In the sunset, flowers and fruits are fragrant, and things change for stars to see vicissitudes.
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.
When I read the second chapter "Exponential Function, Logarithmic Function and Power Function", I said:
Morning fog blocks traffic, and mushroom clouds cover the sky;
Fossil dating is clever, and sentences in the sea are as fast as the wind.
Exponential logarithms reflect each other, and the cubic square looks symmetrical;
Explain infinite things, and the three function families create miracles.
After studying these two chapters, read them carefully and don't feel anything.
Second, the mathematical problems of poetry
Mathematics 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 solving mathematical problems. 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 formulas or poems.
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 is: "Today, there is a pool of one party, and all parties stop at the quartet. The two sides are long and the water is 30 inches. There is a kind of common life on the east coast, and there is no zero on the water. Pusheng is slightly flush with the water. Excuse me. In the Yuan Dynasty, there was a calculation book about how to measure fields, Detailed Algorithm: "The ancients measured fields very long, and they measured them completely by rope ruler. Although there is a general method for shapes, only the square field method is easy to detail. If the vortex is oblique and concave, it must be filled. However, millet is actually a field product, and the division method of two or four acres is powerful. "
Cheng Dawei's Arithmetic Zongzong in Ming Dynasty is a popular and practical mathematical work, and also a representative work of digital poetry. Seventeen volumes of The Arithmetic Zongzong were widely circulated in the late Ming and early Qing Dynasties, which 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 songs and formulas, turning boring math problems into wonderful poems. Cheng Dawei also wrote a similar mathematical poem on drinking with a binary linear equation: "There are many customers in restaurants, and the name of thin wine is thick and mellow. A bottle of good wine for three people and a bottle of thin wine for one person. * * * A total of 19 people were drunk and 33 people were drunk. How many alcoholic drinks are there? " The main idea of this poem is: a bottle of good wine can make three people drunk; 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 "uncountable things" in the famous Art of War by Sun Tzu. The original text of this calculation is: "Today's things are uncountable, the number of three and three leaves two, the number of five and five leaves three, and the number of seven and seven leaves two. What is the geometry of things? Answer 23. " This problem spread to later generations, and many interesting names appeared, such as "Ghost Valley suan" and "Han Xin Point Soldiers". Cheng Dawei wrote a mathematical solution in the form of a poem in Arithmetic Tongzong: "Three people are seventy sparse, five trees are twenty-one, and seven children and a half months are just reunited. Divide by one hundred and five." This poem contains the famous "remainder theorem". Multiply the remainder of 7 by 15. If the result is greater than 105, subtract the multiple of 105. The results of the above problems are: (2× 70)+(3× 21)+(2×15)-(2× 665).
In the works of Indian scholar Bashgaro, there is also such a mathematical poem: "Fragrant flowers attract bees to collect honey. Countless people flew into the flowers. How many? " And analyze the conditions: half of all square roots, the other two are added together; A few ninth of the total number, wandering outside playing games. "If unreasonable equations 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 came out cleanly and was blown into clean water at once. The fisherman is busy observing. The flower is two feet away from its 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, count into poetry:
The most commonly used number in poetry is one. Although "one" is a number concept, in fact, if the word "one" is used properly in poetry, it will produce beautiful artistic effects.
For example, the poet Chen in the Qing Dynasty wrote the poem "One" with the title "A picture of Qiu Jiang fishing alone": "A sail, a paddle and a boat, a fisherman hooks, 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 power, she wrote an inscription for court painter Wei Xian's "Fishing in the Spring River": "A pot of wine, a pole, 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 free 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 the Yuan Dynasty: "Year after year, day after day, autumn after autumn, one generation urges another generation, gathering together and parting, suffering and sorrow. A couch and a dream, find an acquaintance, he will know each other for a while, and we will know each other, blow once and sing once. " In this poem. 38860 . 68686868686
Some poems embed the number 1- 10 in the poem. Shao Kang, a philosopher in the Song Dynasty, said, "By the twenty-third mile, 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, depicting a quiet and elegant pastoral scenery, which evokes people's endless feelings and longings. Wu Cheng'en, a writer in Ming Dynasty, wrote a poem about night scenes, which is very artistic. 7,000 counties are closed. Six palaces and five houses return to the official residence, and the four seas and three rivers stop fishing for nylon. Two rotten tower bells are ringing and a bright moon is full of Kun. "The beauty of this poem is that the numbers inside are from big to small, and it is beautifully written at night. The contrast between these two poems 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, she opened it and wrote only fourteen numbers. Clever Zhuo Wenjun immediately understood her husband's meaning: the number "seven". Because "seven" and "wife" are homophonic, it is obvious that Sima Xiangru has the intention of preventing his wife from marrying another. So, full of grief and indignation, she wrote a song digital poetry: "After a farewell, the two places hung together, saying it was March and April, but who knows five or six years! The lyre has no intention to play, the eight-part essay can't be circulated, the nine chains are endless, and the Shili Pavilion is eager to wear. All aspects are thinking, all aspects are thinking. There are thousands of words to say, and I am tired and tired. On the ninth day of the ninth lunar month, I watched the lonely geese, and the full moon in August was not round. In July and a half, I burned incense and asked for heaven, and everyone shook their hearts in the dog days of June, and they were chilling in May. Lang Lang, I hope you are a woman and I am a man in the next life. " You see, how well this digital poetry wrote, the number changed from one to 10,000 and then from 10,000 to one. It can be described as mixed feelings. No wonder Sima Xiangru became more and more ashamed after reading it, and finally got Zhuo Wenjun to Chang 'an with his head held high.
Fourth, digital couplets:
According to legend, when Zheng Banqiao was appointed as the Shandong magistrate, he saw a Spring Festival couplets posted on a dilapidated door. The first part is: 2345. The second part is 6789. Zheng Banqiao immediately sent someone to deliver clothes and food. The officials were surprised to ask why, and they replied with a smile: the first part lacked clothes, and the second part lacked food.
Couplets written in numbers like the above are rare, and there are also many couplets embedded in numbers. But it is rare to see couplets embedded in ten cardinal numbers. Here are two homophonic couplets:
The boy looked at the rafters, one two three four five six seven eight nine X;
Mr. Wang lives in A, B, C, D, E, G, N, N.
It makes people laugh after reading it. It turns out that Mr. Wang's life is like a child's lip service, and it is not worth taking seriously. For example, the following couplet contains ten cardinal numbers, which 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, "It's very late to sit alone with two or three poets, sail four oars and sail five sails, and cross six beaches and seven bays." Su Dongpo also used numbers to encourage: "Ten years of cold window, into nine." 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.
Verb (abbreviation of verb) stresses poetry with mathematical knowledge.
There are many poems, but we can't see their connection with mathematics literally, but if we think carefully and rethink the contents of poems with mathematical knowledge, we will have a brand-new understanding.
For example, in the opera Third Sister Liu, she sang with three scholars (Tao, Li and Luo). Luo Xiucai said, "Little sparrow is not trying to be brave. Three hundred dogs are divided into four parts. One is less than three, and more than three is singular. See how you distinguish. " Third Sister Liu said, "Ninety-nine went hunting and ninety-nine herded sheep. Ninety-nine guards the door. There are three odd minions left. " After calculation, we can find that 300 = 99+99+99+3. This is exactly the problem of integer division in mathematics. If the division is out of balance, there are four kinds of division: 300 = 99+99+99+3 = 99+3+99+99. If the order is not considered, it is 1. 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 difficult to imagine that if Luo Xiucai, who sang with Liu Sanjie in those days, changed the last sentence of the lyrics to "Please explain how many points", then even if Liu Sanjie is very smart, I am afraid it will be difficult to deal with it at the moment.
An intransitive verb a digital poetry without numbers.
Zhu, a poetess in the Song Dynasty, wrote a poem "Heartbroken Mystery": "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; In fact, every sentence in this poem is a puzzle, which adds up to one, two, three, four, five, six, seven, eight, nine and ten.
Seven, digital irony
Many satirical poems can be written with numbers in the poem. For example, a poet in the Qing Dynasty wrote a jingle of "Ode to Sparrows": "One is two, three is four, five is six, seven is eight is ninety, and you have eaten thousands of royal millet. How many phoenixes are there? " During the Daoguang period of the Qing Dynasty, officials were corrupt and addicted to opium, and a smoking hall was set up in the yamen, which was full of smoke. Someone wrote a poem mocking it: "If you enter two or three halls, you will get four or five beds;" There are six or seven smoke lamps and eighty or ninety guns. " It is penetrating to satirize those corrupt officials who are incompetent and incompetent in the imperial court. A few years ago, I read a satirical article about digital poetry. Today, an official said, "One drink and two drinks are not drunk, three or four dances are tireless, five or six o'clock is not sleepy, there are not many young ladies, and 900,000 bribes are not refunded." I wonder 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 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 statue of feudal superstition was overthrown. After reading the sentence "Ten facts are useless", there was a chorus shouting: "Down with it!" We worked together to defeat 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 Articles", saying: "One grain is my honor; A penny is the essence of the people. A little wider, the people will get one more point. Take a penny, I am not worth a penny. " A series of eight "ones" illustrate his concept of clean government 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.