-Xunzi 2. Scholars must doubt first. -Cheng Yi 3. Study, and then you will not know enough.
-Book of Rites IV. It is never too old to learn. -Proverbs 5. It's never too late to learn.
Gorky 6. Repetition is the mother of learning. Dietzgen 7. Never tire of learning, never tire of teaching.
-Confucius 8. Life is limited and knowledge is limited. -Zhuangzi 9. Optical knowledge is still a fool.
-Goethe 10. Learning is expensive, but you get friends. -Tang Zhen 1 1. Learn from doubts and let friends analyze doubts.
-Li Xing 12. Ask if you don't know, and you won't learn. —— Dong Zhongshu 13. It is difficult to learn poorly, so help teachers make friends.
—— Tang Bin 14. Isn't it pleasant to study from time to time? -Confucius 15. If you ask, you will have a teacher, and if you teach, you will have friends. -ludian 16. The mind is free from distractions, but it is the road to ecstasy.
-Yuan Mu 17. Memorizing is not equal to mastering knowledge. -Montaigne 18. Love makes diligence, and diligence makes genius.
—— Guo Moruo 19. Wisdom comes from diligence, and genius lies in accumulation. -Hua 20. Learning is a sweet fruit that grows on bitter roots.
-Ricardo 2 1. Learning without thinking is useless, thinking without learning is dangerous. -Confucius 22. Diligence and knowledge are the best lovers.
-anonymous 23. There is a road to diligence in Shushan, and there is no limit to learning the sea. Anonymous for 24 hours. Learning is like sailing against the current. If you don't advance, you will retreat.
-"Augmented Sage" 25. Sharpen the knife and learn to be smart. -Vietnamese proverb 26. A wise man has long ears and short tongue.
-flaig 27. If you listen widely, you will learn, and if you win friends, you will learn. -Wei Yuan 28. A wise man has long ears and short tongue.
-flaig 29. People who are suspicious have never learned; Learning requires doubt. -Zhang Zai 30. Black hair doesn't know how to study early, but Bai Shoufang regrets studying late.
-Yan Zhenqing 3 1. Scholars read books and learn every time they see something new. -Zhang Zai 32. A wise man has long ears and short tongue.
-flaig 33. Everything is clear, and human feelings are articles. -Cao Xueqin 34. Learning is labor, which is full of thoughts.
-Ushchinski is 35 years old. Don't advance, don't know the distance. If you don't study, you won't understand. -Proverbs 36. Gain knowledge in learning and courage in fighting.
Anonymous number 37. Reading is learning, refining is sorting, and writing is creating. -Wu Han 38. Cherish time, concentrate and study hard is a good way to learn.
-Cai Shangsi 39. Step up your study, grasp the center, and be better than miscellaneous. Zhou Enlai is 40 years old. The author may not be able to write old, but he must learn old.
-Anonymous 4 1. It is better to study idle than to study idle. Joe Bells is 42 years old. The three conditions of learning are: more observation, more hardship and more research.
-Garfield 43. The first sign of an educated mind is being good at asking questions. Plekhanov is 44 years old. Knowing everything at once means knowing nothing.
-Pavlov 45. The key to learning a lot is not to learn a lot at once. Locke 46. If you don't work hard, you will seek quick results. In the end, you will only praise for a few days, which is always embarrassing.
47 Zheng Banqiao. Any valuable knowledge I learned was acquired by self-study. -Darwin 48. Learning is the reward of hard work, and thousands of books is the window of fireflies.
Today, three winters are enough. Who laughs and is empty? Anonymous 49. The starting point of inventing tens of millions is to ask. Man is better than nature, only in all aspects.
-Tao Xingzhi 50. If you don't understand, you must ask. In order to understand the truth, it is worthwhile to be beaten. -Sun Yat-sen 5 1. Many deceivers despise learning, stupid people envy learning, and smart people use learning.
Bacon 52. The omnipotent person is really omnipotent, and the omniscient expert is really omnipotent. -Zou Taofen 53. Curious people only make five kinds of fools; He who is ashamed to ask questions is a fool all his life.
Anonymous 54 Learning is an extremely precious thing, and it is not shameful to absorb it from any source. Abu Ri Faraz is 55 years old. Learning is not expensive.
..... It's better to know one thing than ten things. -Dai Zhen 56. People are learning things every day, and what they often learn is to find out that what they learned yesterday is wrong.
Don't go to bed when you can't tell yourself what you learned today. 58 Fort Lee Heaton. I didn't get any other benefits from studying hard, but I became more and more aware of my ignorance.
Descartes in 59 years. It is false to regard too much knowledge as decoration; It is the quirk of scholars to judge things completely according to the laws of learning. Bacon is 60 years old. You should study at any time and learn everything; We should concentrate on learning more and everything.
-Gorky 6 1. Less and less eager to learn, like sunrise; Strong and eager to learn, such as the light of Japan and China; Eager to learn is like the light of a candle. -Liu Xiang 62. It is false to regard learning too much as decoration; It is the quirk of scholars to judge things completely according to the laws of learning.
Bacon 63. Diligence is like a seedling in spring, but it will not thrive. Learning is like a grindstone. If you don't see it, you lose.
-Tao Yuanming 64. Learning this thing doesn't depend on whether anyone teaches you. The most important thing is whether you have consciousness and perseverance. 65 fabrice. Successful scientists are often people with a wide range of interests.
Their originality may come from their erudition. 66 beveridge. The teacher's position is' teaching thousands of religions and teaching people to seek truth'; A student's duty is to' learn from others and apply what he has learned'.
-Tao Xingzhi 67. By analogy, we can know the ten by smelling one, absorb the diligence and lack of knowledge of scholars, and then we can achieve mastery through a comprehensive study. -Zhu 68. The kungfu of learning is the kungfu of chewing slowly.
Just like eating, it's good for the human body to chew until it's chewed. 69 Tao Zhu. Knowledge is not a complete, pure and unchangeable thing.
It is always innovating and always moving forward. Pliny Schnikov is 70 years old. What matters is not the quantity of knowledge, but the quality of knowledge. Some people know a lot, but don't know the most useful things.
-Tolstoy 7 1. To climb the peak of science and culture, we must break through the unfavorable conditions and make use of the favorable conditions provided by life to create new conditions. 72 Gao Shiqi. Learning a foreign language is not difficult. Learning a foreign language is like making friends. The more friends you have, the more familiar you become. When you meet every day, your friends will become very close.
73 Gao Shiqi. Reading history makes people wise, poetry witty, mathematics subtle, natural philosophy subtle, ethics grave and logic able to contend. —。
2. Ask for poems about mathematics ~ ~ There are many poems that urgently express mathematical ideas and concepts.
For example, the new high school mathematics textbook edited by Academician Zhang Jingzhong (experimental textbook of new curriculum standard of Hunan Education Press) has a poem in each chapter. For example, the first chapter, "Collection, Mapping and Function", talks about the sunset, flowers and fruits, and the vicissitudes of life.
Causal changes are related, and a good strategy is to break the chaos? The basic theory of set is rigorous, and the mapping function is light yellow. Look at the chart to discuss the ups and downs, and Kehai has a plan to sail.
In the second chapter, "Exponential Function, Logarithmic Function and Power Function", I said: the morning fog blocked the traffic, and the mushroom cloud covered the sky; The age of fossils is calculated skillfully, and the sentences of Wen Haisuo are as fast as the wind. Explain infinite things, and the three families of functions make great achievements. After studying these two chapters, read them carefully and don't feel anything.
Secondly, the mathematics of poetry is abstract and boring. How to make mathematics easy to understand and loved by people? In this respect, Chinese ancient mathematicians made many attempts, among which ballads and formulas were one, which made people feel the charm of poetry while answering mathematical questions. Starting from Yang Hui in the Southern Song Dynasty, Zhu Shijie, Ding Ju and Jia Heng in the Yuan Dynasty, Liu Shilong and Cheng Dawei in the Ming Dynasty all put forward various algorithms in the form of verse, or put forward various mathematical problems in the form of poetry.
There are twelve mathematical problems in Zhu Shijie's "Meeting with the Source" and "Or Asking Songs", all of which are put forward in the form of poems. For example, the first question: "There is a square pool today, which stops at every square foot.
The shape of both sides of the reef gradually became larger, and the water flowed out 30 inches. There is a cattail on the east coast, and there is no zero on the water.
The pier is slightly flush with the water, so how to determine the three types (water depth, pier length and pier length)? "In the Yuan Dynasty, there was a calculation book about the method of measuring fields," Detailed Algorithm ":"The ancients measured fields for a long time, and all of them were measured by rope ruler. Although there is a form of universal law, only Tian Fang's law is easy to elaborate.
If you see the vortex inclined downward, you must make up for it. However, millet is actually a field product, and the method of dividing two acres or four acres is very strong.
"Cheng Dawei's Algorithm Summary of Ming Dynasty is a popular and practical mathematical work, and also a masterpiece of digital poetry. Seventeen volumes of Algorithmic Tongzong, which was widely circulated in the late Ming and early Qing Dynasties, made outstanding contributions to the popularization of folk mathematics knowledge.
It took Cheng Dawei nearly 20 years to finish this book. At first, he was a businessman. When he was in business, he collected books on arithmetic and writing from all over the country and compiled them into ballads, turning boring math problems into wonderful poems, which made people catchy and strengthened the affinity of mathematics popularization. Cheng Dawei also has a similar drinking mathematical poem with a binary linear equation: "There are many drinkers in restaurants, and the name of thin wine is thick and mellow.
One bottle of good wine makes three people drunk, and three bottles of thin wine make one drunk. * * * drank 19 times, and all 33 guests were drunk.
Excuse me, Gao Ming is a scholar. How much alcohol does he have? "The main idea of this poem is that a bottle of good wine can drunk three guests; Three bottles of thin wine can get the guests drunk. 33 guests were drunk and always drank 19 bottles of wine.
How many bottles of good wine and thin wine are there? There is a problem of "I don't know the number of things" in the famous Shu Jing. The original text of this calculation is: "Today, there are countless things, three and three numbers leave two, five and five numbers leave three, and seven and seven numbers leave two. What is the geometry of things? Answer 23.
"This problem has spread to later generations, and many interesting names have appeared, such as' Guigu Calculation' and' Han Xin Point Soldiers'. Cheng Dawei wrote a mathematical solution in the form of a poem in "Arithmetic Unity": "Three people walk in seventy miles, five trees and twenty-one plum blossoms, and seven children reunite in the middle of the month. Divide by 105 and you will know.
This poem contains the famous "remainder theorem". That is, the remainder is divided by 3 times 70, the remainder is divided by 5 times 2 1, and the remainder is divided by 7 times 15. If the result is greater than 105, reduce the multiple of 105.
The result of the above problem is: (2 * 70)+(3 * 21)+(2 *15)-(2 *105) = 23. In the works of Indian scholar Bashgaro, there is also such a mathematical poem: "Jasmine fragrance attracts bees to collect honey."
Bustling and countless, a group flew into the flowers. How many people are there in this group? And analyze the conditions: half of all square roots, the other two are added together; A few ninth of the total, wandering outside playing games.
"If unreasonable equation operations are listed, it can be concluded that this group of bees is 72. In addition, there is a mathematical poem about lotus: "Pingping Lake is crystal clear, and red-violet is born on a half-foot stone;" "Out of the mud but not stained, clean and graceful, suddenly blown to the clear water.
The fisherman looked at it and hurried forward. The flowers were two feet away from their original position. Please solve the problem. How do you know the depth of this lake? "What a poetic algebraic problem this is! You see, the red lotus growing in the lake is half a foot long and has been blown aside by the wind. The distance between the flowers on the top of the red lotus and the original water surface is 2 feet. How deep is this lake? According to Pythagoras theorem, the depth of this lake is 3.75 feet. Third, the number of poems: the most common number of poems is one.
Although "one" is a numerical concept, in fact, if the word "one" is used properly in poetry, it will produce beautiful artistic effects. For example, Chen, a poet in Qing Dynasty, wrote a poem entitled "One Picture of Qiu Jiang Fishing Alone": "One sail, one paddle, one boat, one fisherman, one hook, one bow, one smile, one bright moon and one Qiu Jiang.
"In the Five Dynasties, when Li Yu, the queen of the Southern Tang Dynasty, was in office, she wrote an inscription for the painting" Fishing in the Spring River "by the court painter Wei Xian:" The waves are full of snow, and the peaches and plums are silent; A pot of wine, a club, how many people are there in the world? " "A spring breeze, a boat, a cocoon and a light hook; Flowers are full of Zhu, wine is full of Europe, and you are comfortable in the waves.
"The image of a free and easy fisherman is vividly portrayed. Another example is the poem "The Wild Goose Falls to Win" in Yuan Dynasty: "One old year, one day, one autumn after another, one generation urges another, one gathers and one leaves, one suffers and one grieves.
Lying on the couch, I will find an acquaintance in my dream all my life. He will know each other for a while, and we will all know each other, play once and sing once. The 22 words "one" in the poem are repeated constantly, reflecting the illusory bitterness of life.
His writing is strange, but he wins with slang. Some poems will embed one to ten numbers in the poem.
Shao Kang, a philosopher in the Song Dynasty, said: "When you go twenty or thirty miles, there are four or five smoke villages, six or seven pavilions, and eighty or ninety flowers." The beauty of this poem is that it is embedded in ten cardinal numbers in turn, and a few words describe a quiet and elegant pastoral scenery, which evokes people's endless feelings and longings.
Math Famous Words Math Famous Words God created integers, and all other numbers are man-made. -Kroneck Pure mathematics, in its modern development stage, can be said to be the most primitive creation of human spirit. -the bald head is infinite! No other problem has touched the human mind so deeply. Hilbert found that every new group is mathematical in form, because we can't have other guidance. Darwin gave me five coefficients, and I talked about drawing an elephant. Give me six coefficients and the elephant will wag its tail. -Cauchy If anyone doesn't know that the diagonal side of a square is an incommensurable quantity, then he doesn't deserve the title of man. -Plato's unparalleled eternity and omnipotence in mathematics, as well as his independent action on time and cultural background, are the direct consequences of its essence. -Eber I have heard someone say that I am an opponent and an enemy of mathematics, but no one respects mathematics more than me. Because it accomplished what I didn't get. The essence of Gothic mathematics lies in its freedom. -Cantor In the field of mathematics, the art of asking questions is more important than the art of answering questions. -Cantor No problem can touch people's emotions as deeply as infinity. Few other concepts can stimulate reason to produce rich thoughts like infinity, but there is no other concept that needs clarification like infinity. -Hilbert number rules the universe. The queen of arithmetic and mathematics. Gauss mathematics is an infinite science. -Herman Weil As long as a branch of science can ask a lot of questions, it is full of vitality, and the lack of questions indicates the termination or decline of independent development. -Hilbert (arithmetic) is the oldest branch of human knowledge, perhaps the oldest; However, some of its deepest secrets are closely related to its most ordinary truth. -Smith But mathematics enjoys a high reputation for another reason: it is mathematics that gives all kinds of sophisticated natural sciences a certain degree of reliability. Without mathematics, they can't get such reliability. Every new group discovered by Albert Einstein is in mathematical form, because we can't have other guidance. -Darwin Mathematics is the tool of knowledge and the source of other knowledge tools.
4. Yesterday afternoon, Teacher Zhang assigned a math thinking question (writing poems). Yesterday afternoon, Teacher Zhang assigned a math thinking question. I racked my brains at night and couldn't figure it out.
Just when I was (puzzled), my father came over and gave me a helping hand. With a little help from him, I was suddenly enlightened. It really is (another village). So I solved the problem quickly.
Mei has been praised by people since ancient times. There are countless ancient poems praising Mei. (There are some plums in the corner, and hanling is alone, knowing from a distance that it is not snow, because it smells good) is an example.
Mei's unique indomitable spirit of standing proudly in the snow is really touching. Xiaoming is a naughty boy. He doesn't know the importance of studying after the fifth grade, and his mind is not on his studies all day.
Can you persuade him with two poems? Young people who don't work hard are pathetic. 4. With the spring breeze, the spring rain comes quietly at night, moistening things silently, really (sneaking into the night with the wind, moistening things silently).
5. Famous sayings about mathematics 1. Mathematics is a rational spirit, which enables human thinking to be applied to the most perfect degree. Klein
The scientific level of a country can be measured by the mathematics it consumes. -Rao
3. Mathematics, if viewed correctly, has not only truth, but also supreme beauty. Bertrand Russell
What pleases me most about mathematics is what can be proved. Bertrand Russell
Mathematics, if viewed correctly, has not only truth, but also supreme beauty. Bertrand Russell
6. The main goal of mathematics is the public interest and the explanation of natural phenomena. Fourier transformation
7. Mathematics, like music or poetry, obviously has aesthetic value. -jacoby
8. New mathematical methods and concepts are often more important than solving mathematical problems themselves. -Hua
9. Mathematics is a variety of proof skills. -Wittgenstein
10, mathematics is the highest achievement of human thinking. Misra
1 1. The beauty of mathematics is naturally and clearly displayed. Halmos
12. Mathematics is the brightest pearl in the crown of human wisdom. -Courtney
13, queen of mathematics and science; Queen of arithmetic and mathematics. Gauss
6. The sentence about mathematics Gauss (Prince of Mathematics) said: "Mathematics is the king of science."
Russell said, "Mathematics is symbol plus logic."
Pythagoras said, "Numbers dominate the universe."
Halmos said, "Mathematics is a unique art."
Misra said: "Mathematics is the highest achievement of human thinking."
Laplace said: "In mathematics, the main tools for us to find truth are induction and simulation."
Roentgen said: "The first is mathematics, the second is mathematics, and the third is mathematics."
Pierre (Canadian biologist) said: "Ecology is essentially a mathematics."
Fourier said: "The main goal of mathematics is the public interest and the explanation of natural phenomena."
Lobachevsky said: "No matter how abstract any branch of mathematics is, it will be applied to the real world one day."
Leibniz said: "With one, everything can be created from nothing."
Aristotle said, "Thinking begins with doubt and surprise."
Knowles said: "Mathematicians are fascinated by nature. Without fascination, there is no mathematics."
Russell said, "What makes me most happy about mathematics is what can be proved."
Paulia said, "Start with the simplest."
Gauss said, "Less is better, but better." "Half the proof is equal to zero."
Wittgenstein said: "Mathematics is all kinds of proof skills."