When numbers are invisible, they are less intuitive, while when shapes are few, they are difficult to be nuanced. Numbers and shapes are interdependent, so how can they be divided into flying on both sides?
1. Science is the knowledge of seeking truth from facts, and nothing can be false. -Hua Luogeng
2. The ability to think independently is very necessary for engaging in scientific research or any other work. In history, any major invention in science is due to the inventor's giving full play to this original spirit. -Hua Luogeng
3. All the scientific workers who have made great achievements are experts in using time without exception, and they are also people who are determined to put a lot of labor into a lot of time-Hua Luogeng
4. Everyone must form the habit of self-study, even the students who are in school today, because they will leave school sooner or later! Self-study is the ability to study and think independently. It is up to the traveler himself to walk. -Hua Luogeng
5. Genius is unreliable, cleverness is unreliable, and it is unimaginable to pick up great scientific inventions conveniently. -Hua Luogeng
6. We'd better regard our own life as the continuation of our predecessors' lives, which is a part of the present life and the beginning of future generations' lives. If this continues, science will be more brilliant and society will be better every day. -Hua Luogeng
7. Cleverness lies in learning, and genius lies in accumulation. ..... The so-called genius, in fact, depends on learning. -Hua Luogeng
8. There is no smooth road to science, and there are countless reefs and shoals in the long river of truth. Only herb gatherers who are not afraid of climbing, only those who are not afraid of the waves, can climb the peak to collect fairy grass and go deep into the water to find the pearl. -Hua Luogeng
9. In the long March of seeking truth, only by studying, constantly studying, diligently studying, and creatively studying can we climb mountains and mountains. -Hua Luogeng
1. I think that people have two shoulders and should play a role at the same time. I want to carry the burden of door-to-door delivery with one shoulder and send scientific knowledge and tools to the workers' master; The other shoulder can be used as a ladder for young people to climb a higher level of science. -Hua Luogeng
11. Time is accumulated by minutes, and those who are good at using sporadic time will make greater achievements-Hua Luogeng
12. Accumulate meritorious deeds over time, and cherish every inch. -Hua Luogeng
13, self-study, not afraid of a low starting point, not afraid of the end. -Hua Luogeng
14. Grasp what interests you the most, learn from the shallow to the deep step by step ...-Hua Luogeng
15. Learning and research are like climbing a ladder. If you want to climb up step by step, you must be able to wrestle in an attempt to reach the sky with four or five steps. -Hua Luogeng 2. Famous sayings and epigrams about mathematics
Mathematics is a variety of proof skills. Wittgenstein, British philosopher
The first is mathematics, the second is mathematics, and the third is mathematics. German experimental physicist Roentgen
Mathematicians are fascinated by nature. Without fascination, there is no mathematics. Nouvelles
The main goal of mathematics is the public interest and the explanation of natural phenomena. The French mathematician and physicist Fourier < P > what delights me most in mathematics is what can be proved. Russell, British philosopher and historian
In mathematics, the main tools for us to find truth are induction and simulation. Famous sayings about mathematics French mathematician and astronomer Laplace
New mathematical methods and concepts are often more important than solving mathematical problems themselves. China mathematician Hua Luogeng
No subject can clarify the harmony of nature more clearly than mathematics. Carus,Paul
The strongest triangular shape in mathematics is precisely the most fragile relationship emotionally. A contemporary writer, whose real name is Wang Xiaodi and whose pen name is Jiu Yehui Jiu Yehui,
No matter how abstract any branch of mathematics is, it will be applied to the real world one day. Russian mathematician Lobachevsky
If others thought about mathematical truth as deeply and continuously as they did, they would make the same discovery. American theologian Joan Edwards
Mathematical methods permeate and dominate all theoretical branches of natural science. It has increasingly become the main symbol to measure scientific achievements. Von Newman, Hungarian mathematical genius in Princeton, USA
The universe is big, the particles are tiny, the speed of rockets, the ingenuity of chemical engineering, the change of the earth, the mystery of biology, and the complexity of daily use, and mathematics is everywhere. Hua Luogeng, a mathematician in China. 3. Hua Luogeng, a famous mathematician in China, once said: "The combination of numbers and shapes is good in every way, and there are many cracks
. 1. Hua Luogeng, a famous mathematician in China, once said:" The combination of numbers and shapes is good, and everything will be over if it is separated by cracks. "
As shown below, a square cardboard with a side length of 1 is pasted with an area of
1 in turn.
18,
116, …,
121, please write the expression of the area of the last remaining unpainted part:
121121
. Addition and subtraction of rational numbers. Analysis: According to the meaning of the question, the area of the rectangular piece of paper pasted each time is equal to the area left after pasting, so the area left at last is the area of the rectangular piece of paper pasted last. Solution: ∵ First time left: 1-12=12,
Second time left: 12-14=14,
Third time left: 14.
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. +1/2 n = 1-1/2 n
3.1/2 to the 1th power, I hope you like it! 4. Talking about the combination of numbers and shapes
Numbers and shapes are the two oldest and most basic research objects in mathematics, and they can be transformed into each other under certain conditions. The object of mathematics research in middle school can be divided into two parts: number and shape. There is a connection between number and shape, which is called the combination of number and shape, or the combination of number and shape. As a mathematical thinking method, the application of the combination of numbers and shapes can be roughly divided into two situations: either clarifying some properties of shapes with the help of the accuracy of numbers, or clarifying some relationship between numbers with the help of geometric intuition of shapes, that is, the combination of numbers and shapes includes two aspects: the first situation is "solving shapes with numbers" and the second situation is "helping numbers with shapes". "Solving shapes by numbers" means that some shapes are too simple to see any laws by direct observation, so it is necessary to assign values to the shapes, such as side length and angle. Remarks: This answer is taken from. If you don't understand anything, you can go and look at learning. 5. There are many ancient poems that use the combination of reality and fiction.
Reality means what you see in front of you, while emptiness means the product of imagination and association. Transposition of subject and object (imagining each other), writing dreams, etc. are all manifestations of emptiness. Here's a little example: a very familiar poem: Being a stranger alone in a foreign land, thinking twice about your relatives every festive season. Knowing where your brother climbs from afar. Compared with "being in a foreign land" and "being a stranger" in reality, we can show our homesickness from two aspects. Another example is: every winter solstice in Handan post, I hug my knees and sit in front of the lamp. If I want to sit at home late at night, I should also say "homesick". In three or four sentences, I write "homesick" on the front. What is touching is that he imagined the scene when I was homesick. What did you say? This leaves readers with a vast world of imagination. Everyone who has enjoyed family happiness and had similar experiences can think a lot according to their own life experience. This technique (subject-object translocation) is called "thinking on behalf of others", which makes the emotional expression more subtle, tortuous and moving. Another example is Wang Changling's farewell to Wei Er: drunk orange pomelo in Biejiang Building, and the river wind draws rain into the boat to cool down. What are the benefits of the last two sentences? The author imagines that his friend is tossing and turning alone in Mizunokami, Hunan Province, worrying about listening to apes, which makes his reluctance and concern for his friend's departure more profound and touching. 6. Who can provide some classic examples of the combination of numbers and shapes
For example, 1. The mean value theorem and its geometric meaning, the radius is not less than half a chord (this figure can be found on the Internet)
2. For example, the range of y=|x|+|x-1| can be studied with the help of geometric figures, and its geometric meaning is that the distance from a point on the number axis to +the number axis. =1.
3. Linear programming problem, which is also a classic combination of numbers and shapes.
4. Pythagorean theorem mentioned upstairs is also good, and the square is the classic figure of the square.
5. For most function problems, by studying their images, we can get the properties of the function.
Let's talk so much first, then add it.