express them in order: (1) Decompose 100 yuan into the sum of two numbers: (2) Decompose 100 yuan into 3 numbers The sum of the numbers: 550=100 460=100 370=100280=100 6220=1005230=1004420=1003340=100 (3 ) Decompose 100 yuan into the sum of 4 numbers (4) Decompose 100 yuan into the sum of 5 numbers 42220=100 222220=100 332 20=100 Students explore, seek novelty, and find original answers with a discoverer's mentality. This also verifies what Suhomlinsky said: "Deep in the human soul, there is a deep-rooted This is the need for students to be a discoverer, researcher, and explorer. ”

This kind of illustrated application questions enables students.

3. Application of primary school mathematics in life (example)

Original publisher: China Academic Journal Network

Summary of application of mathematics in life: We insist that mathematics comes from life, is rooted in life, and in turn is applied and serves life. It makes students' application of mathematics process interesting and life-oriented, providing a broad space for students to apply mathematical knowledge in life and improve their mathematical ability. Keywords: Mathematics; Picture in Life Classification Number: g623.5 Learning mathematics is to be able to apply it in real life. Mathematics is used by people to solve practical problems. In fact, mathematical problems occur in life. For example, when you go shopping, you naturally need to use addition and subtraction, and when building a house, you always need to draw drawings. There are countless problems like this. This knowledge comes from life, and is finally summarized into mathematical knowledge by people, which solves more practical problems. I once saw such a report: A professor asked a group of foreign students: "How many times will the minute hand and the hour hand overlap between 12 o'clock and 1 o'clock?" Those students took the watch off their wrists and started to move the hands; and this When a professor talks about the same problem to Chinese students, the students will use mathematical formulas to calculate it. The comment said that it can be seen that Chinese students transfer their mathematical knowledge from books to their brains and cannot use it flexibly. They rarely think of learning and mastering mathematical knowledge in real life. Mathematics should be learned in life. Some people say that the knowledge in books now has little connection with reality. This shows that their knowledge transfer ability has not been fully exercised. It is precisely because they cannot understand and apply mathematics well in daily life that many people do not pay attention to mathematics. I hope that students can learn mathematics in life and use mathematics in life. Mathematics is inseparable from life. If you learn it deeply and thoroughly, you will naturally find that mathematics is actually very useful. 1. Understand the reality of life in the application of mathematical knowledge. In the past, our mathematics teaching often paid more attention to solving existing mathematical problems, which are problems that have been dealt with in textbooks. Students only need to follow the learned solutions

4. Application of mathematics in life

Mathematical knowledge and mathematical ideas are widely used in industrial and agricultural production and people's daily life. For example, people need to keep accounts after shopping for year-end statistical inquiries; go to the bank to handle savings; check the water and electricity bills of each household, etc. These make use of arithmetic and statistical knowledge.

In addition, "pull-type automatic retractable doors" at the entrances of communities and government agencies; the smooth connection of the straights and curves of sports ground runways; the calculation of the height of buildings that cannot be approached at the bottom; and the two-way operation of tunnels are gradually being adopted by more and more operators . Once, I went shopping at Wumart Supermarket, and an eye-catching sign attracted me. It said that I could get discounts on teapots and teacups. This seemed to be rare. What’s even more strange is that there are actually two discount methods: (1) sell one and get one free (that is, buy a teapot and get a teacup for free); (2) 10% off (that is, pay 90% of the total purchase price). There are also prerequisites: purchase more than 3 teapots (teapots are 20 yuan/piece, teacups are 5 yuan/piece). From this, I can't help but think: Is there any difference between these two preferential methods? Which one is cheaper? I naturally thought of functional relationship expressions, and determined to apply the functional knowledge I learned and use analytical methods to solve this problem. I wrote on the paper: Suppose a customer buys tea cups x and pays y yuan, (x>3 and x∈N), then use the first method to pay y1=4*2(x-4)*5= 5x+60; Use the second method to pay y2=(20*4+5x)*90%=4.5x+72. Then compare the relative sizes of y1y2. Let d=y1-y2=5x+60-(4.5x+ 72)=0.5x-12. Then we have to discuss: When d>0, 0.5x-12>0, that is, x>24; When d=0, x=24; When d/Article_View?ID=20&page =1 2. Application of quadratic function When enterprises carry out construction, breeding, afforestation, product manufacturing and other large-scale production, the relationship between profit and investment can generally be expressed by a quadratic function. Business operators often rely on this knowledge to predict the prospects for business development and project development. They can predict the future benefits of the company through the quadratic functional relationship between investment and profit, thereby determining whether the economic benefits of the company have been improved, whether the company is in danger of being merged, whether the project has development prospects, and other issues. Commonly used methods include: finding the maximum value of a function, the maximum value on a certain monotonic interval, and the function value corresponding to an independent variable. 3. Applications of trigonometric functions The applications of trigonometric functions are extremely wide. Here we only talk about the simplest and most common type - the application of acute-angle trigonometric functions: the "greening" problem. In mountain forest greening, trees must be planted at equal distances on the hillside, and the distance between two trees on the hillside projected onto the flat ground must be consistent with the distance between the trees on the flat ground. (As shown on the left) Therefore, before planting trees, forestry personnel must calculate the distance between two trees on the hillside. This requires the knowledge of acute angle trigonometric functions. As shown in the figure on the right, let C=90, B=α, the distance to the flat ground is d, and the distance to the hillside is r, then secα=secB =AB/CB=r/d. The problem of ∴r=secα*d is now easily solved. Part 2 Application of Inequalities Commonly used inequalities in daily life include: linear inequalities of one variable, quadratic inequalities of one variable and mean inequalities. The applications of the first two types of inequalities are exactly the same as those of their corresponding functions and equations, and the average value inequality plays a role that cannot be ignored in production and life. Next, I will mainly talk about the applications of mean inequality and mean theorem. In production and construction, many practical problems related to optimal design can usually be solved by applying mean inequality. Although the author has not personally experienced the application of mean inequality knowledge in daily life, it is not difficult to find from news media such as TV and newspapers and the word problems we have done that mean inequality and extreme value theorem can usually have the following aspects: Extremely important applications: (Focus on the "Packaging Can Design" problem after the table)

5. What are some examples of the application of mathematics in life

1. Use your feet when riding a bicycle The number of meters traveled by pedaling a bicycle in one cycle. We can measure the radius of the wheel and then use the formula for the circumference of a circle to find it.

2. Calculation of mathematical addition, subtraction, multiplication and division. Such as the purchase and sale of goods, calculation of dates, calculation of time.

3. Calculation of area. The area of ??your own house, the area of ??the park, the activity area of ??the playground, etc.

4. Statistical calculations. When you are late, you need to register with the duty officer and write down your grade and class name. This way the school will know which class has the most late arrivals this week and which class has the least late arrivals.

5. Calculation of wages. Financial income and expenses, daily consumption management, etc.

Extended information:

Introduction to several branches of mathematics

1: History of mathematics

2: Mathematical logic and foundation of mathematics

a: Deductive logic (also known as symbolic logic) b: Proof theory (also known as metamathematics) c: Recursion theory d: Model theory e: Axioms *** Theory f: Mathematical foundations g: Mathematical logic and other disciplines based on mathematics

3: Number theory

a: Elementary number theory b: Analytical number theory c: Algebraic number theory d: Transcendental number theory e: Diophantine approximation f: Geometry of numbers g : Probabilistic number theory h: Computational number theory i: Number theory other disciplines

4: Algebra

a: Linear algebra b: Group theory c: Field theory d: Lie groups e: Lie algebra f: Kac-Moody algebra g: Ring theory (including commutative rings and commutative algebras, associative rings and associative algebras, non-associative rings and non-associative algebras, etc.) h: Module theory i: Lattice theory j: Universal algebraic theory k: Category theory l: Homology algebra m: Algebraic K theory n: Differential algebra o: Algebraic coding theory p: Other subjects of algebra

5: Algebraic geometry

6: Geometry

a: Basics of geometry b: Euclidean geometry c: Non-Euclidean geometry (including Riemannian geometry, etc.) d: Spherical geometry e: Vector and tensor analysis f: Affine geometry g: Projection Geometry h: Differential geometry i: Fractal geometry j: Computational geometry k: Geometry other subjects