1. Poems and famous quotes about learning and thinking about problems

Quotes about learning 1. There is no end to learning.

—— Xunzi 2. Scholars must first understand doubts. ——Cheng Yi 3. Learn and then don’t know enough.

——Book of Rites 4. Live and learn. —— Proverb 5. It’s never too late to learn.

—— Gorky 6. Repetition is the mother of learning. ——Di Cigen 7. Be tireless in learning and teaching.

—— Confucius 8. Life has its limits, but knowledge has no limits. —— Zhuangzi 9. Learning knowledge alone is still a fool.

—— Goethe 10. Learning is as valuable as teachers and friends. ——Tang Zhen 11. Teachers use doubts, and friends use doubts to resolve.

—— Li Xing 12. If you don’t know, ask; if you can’t, learn. ——Dong Zhongshu 13. It is difficult to be poor in learning, so help your relatives and teachers to make friends.

——Tang Bin 14. Isn’t it a pleasure to learn and practice from time to time? —— Confucius 15. To learn, you must have a teacher, and to teach, you must have friends. ——Lu Dian 16. Keeping your intentions clean is the key to immersion.

—— Yuan Mu 17. Memorizing things thoroughly does not mean mastering knowledge. —— Montaigne 18. Love of learning leads to diligence, and diligence leads to genius.

—— Guo Moruo 19. Intelligence comes from diligence, and genius comes from accumulation. - Hua Luogeng 20. Knowledge is a sweet fruit growing from a bitter root.

—— Ricardo 21. Learning without thinking is in vain, thinking without learning is peril. —— Confucius 22. Diligence and knowledge are the most beautiful lovers.

—— Anonymous 23. There is a road to the mountain of books, and diligence is the path, and there is no limit to the sea of ??learning, and hard work is the boat. - Anonymous 24. Learning is like sailing against the current. If you don't advance, you will retreat.

—— "Zengguang Xianwen" 25. A knife must be sharpened to be sharp, and a person must learn to be smart. ——Vietnamese Proverb 26. A wise person has long ears and short tongue.

——Fleg 27. He who has heard a lot will be wise, and he will learn easily by defeating his friends. ——Wei Yuan 28. Smart people have long ears and short tongues.

——Fleg 29. He who does not doubt when he is doubtful has never learned; to learn, he must doubt. —— Zhang Zai 30. Black-haired people don’t know how to study hard, and white-haired people regret studying late.

—— Yan Zhenqing 31. Scholars read books and learn new ideas every time they see them. —— Zhang Zai 32. Smart people have long ears and short tongues.

——Fleg 33. Insight into worldly matters is knowledge, and understanding of human feelings is knowledge. ——Cao Xueqin 34. Learning is labor, labor full of ideas.

—— Ushensky 35. If you don’t move forward, you won’t know the distance, and if you don’t learn, you won’t understand the truth. ——Proverb 36. Knowledge is obtained through learning, and courage is obtained through fighting.

——Anonymous 37. Reading is learning, excerpting is organizing, and writing is creating. ——Wu Han 38. Saving time, concentrating, and studying hard are a good way to learn.

—— Cai Shangsi 39. Step up your studies, grasp the center, and rather be refined than miscellaneous, and specialize rather than numerous. ——Zhou Enlai 40. The author may not be able to write until he is old, but he must learn from it.

——Anonymous 41. Studying in idleness is not better than studying in idleness. - John Bayless 42. The three conditions for studying are: more observation, more hardship, and more research.

—— Garfield 43. The first sign of an educated mind is being good at asking questions. ——Plekhanov 44. To know everything at once means knowing nothing.

—— Pavlov 45. The secret to learning a lot is not to learn a lot at once. —— Locke 46. Seeking quick results without working hard will only end up being pompous for a long time and embarrassing for an old age.

—— Zheng Banqiao 47. Any valuable knowledge I have learned is from self-study. ——Darwin 48. Diligence leads to knowledge, and thousands of books can be read through the window.

Three winters are enough for today, who laughs at being empty? ——Anonymous 49. Thousands of inventions start with one question. Manpower is better than nature's work, just ask in every matter.

—— Tao Xingzhi 50. If you don’t understand knowledge, ask questions. In order to understand the truth, it is worth getting beaten. —— Sun Yat-sen 51. Deceitful people despise knowledge, foolish people envy knowledge, and smart people use knowledge.

—— Bacon 52. A man who is omnipotent is really capable of nothing, and an expert who is expert in everything is really expert in nothing. ——Zou Taofen 53. A person who is eager to ask questions is only five kinds of fools; a person who is ashamed to ask questions will be a fool for life.

——Anonymous 54. Knowledge is an extremely precious thing, and it is not shameful to absorb it from any source. ——Abul · Faraz 55. Learning is more valuable than knowledge.

… It is better to know ten things but not reach the ground than to know one thing but not reach the ground. ——Dai Zhen 56. People learn something every day, and what they often learn is to discover that what they learned yesterday is wrong.

—— B.V57. Don’t go to bed when you can’t tell yourself what you learned today. ——Fort Lichtenstein 58. My efforts in studying have not yielded any other benefits, except that I am increasingly aware of my ignorance.

—— Descartes 59. It is false to use knowledge too much for decoration; it is the eccentricity of scholars to judge things entirely based on the rules of knowledge. ——Bacon 60. You should study at any time and learn everything; you should concentrate your efforts to know more and know everything.

—— Gorky 61. Few but eager to learn, like the rising sun; strong but eager to learn, like the light of the sun; ambitious but eager to learn, like the light of a candle. ——Liu Xiang 62. It is false to use knowledge too much for decoration; it is the eccentricity of scholars to judge things entirely based on the rules of knowledge.

—— Bacon 63. Diligent study is like a seedling rising in spring, but it will not grow with each passing day. Studying is like a sharpening stone. If you don't see the damage, you will lose some money.

—— Tao Yuanming 64. Learning this matter does not depend on whether someone teaches you. The most important thing is whether you have awareness and perseverance. —— Fabre 65. Successful scientists are often people with a wide range of interests.

Their originality may come from their erudition. —— Beveridge 66. The teacher’s duty is to ‘teach thousands of things and teach people to seek truth’; the student’s duty is to ‘learn thousands of things and learn to be a real person’.

—— Tao Xingzhi 67. Learn one thing and learn ten things. When a scholar studies deeply and is familiar with the principles, he can understand them all and achieve this. —— Zhu Xi 68. The art of learning is the art of chewing and eating slowly.

Just like eating, it must be chewed thoroughly to facilitate digestion, and then it will be beneficial to the human body. ——Tao Zhu 69. Knowledge is not something that is complete, pure, and rigid.

It is always innovating and always moving forward. —— Priyanishnikov 70. What matters is not the quantity of knowledge, but the quality of knowledge. Some people know a lot, but they don’t know the most useful things.

—— Tolstoy 71. To climb the peak of scientific culture, we must break through the limitations of unfavorable conditions, take advantage of the favorable conditions provided by life, and create new conditions. ——Gao Shiqi 72. Learning a foreign language is not difficult. Learning a foreign language is like making friends. The more you make friends, the better you get to know them. If you meet every day, you will become close to each other.

—— Gao Shiqi 73. Reading history makes people wise, reading poetry makes people smart, mathematics makes people thoughtful, natural philosophy makes people sophisticated, ethics makes people solemn, and logic makes people eloquent. —. 2. Looking for poems about mathematics~~Urgent

There are many poems that use poetry to express mathematical ideas and concepts.

For example, in the new curriculum high school mathematics textbook edited by Academician Zhang Jingzhong (the textbook is the new curriculum standard experimental textbook of Hunan Education Press), there is a poem in each chapter. For example, in the first chapter "Sets, Mappings and Functions", it is said: The sun sets, the moon rises, the fragrance of flowers and fruits, and the changes of things and the stars show the vicissitudes of life.

There are many connections between cause and effect. How can we find a good strategy to overcome confusion? The foundation theory of set is rigorous, and the mapping function is pale and yellow. Looking at the list of pictures and talking about lifting, Kehai has tips for sailing.

When it comes to the second chapter "Exponential Functions, Logarithmic Functions and Power Functions", it says: The vast morning fog hinders traffic, the mushroom core clouds cover the sky; The fossil years are cleverly calculated, and the text is written as fast as Wind. Exponents and logarithms complement each other, and cubes and squares are symmetrical; they can explain a thousand infinite things, and three families of functions have done wonders. After studying these two chapters, read them carefully and get a different feeling.

2. Poetry Mathematics Questions Mathematics is very abstract and boring. How to make mathematics easy to understand and popular with people? In this regard, ancient Chinese mathematicians have made many attempts. Songs and formulas are One of them allows people to feel the charm of poetry while solving mathematical problems. Starting from Yang Hui in the Southern Song Dynasty, Zhu Shijie, Ding Ju, Jia Heng in the Yuan Dynasty, Liu Shilong, Cheng Dawei in the Ming Dynasty, etc. all used the form of songs to propose various algorithms or used poetry to propose various mathematical problems.

There are twelve mathematical problems in Zhu Shijie's "Four Yuan Jade Mirror" and "Or Wen Ge Lu", all of which are posed in the form of poetry. For example, the first question: "Now there is a square pond, with four feet of water on each side.

The two banks of Jia Sheng are long in shape, and the water is thirty inches long. On the east bank, there is a kind of Pu, and there is no zero in the water. .

If the jiapu is slightly flush with the water, how can we determine the three parameters (water depth, pu length, and jiap length)? "There is a calculation method in the Yuan Dynasty called "Xingming Algorithm": "In ancient times, measuring fields was relatively smooth and long, and they all relied on ropes and rulers to measure. Although there are general methods for a shape, the method of square fields is easy to specify.

If you see eddies that are slanted and concave, you must straighten them up. Take it as a square. But the millet is actually a field plot, and the acres divided by two and four are powerful.

"Algorithm Tongzong" written by Cheng Dawei in the Ming Dynasty is a popular and practical mathematics book, and it also incorporates numbers into poetry. Representative work. "Algorithm Tongzong" is a seventeen-volume book that was widely circulated in the late Ming and Qing dynasties and made an outstanding contribution to the popularization of folk mathematics knowledge.

This book took nearly 20 years to complete. Cheng Dawei was originally a businessman. While doing business, he collected arithmetic and writing books from various places and compiled them into songs and formulas. Boring mathematical problems are turned into beautiful poems, which are catchy and strengthen the affinity of popularizing mathematics. Cheng Dawei also has a similar mathematical poem about drinking with linear equations of two variables: "There are many drinkers in the restaurant, and the thin wine is famous for its honesty and mellowness."

One bottle of good wine will make three guests drunk, and three bottles of thin wine will make three people drunk. One person. *** Nineteen people drank together, and thirty-three guests were drunk.

I would like to ask a wise man how much wine he has and how rich he is? "The general idea of ??this poem is: One bottle of good wine can make three guests drunk; three bottles of thin wine can make one guest drunk. If 33 guests are drunk, they will drink 19 bottles of wine in total.

How many bottles of good wine and thin wine are there? There is a question in the famous "Sun Zi Suan Jing" about "I don't know the number of things". The original text of this problem is: "There are things today but I don't know the number." The number of threes and threes leaves two, the number of fives and fives leaves three, the number of sevens and sevens leaves two, what is the geometry of the object? The answer is twenty-three.

"This problem spread to later generations and has had many interesting names, such as "Guigu Suan", "Han Xin Ordering Soldiers", etc. Cheng Dawei used the form of poetry in "Algorithm Tongzong", He wrote the mathematical solution: "Three people walking together are seventy-nine, five trees have twenty-one plum blossoms, and seven children are reunited at the first half of the month. Divide one hundred and five and you will know."

"This poem contains the famous "remainder theorem". That is, take the remainder of division by 3 and multiply it by 70, add the remainder of division by 5 and multiply by 21, and multiply the remainder of division by 7 by 15 , if the result is more than 105, subtract the multiple of 105.

The result of the above problem is: (2*70)+(3*21)+(2*15)-(2*105)= 23. There is also such a mathematical poem in the works of Indian scholar Bashikara: "The fragrance of frangipani flowers attracts bees to collect honey.

There was an endless hustle and bustle, and a group flew into the flowers. How many people are there in this group? Let's analyze the conditions: half the square root of the whole, there are two more together; a few ninths of the total, wandering around playing games.

"If you list the irrational equations, you can find that there are 72 bees in this group. There is also a mathematical poem about lotus: "The water of Pingping Lake is clear and can be seen, and the stone is half a foot red. The lotus stands tall and tall out of the mud, unstained, and is suddenly blown to the clear water.

The fisherman hurriedly moved forward while watching, and the flower was two feet away from its original position. If you can calculate it, please solve the problem. How do you know the depth of the lake? "This is such a poetic algebra question! Look, the length of the red lotus growing in the lake is half a foot above the lake. It is blown to one side by the wind. The distance between the flower on the top of the red lotus and the original water surface is 2 feet, how deep is the lake? According to the Pythagorean theorem, the depth of the lake is 3.75 feet. 3. Numbers in poetry: The most common number in poetry is one. It is a numerical concept. In fact, the appropriate application of the word "一" in poetry will produce beautiful artistic effects. For example, the Qing Dynasty poet Chen Qiufang wrote a poem with the word "一" titled "Picture of Fishing Alone on the Autumn River". : "A sail, an oar, a boat, a fisherman and a fishing hook, a bow and a smile, a bright moon and an autumn river.

"When Li Yu, the later master of the Southern Tang Dynasty, was in power during the Five Dynasties, he wrote two inscriptions for the "Picture of Fishing on the Spring River" written by the court painter Wei Xian: "The waves are like a thousand layers of snow, and the peach and plum trees are like a team of spring without words; A pot of wine, a pole, how many people in the world are like Nong. ""One spring breeze, one leaf on the boat, one cocoon thread and one light hook; the flowers are all over the lake, the wine is over the Ou, and you are free in the vast expanse of waves.

"The images of free and easy fishermen are vividly portrayed. Another example is a poem from the Yuan Dynasty called "The Order of Wild Geese Falling and Leading to Victory": "Every year grows older, and every day passes. Autumn after autumn, one generation urges the other, one gathers and one parting, one suffers and one sad.

Lying on the same bed and lying on the same body, looking for an acquaintance in a lifetime of dreams, he and we all know each other, play and sing once. "The 22 "one" characters in the poem are repeated continuously, reflecting the illusory misery of life.

The writing method is strange and uses slang. Some poems will inlay numbers from one to ten into the poem. .

Shao Kang, an acting scholar of the Song Dynasty, said: "After walking for two or three miles, there are four or five houses in Yancun, six or seven pavilions, and eighty or ninety flowers." "The beauty of this poem lies in the sequential embedding of ten cardinal numbers and a few words, depicting a quiet and elegant pastoral scene, arousing people's endless thoughts and fascination.

3. Famous Quotes about Mathematics Famous Quotes about Mathematics

Famous Quotes about Mathematics God created the integers, and all other numbers are man-made.——Kronnecke The science of pure mathematics has its modern development stage, can be said to be the most original creation of the human spirit.——Huaidehai Infinite! No other problem has touched the human mind so deeply. - Hilbert discovered that every new group is mathematical in form, because we can have no other guidance. - Darwin gave me five Coefficients, I will draw an elephant; give me six coefficients and the elephant will wag its tail. - Cauchy If anyone does not know that the diagonals of a square and the same sides are incommensurable quantities, then he is not worthy The title of man. - Plato The incomparable permanence and omnipotence of mathematics and its independence of time and cultural background are direct consequences of its nature. - Ebo I have heard someone say that I am an opponent of mathematics, It is the enemy of mathematics, but no one respects mathematics more than me, because it has accomplished achievements that I have never achieved. - The essence of Gothic mathematics lies in its freedom. - Cantor proposed in the field of mathematics The art of asking questions is more important than the art of answering them. - Cantor No question can touch people's emotions as deeply as infinity, and few other concepts can stimulate the mind to produce fruitful thoughts like infinity. Yet no other concept demands elucidation as much as infinity.—Hilbert numbers rule the universe.—Pythagorean mathematics, the queen of science; Arithmetic, the queen of mathematics.—Gaussian mathematics is Infinite science. - Herman Weyl As long as a branch of science can raise a large number of questions, it is full of vitality, while the lack of problems heralds the termination or decline of independent development. - Hilbert (arithmetic) It is the oldest, perhaps the oldest, branch of human knowledge; yet some of its most profound secrets are intimately connected with its most prosaic truths. - Smith But there is another reason for the great reputation of mathematics: it is mathematics that gives gives the various precise natural sciences a degree of reliability which they would not have achieved without mathematics. - Every new group discovered by Albert Einstein was mathematical in form, for we No other guidance is possible. - Darwin Mathematics is the instrument of knowledge and the source of other instruments of knowledge. All the sciences of order and measurement are related to mathematics. - Descartes. 4. Yesterday afternoon, Teacher Zhang assigned a mathematical thinking question (write a poem)

Yesterday afternoon, Teacher Zhang assigned a mathematical thinking question. In the evening, I racked my brains and couldn't figure out the solution.

Just when I was in doubt and had no way out, my father came over and gave me a helping hand. After some advice from him, I suddenly became enlightened. So I quickly solved this problem.

2. Plum has been praised by people since ancient times. There are countless poems by the ancients praising plum blossoms. (There are several plum blossoms in the corner, Ling Han blooms alone. He knows it is not snow because there is a faint fragrance) is an example.

Mei’s unique and tenacious spirit that stands proudly in the wind and snow is indeed touching. 3. Xiao Ming is a naughty child. He is in fifth grade and still doesn’t know the importance of studying. He doesn’t focus on studying all day long.

Can you persuade him with two lines of poetry? (If young people don’t work hard, old people will be sad). 4. The spring rain, accompanied by the spring breeze, comes quietly at night, nourishing all things silently. It is really (sneaking into the night with the wind, moisturizing everything silently). 5. Famous quotes about mathematics

1. Mathematics is a rational spirit that enables human thinking to be used to the most perfect degree. ——Klein

2. The scientific level of a country can be measured by the mathematics it consumes. ——Rao

3. Mathematics, if viewed correctly, not only possesses truth, but also possesses supreme beauty. ——Russell

4. What delights me most in mathematics are those things that can be proven. ——Russell

5. Mathematics, if viewed correctly, not only possesses truth, but also possesses supreme beauty. ——Russell

6. The main goal of mathematics is the public interest and the explanation of natural phenomena. ——Fourier

7. Mathematics, like music or poetry, obviously does have aesthetic value. ——Jacobi

8. New mathematical methods and concepts are often more important than solving mathematical problems themselves. ——Hua Luogeng

9. Mathematics is a variety of proof techniques. ——Wittgenstein

10. Mathematics is the highest achievement in human thinking. ——Mizra

11. The beauty of mathematics lies naturally and clearly. —— Halmos

12. Mathematics is the most brilliant pearl in the crown of human wisdom. ——Court

13. Mathematics, the queen of science; arithmetic, the queen of mathematics.

――Gauss 6. Sentences about mathematics

Gauss (the prince of mathematics) said: "Mathematics is the king of science"

Russell said: "Mathematics is symbols plus logic"

Pythagoras said: "Number governs the universe"

Halmos said: "Mathematics is a unique art"

Misra said : "Mathematics is the highest achievement in human thinking"

Laplace said: "In mathematics, our main tools for discovering truth are induction and simulation"

Roentgen said : "The first is mathematics, the second is mathematics, and the third is mathematics"

Pillow (Canadian biologist) said: "Ecology is essentially 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 one day be applied In this real world"

Leibniz said: "From one, from nothing, all things can arise"

Aristotle said: "Thinking questions and wonders. Start"

Novales said: "A mathematician is essentially a fascination. Without fascination, there would be no mathematics."

Russell said: "The thing that delights me most in mathematics is are those things that can be proven"

Polya said: "Start from the simplest"

Gauss said: "It would be better to have less, but to be better" "Two points One proof is equal to 0"

Wittgenstein said: "Mathematics is a variety of proof techniques"