1. What is Hua Luogeng’s famous saying about numbers and shapes
When numbers are invisible, it is less intuitive, and when shapes are few, it is difficult to understand the details. Numbers and shapes are inherently dependent on each other. Can be divided into two sides to fly.
1. Science is a science that seeks truth from facts and cannot be false in the slightest. ——Hua Luogeng
2. The ability to think independently is very necessary for engaging in scientific research or any other work. In history, any major scientific invention is due to the inventor giving full play to this original spirit. ——Hua Luogeng
3. All the more accomplished scientific workers are, without exception, experts at utilizing time, and they are also people who are determined to invest a lot of time in a lot of work——Hua Luogeng
p>4. Everyone must develop the habit of self-study. Even students in school today must develop the habit of self-study, because sooner or later they will leave school! Self-study is the ability to learn independently and think independently. Traveling still depends on the traveler himself. ——Hua Luogeng
5. Genius is not trustworthy, intelligence is unreliable, and it is unimaginable to pick up great scientific inventions by chance. ——Hua Luogeng
6. It is best for us to regard our own life as the continuation of the lives of our predecessors, a part of the same life today, and the beginning of the lives of future generations. If this continues, science will become more brilliant day by day, and society will become more beautiful day by day. ——Hua Luogeng
7. Intelligence lies in learning, and genius lies in accumulation. ...The so-called genius actually relies on learning. ——Hua Luogeng
8. There is no smooth road in science, and there are countless rocks and shoals in the long river of truth. Only herb collectors who are not afraid of climbing, and tide-drifters who are not afraid of huge waves, can climb to the top to collect fairy grass and go deep into the water to find Li pearls. ——Hua Luogeng
9. In the long march of seeking truth, only by learning, constantly learning, diligent learning, and creative learning can we cross mountains and ridges. ——Hua Luogeng
10. I think that people have two shoulders, which should play a role at the same time. I want to use one shoulder to carry the burden of door-to-door delivery, and deliver scientific knowledge and scientific tools to the hands of master workers. The other shoulder can be used as a ladder for young people to climb to a higher level of science. ——Hua Luogeng
11. Time is accumulated by minutes and seconds. Only those who are good at using sporadic time will achieve greater results. ——Hua Luogeng
12. Day Over the months, I have accumulated meritorious deeds, and I have made every effort to save every inch of my life. ——Hua Luogeng
13. Self-study, don’t be afraid of a low starting point, but be afraid of not reaching the end. ——Hua Luogeng
14. Grasp what you are most interested in, learn from the shallower to the deeper, step by step...——Hua Luogeng
15. Learning and research are like climbing a ladder, one step at a time If you climb up one step at a time, trying to take four or five steps at a time and reach the sky from flat ground, you must be able to fall. ——Hua Luogeng 2. Four-character aphorisms about mathematics
Mathematics is a variety of proof techniques. British philosopher Wittgenstein
The first is mathematics, the second is mathematics, and the third is mathematics. Mathematics famous sayings by German experimental physicist R?ntgen
Mathematicians are essentially obsessed. Without obsession, there would be no mathematics. Nuvales
The main goals of mathematics are the public interest and the explanation of natural phenomena. French mathematician and physicist Fourier
What delights me most in mathematics are those things that can be proven. British philosopher and historian Russell
In mathematics, our main tools for discovering truth are induction and simulation. Famous quotes about mathematics by French mathematician and astronomer Laplace
New mathematical methods and concepts are often more important than solving mathematical problems themselves. Chinese mathematician Hua Luogeng
No subject can illustrate the harmony of nature more clearly than mathematics. Carus,Paul
The strongest triangle in mathematics is also the most fragile relationship emotionally. Contemporary writer, whose real name is Wang Xiaodi and whose pen name is Jiuyehui Jiuyehui "The Year in a Hurry"
No matter how abstract any branch of mathematics is, it will one day be applied to the real world. Mathematics Quotes Russian Mathematician Lobachevsky
If others thought about mathematical truths as deeply and persistently, they would make the same discoveries. American theologian Joan Edwards
Mathematical methods penetrate and dominate all theoretical branches of natural science. It has increasingly become the primary measure of scientific achievement. Von Neumann, the Hungarian mathematical genius at Princeton in the United States Von Neumann
The universe is huge, the particles are tiny, the speed of rockets, the ingenuity of chemical engineering, the changes in the earth, the mysteries of biology, and the complexity of daily life. Mathematics is used everywhere.
Chinese mathematician Hua Luogeng 3. The famous Chinese mathematician Hua Luogeng once said this: "The combination of numbers and shapes is good in every way, but there are many separations
There are many: 1. The famous Chinese mathematician Hua Luogeng once said this: : "The combination of numbers and shapes is good in every way, and everything will stop if there is separation."
As shown below, on a square cardboard with a side length of 1, the area is
12 ,
14,
18,
116,...,
1210 small rectangular pieces of paper, please write down the last remaining The expression of the area of ??the unpaved part:
12101210
.Test points: regular type: changing types of graphics; mixed operations of addition and subtraction of rational numbers. Analysis: According to the meaning of the question, each time The area of ??the pasted rectangular piece of paper is equal to the area remaining after pasting, so the last remaining area is the area of ??the last pasted rectangular piece of paper. Solution: ∵ The first remaining area: 1-12=12,
< p> The remaining time for the second time: 12-14=14,The remaining time for the third time: 14-18=18,
∴ The remaining time for the nth time: 12n, < /p>
2.1. From the graph we can get: 1/2 + 1/4 + 1/8 + 1/16 + 1/16 = 1
So 1/2 + 1/4 + 1/8 + 1/16 + 1/16 = 1 - 1/16 = 15/16
2. 1/2 + 1/4 + 1/8 + 1/16 + 1/. 2^n = 1 - 1/2^n
3.1/2 to the 10th power. I hope you like it! 4. Let’s talk about the “combination of numbers and shapes”
Numbers and shapes are The two oldest and most basic research objects in mathematics can be transformed into each other under certain conditions. The objects of middle school mathematics research can be divided into two parts: numbers and shapes. Numbers and shapes are connected, and this connection is called. It is the combination of numbers and shapes, or the combination of shapes and numbers. As a mathematical thinking method, the application of the combination of numbers and shapes can be roughly divided into two situations: either using the accuracy of numbers to clarify certain properties of shapes, or using the geometry of shapes. Intuition is used to clarify a certain relationship between numbers, that is, the combination of numbers and shapes includes two aspects: the first case is "using numbers to solve shapes", and the second case is "using shapes to help numbers" and "using numbers to solve shapes." "That is, some graphics are too simple, and no rules can be seen through direct observation. At this time, you need to assign values ????to the graphics, such as side lengths, angles, etc. Note: This answer is excerpted from "If you don't understand anything, you can go and take a look." Study and learn. 5. Ancient poems that use the combination of virtual and real.
There are many of them. Writing dreams and so on are all manifestations of "virtuality". Here is a little example: a very familiar poem: Alone as a stranger in a foreign land, I miss my family even more during the holidays. I know from afar that my brothers have climbed to the heights, and there is one less person planting dogwood trees. . Here the author imagines that his brothers at home miss him, contrasting it with the reality of "being in a foreign land" and "being a stranger", showing his homesickness from two aspects. Another example: During the winter solstice in Handan Station, hugging one's knees in front of the lamp The shadow accompanies me. I think of sitting at home late at night, and talking about people who have traveled far away. In three or four sentences, write "homesickness" on the front. The touching part is: the scene he imagined when he was homesick. , but it is how much my family misses me. During this winter solstice festival, because I traveled far away from home, my family must have been very unhappy. When I hugged my knees in front of the lamp and missed my family until late at night, my family members were probably the same. If you haven't slept yet, sit in front of the lamp and "talk about people who travel far away"! What was "said"? This leaves readers with a vast world for imagination. Everyone who has enjoyed family happiness and has had similar experiences can think a lot based on their own life experience. This technique (change of subject and object) , is called "thinking on behalf of others", which makes the expression of emotions more subtle, tortuous and moving. Another example is Wang Changling's Farewell to Wei Er: Farewell to the river tower drunk with the fragrance of oranges and pomelo, the river breeze brings the rain into the cool boat. Recalling the king in the Xiaoxiang moon, I feel sad Listen to the ape's dream. [This is a question in the college entrance examination, asking what are the benefits of the last two sentences. The author imagines his friend tossing and turning alone on the Xiang River, worried about listening to the ape's cry, which makes him feel sad about his friend's departure. The reluctance and concern are more profound and touching...
6. Who can provide a few more classic examples of the combination of numbers and shapes
Such as 1. The mean value theorem and its geometric meaning, the radius is not less than a half chord (this picture can be found online)
2. For example, the value range of y=|x|+|x-1| can be studied with the help of geometric figures. Its geometric meaning is the distance from a certain point on the number axis from x to 0 + a certain point on the number axis from x to 1 The sum of the distances is always greater than or equal to 1. Therefore, the range is y>=1.
3. Linear programming problem, which is also a very classic problem of combining numbers and shapes.
4 .The Pythagorean theorem mentioned above is also good, and the classic figure of a square is inside a square.
5. For most function problems, by studying their images, you can get the properties of the function
That’s all for now, I’ll add more later