There are many poems that 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 sides of the reef are getting bigger and bigger, and water comes out 30 inches. There is a cattail on the east coast, and there is no zero on the water. " The dock is slightly flush with the water. 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 drew quantities 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 a field, and the method of dividing it into two or four acres is strong." Cheng Dawei's Algorithm Classic of Ming Dynasty is a popular and practical mathematical work, and also a representative work 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 33 guests were drunk. " I wonder if a wise man is a scholar? How much wine did you drink? "The main idea of this poem is: 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? The answer is 23. "This problem has spread to later generations, and many interesting names have appeared, such as" Ghost Valley Calculation "and" Han Xin Point Soldiers ". Cheng Dawei wrote a mathematical solution in the form of poetry in "Algorithm Unification": "Three people are seventy, five trees are twenty-one, and seven children meet again in the middle of the month, divided by 105." 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 smells sweet and attracts bees to collect honey. "Bustling, countless, a group of flying 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 to play 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;" Mud is not stained, clean and graceful, and it is suddenly blown above the clear water. The fisherman looked at it and hurried forward. The flowers were two feet away from their original position. If you can count, 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, the poet Chen in Qing Dynasty wrote a poem "One" with the title of "One Picture of Qiu Jiang Fishing Alone": "A sail, a paddle, a boat, a fisherman, a hook, a bow and a smile, a bright moon and a 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 court painter Wei Xian's" Fishing in the Spring River ":"The waves are full of snow, and the peaches and plums are silent. "A pot of wine, a stick, how many people are there in the world?" A spring breeze, a boat, a cocoon and a light hook flower are everywhere, wine is everywhere, and you are free in the waves. "The free and easy fisherman image be 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. "I have been lying on the sofa all my life and have always dreamed of finding an acquaintance. After a while, we all got to know each other, playing once and singing 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 sequence, and a few words depict a quiet and elegant pastoral scenery, which evokes people's endless regrets and longings. Wu Cheng'en, a writer in the Ming Dynasty, wrote a poem about the night scene, with a very broad artistic conception: "The Shili Pavilion is full of stars. Eight rivers seal ships and seven thousand counties seal them. Six palaces and five houses belong to the official residence, and the four seas and three rivers go fishing. "Two rotten towers are ringing, and a bright moon is full of Kun." The beauty of this poem is that the numbers in the poem are from big to small, and it is beautifully written at night. Reading two poems in contrast is wonderful. There are many sad stories about numbers entering poetry. It is said that shortly after Zhuo Wenjun and Sima Xiangru got married, Sima Xiangru went to Chang 'an to be an official and never returned for five years. Wen Jun misses it very much. One day, she suddenly received a letter from her husband, and she was naturally overjoyed. Unexpectedly, when I opened it, I only wrote fourteen numbers: "one two three four five six seven eight nine billion". Brilliant Zhuo Wenjun immediately understood what her husband meant: the number "seven" appeared twice. Because "seven" is homophonic with "wife", it is obvious that Sima Xiangru has the intention of preventing his wife from marrying another woman. So, filled with grief and indignation, she wrote a digital poetry: "After a farewell, the two places are hanging from each other, saying March and April, but who knows five or six years! The lyre has no intention to play, the eight lines have no transmission, the nine-line chain has never been broken, and the Shili Pavilion wants to wear it. I thought about it in every possible way, but I was helpless and could only blame Lang. A thousand words, bored, looking at the lonely geese for nine days, the Mid-Autumn Festival in August is not round. In July and a half, I burned incense and held candles to ask the sky. In the dog days of June, everyone shakes my heart. Durian in May is like fire, but it is drenched with cold rain. April loquat is not yellow, and I want to be fascinated by the mirror. Peach blossoms follow the water in March, and kite strings break in February. Hey! Lang Lang, I wish you were a woman and I was a man in the next life. " You see, this digital poetry is so well written. Numbers range from 10,000 to 10,000 and then to one. It can be said that it is full of emotions. No wonder Sima Xiangru felt even more ashamed after reading it, and finally let Zhuo Wenjun take the high-speed train to Chang 'an. 4. Digital couplets: According to legend, when Zheng Banqiao was the magistrate in Shandong, he saw a Spring Festival couplets posted on a dilapidated door, the first part of which was 2345. Downline: six seven eight nine. Zheng Banqiao immediately sent someone to deliver clothes and food. The officials were surprised to ask why, and they replied with a smile: the lack of one in the first part is the lack of food and clothing, and the lack of ten in the second part is the lack of food. Couplets written entirely with numbers like the above are rare, but there are many couplets embedded with numbers. But there are few couplets embedded with ten cardinal numbers. There are two harmonies here: the boy watching the raft, one two three four five six seven eight nine X; Sir, life, A, B, C, D, E, G, N, N, makes people laugh. It turns out that Mr. Wang's life is like a child's words, and it is not worth taking seriously. Another example is the following couplet, which has ten cardinal numbers. It is very rare and worth appreciating carefully. According to legend, Su Dongpo and Xueyou went to Beijing to catch the exam. Because of the flood, the ship was difficult to travel and the time was delayed. Seeing that they were going to be late for the exam, Xueyou sighed, "One leaf is alone, sitting on two or three poets, crossing six beaches and seven bays with four oars and five sails, which is very late." Su Dongpo also encouraged him by joining the league with numbers: "After ten years of cold window, I entered 98 academies, but abandoned my worldly desires. I studied the Five Classics and Four Books hard and took the exam three times and twice. I must go in today! " The first part counts from one to ten, and the second part counts backwards from ten to one, which not only skillfully and appropriately uses numbers, but also vividly expresses the difficulty of students studying hard at a cold window and rushing to Beijing for exams. 5. Rereading Poetry with Mathematical Knowledge There are many poems, and literally you can't see their connection with mathematics. However, after careful thinking and rethinking the content of poetry with mathematical knowledge, you will have a new understanding. For example, in the opera Sister Liu, Sister Liu sang against three scholars (Tao, Li and Luo), and Luo Xiucai said, "Little sparrows don't show off their bravado, and 300 dogs share their food. One less and three more are singular, depending on how you distinguish them. " Sister Liu said, "Ninety-nine went hunting and ninety-nine came to see the sheep." Ninety-nine guards were at the gate, leaving three strange minions. "You can find 300 = 99+99+99+3 by calculation. This is exactly the problem of integer division in mathematics. If it is not disorderly split, there are four split modes: 300 = 99+99+99+3 = 99+99+3+99 = 99+3+99 = 3+99+99 = 3+99+99. Obviously, if the sequential splitting is taken into account, the number of the above splits is 4; Regardless of order, there are 1 species. At this time, there can be a more general question: "How many different ways are there to divide 300 into the sum of four odd numbers in sequence? "It is not hard to imagine that if Luo Xiucai, who sang with Liu Sanjie in those days, changed the last sentence of the lyrics to:" Please make it clear how many points there are ",then even if Liu Sanjie is very smart, I am afraid it will be difficult to cope for a while. 6. Digital riddle-A poetess in digital poetry Song Dynasty Zhu has a "heartbroken riddle": "Come downstairs, money will fall; Ask heaven where people are; Hate the prince, have been there; It is difficult to be with friends; Regret that I missed my mouth; Those that have been handed in and those that have not; Why ask in vain; Separate without a knife; From now on, never rely on your enemy; A thousand miles of lovesickness disappears. "In fact, every sentence of this poem is a crossword puzzle, which adds up to one, two, three, four, five, six, seven, eight, nine and ten. Seven, digital satirical poems can write many satirical poems by using numbers into poems. For example, a poet in the Qing Dynasty wrote a doggerel titled Ode to a Sparrow: "One, two, three, four, five, six, seven, eight and ninety have all eaten up a thousand kinds of royal millet. How many phoenixes are there "During the Daoguang period of the Qing Dynasty, officials were corrupt and addicted to cigarettes, and there was a smoking hall in the yamen, which was filled with smoke. Someone wrote a poem mocking it: "If you enter two or three halls, you will get four or five beds;" Six or seven smoke lamps and eighty or ninety guns. "Ironically, those incompetent corrupt officials in the imperial court are extremely penetrating. A few years ago, I read a digital poetry that satirized some officials today: "After one or two drinks, I danced tirelessly for three or four times, I was not sleepy at 5: 06, and there were not many young ladies, so I didn't stop taking bribes. "I don't know what these officials will think when they see it. There is an ancient folk poem about a clay bodhisattva: "Without a word, there is no light in my eyes;" Don't eat three meals, four bodies are not diligent; Regardless of the grain, the six gods have no owner; I know nothing about this, I am awesome; Nine people can't sit still and are completely incompetent. "The following are the top ten" crimes "of clay sculpture, which can be regarded as a battle. It is said that I read this poem when the idol advocating feudal superstition was overthrown. After reading the sentence "ten facts are useless", it was followed by a chorus shouting: "Down with it! "Everyone worked together and knocked down the idol. On the contrary, in the Qing Dynasty, Zhang Boxing, an honest official who was called "the first in the world" by Emperor Kangxi, wrote an article "No Feeding", saying: "One grain is my honor; A penny is the essence of the people. One point wider, one more point for the people; I'm worthless for a penny. " A series of eight "ones" illustrate his concept of honesty and self-discipline. These digital poetry languages are beautiful, novel in form, interesting and beautiful. Reading these mathematical poems can not only open people's thinking world, but also enjoy the beautiful scenery, learn some mathematical knowledge and stimulate students' interest in learning mathematics. I have tried consciously for a long time in teaching and the effect is good. Inspired by mathematical poetry, some students began to try to express some conclusions and methods in mathematics in the form of poetry.