The opening story: Borrowing and returning camels by chance
A long time ago in an Arab tribe, an old man worked hard all his life and left 17 camels before his death. When he was dying, he called his three sons to his side and left a will: "Children, these 17 camels are my life savings, and they are also the most loyal servants of our family. I am dying, so I will leave the camels to you. The eldest brother works the hardest for the family, so let's share half; the second will get one-third; the third, you are still young, let's get one-ninth. Remember, you can't kill the camels..." Before he finished speaking, the old man drove away to Hexi.
The 17 camels left by his father stumped the three brothers. The three brothers discussed together for a long time, but they still couldn't figure out how to divide the 17 camels into 1/2, 1/3, and 1/9 without killing the camels. They
had no choice but to consult the wise men in the tribe.
After thinking carefully for a long time, the wise man said to them: "Let's do this. I will lend you a camel. Now there are 18 camels. This is a good division. The eldest brother gets 1/2, which is 9, and the second eldest brother gets 1/3. , it is 6 horses, and the third child gets 1/9, which is 2 horses. You all get 17 horses in total, and the remaining 1 horse will be returned to me. "
The old man's will was perfectly solved by the wise man's ingenious "borrow one for one".
Borrow and return and factorization
If junior high school students can apply this "borrow and return" method to mathematics learning, the difficult problem will become simpler. Take "factorization" as an example. Factoring: x⁴ +4. Many students find it difficult to start when they see a question like this. After reading the short story above, you smart people will definitely try the method of "borrowing and repaying cleverly". x⁴+4, we borrow a 4x² to form x⁴ +4x²+4, and then return the borrowed 4x², so it becomes x⁴ +4x²+4-4x². Seeing this, I believe students can immediately decompose it into (x²+2)²-4x², and the above formula can be written as (x²+2)²-(2x)², Decompose it further to get (x²+2x+2)(x²-2x+2).
This idea of clever borrowing and clever repayment is actually the splitting and adding of terms in factoring. This is also an important skill in solving mathematical problems.
Mathematics teacher said that this is a combination method, a useful method for solving many mathematical problems, and an important problem-solving method that is widely used.
The great mathematicians did not make it
Leibniz was a famous German mathematician in the 17th century and one of the founders of calculus. He does not know how to decompose the algebraic formula x⁴+a⁴ and thinks that this formula cannot be decomposed anymore.
The British mathematician Taylor in the 18th century said that x⁴+a⁴ can be further decomposed into (x²+√2ax+a²)(x²-√2ax+a²). The Taylor decomposition method is not complicated. It just uses the borrowing and returning method we mentioned earlier.
We can borrow a 2a²x² and return a 2a²x², and then we can make the original formula into a perfect square and complete the factorization.
Original form=(x⁴+2a²x²+a⁴)-2a²x²
=(x²+a²)²-(√2ax)²
=[(x²+a²)+√2a x][(x²+a²)-√2ax]
=(x²+√2ax+a²)(x²-√2ax+a²)
This method of borrowing and returning is what the math teacher calls the matching method. After mastering this method, "factorization" will no longer be difficult to solve. The historical fact of
tells us that it is not too difficult to master the basic concepts and basic methods in algebra and , but it is more difficult to use these methods flexibly to solve some comprehensive problems, which requires mastering some skills.
Borrow and return and literary creation
Mathematical language pursues simplicity and clarity rather than verbosity, while literary language pays attention to rhetoric and has other pursuits. "Writing is like looking at mountains but not liking the plains." Both novels and screenplay creation require plot twists and turns, ups and downs in the advancement of the story, and avoid a straight-forward narrative like chasing pigs in an alley.
Take the primary school students as an example: For example, if the teacher asked to use "come" to make a sentence, four students A, B, C and D responded like this:
Student A: You are here.
Student B: I’m here.
Classmate C: He is here.
Excuse me, will these three students be praised by the Chinese teacher? Let’s look at how classmate Ding answered.
Classmate Ding: The birds on the tree are flying gently.
Obviously, only Ding was praised by the Chinese teacher.
What will happen if the top student comes? The top student said, "It's too easy to make a sentence. I want to write a poem."
Is there Jade Emperor in the sky?
Is there a Dragon King on earth?
I am the Jade Emperor,
I am the Dragon King,
shout to the three mountains and five mountains to clear the way,
shout loudly -
I am coming!
This poem was not written by a top student, but a red flag ballad from the Great Leap Forward period of the last century.
Looking up the information, Baidu knows to tell us:
Mr. Kuang Ronggui was born in Shanshuping Village, Huangpiqiao Township, Shaodong County in 1927. In the 1950s, " People's Literature" once published 12 of his poems on the theme of praising the people and praising the people's communes, which were praised by famous figures such as Mao Zedong and Guo Moruo. His poem "There is no Jade Emperor in the sky, and there is no Dragon King on the earth. I am the Jade Emperor, I am the Dragon King. I command the three mountains and five mountains to clear the way, and here I am." was sung across the country and was selected as a primary school textbook at that time.
means contempt for heaven and earth, fighting with heaven is endless fun, fighting with earth is fun, fighting with people is endless fun.
The script creation of the popular drama "天下久河" also used the borrow-and-return technique.
When Wang Guangyu, the governor of the river channel, committed suicide, he considered that his relatives could not be protected, so he left the account book and handed it over to his beloved daughter Rouer to protect his family at this critical moment. This account book made out of nothing can be called a borrowing, which plays an important role in promoting the development of the plot, creates suspense, and whets the audience's appetite.
Rouer finally saw the emperor after Chen Huang arranged it, and revealed her identity and motives. She explained that the account books recorded many corrupt elements related to the river embankment floods. She hoped that the emperor could protect her and other exiled family members. Yellow River Dam supervisor Jin Fu . At the critical moment, Rouer hurriedly rushed to the scene and shouted to save someone, hoping to provide account books to prove Jin Fu's innocence. End of episode 8. In episode 9 of
, the appearance of Rou'er made things turn around. Mingzhu suggested suspending the execution and looking at the account books first. Suo'etu believed that Jin should be killed first to calm the people. Seeing the two people arguing endlessly, Chen Huang begged Kangxi for verification. Other people present shouted that Jin Fu was honest and selfless. In the end, Kangxi threw the account book into the brazier, pardoned Jin Fu, and imprisoned Jin Wenxiang.
When Kangxi got the account books, he burned them without even looking at them. This was unexpected and reasonable, so it can be called a return. At this point, the method of borrowing and returning has echoed back and forth.
Manchu and Qing emperors and nobles all liked to read the Three Kingdoms, so you should know the story of Battle of GuanduAfter Cao Cao won, although he seized a large number of letters from his subordinates who collaborated with the enemy at Yuan Shao, he burned them without reading them at all. Therefore, the previous borrowing and the returning in episode 9 make logical sense. This method of borrowing and returning is indeed very clever, and it has the artistic effect of making waves from a flat ground.
This borrowing and returning is also in line with the principles of TV drama creation. Some details can be freely used for artistic creativity. Major events respect historical facts and will never be a joke. Therefore, "The Long River" can be called a drama with historical themes.
borrow and return and the logic of finance
borrow and return are widely used in many fields and industries. Let's take another example from the financial industry.
For example, when a young person buys a house, he applies for a thirty-year loan, which is called a first loan, and it takes thirty years to repay the loan, which is called a first repayment. This is a wonderful case of borrowing and repaying.
The lender and lender in this case have a mutually beneficial and win-win relationship. The lender realized his wish to live a better life. With the help of the bank, like magic, he bought a house thirty years in advance and repaid the loan with gradually depreciating banknotes. There is a saying that if success comes too late, happiness will be halved. Therefore, this kind of value exchange across time is a benefit for young people. On the other hand, the bank is also satisfied and has achieved its goal, so why not?
transactions increase well-being, and when a transaction is completed, it is beneficial to both parties.
transactions generate wealth, dT0, this has been proven in theory and practice.
We won’t go into details. Let’s talk about an effect that has been ignored by everyone.
For example, if you want to get rich, you need 10 conditions. Now you only have 3 of them, and you are still short of 7.
So, how do you get these 7 conditions together? The key to
is that you still don’t know what the seven conditions are.
The answer is: trading.
For example, if there is no iron ore, you can buy it.
In frequent transactions and transactions with different people, you will unknowingly gather the other 7 conditions to trigger a reaction.
is like a chemist mixing 10 solutions and shaking the test tube repeatedly.
He didn't know where or when the new compound appeared in the test tube, but it would definitely appear.
Watt 's steam engine was first commercially used, the first publication of " The Wealth of Nations ", and the release of the American Declaration of Independence were all in 1776.
is the result of nature, the chemist, shaking it hard.
We don’t need to talk about complicated transactions, let’s start with the purest information transactions. What is the name of the transaction of
information?
exchange.
is as fierce as a tiger in one operation, and it costs three and a half dollars in one glance at Taobao.
What is difficult for you may be very simple for others, or even given away for free.
Everyone's resources and information may be inadequate. As long as
communicates and trades, it can virtually satisfy the conditions and form explosive growth, reaching an incredible level.
In many cases, whether it is original or not is actually not that important. The real power of
is actually the collision of high-quality information flow and transaction flow.
One inspiration leads to another inspiration, and one growth leads to another growth.
recommends a good book "The Logic of Finance", written by Professor Chen Zhiwu. What is finance? This is a rather difficult question to answer, but the author explains it clearly in an easy-to-understand manner.
Science has not yet become popular, and the media still needs to work hard. Thanks for reading and bye.
