Royal road

With a bang, the wooden door was pushed open, and a thirteen or fourteen-year-old boy dragged a long grass rake into the room.Carefully put the rake in the corner, took off his coat which was full of dirt and grass clippings, ran to the desk, and drank a few sips of water from the clay pot.These are all the hot water that Auntie boiled in the morning, but after a day, they have already cooled down.He didn't dare to drink too much, and when he quenched his thirst, he put down the jar, picked up the clean short jacket on the couch, and put it on.

After carefully dressing and smoothing the cloth with his hands, he picked up a hemp bag from the desk to make a cloth bag, took a deep breath, and strode out the door.

"Huh? Isn't this Aping? Are you going to school?"

"Ah Ping, if it doesn't work, don't delay, you have to find a way to enter the series."

"That's right, don't disappoint your father's military achievements!"

Along the way, many acquaintances saw him, and couldn't help but say a few words of comfort. The young man nodded cautiously, but didn't stop, and trotted all the way to the gate of the mansion. After being checked carefully by the guard, he entered. courtyard gate.

No matter how many times you come to the owner's house, you can't get used to it.It's too gorgeous, and it's not like a place for people like him to come to.A Ping didn't dare to look around in private, and buried his head towards the west side courtyard of the outer courtyard, where the accountant Zhou Kan lived. In addition to working, there is now a secluded school as a school, which specializes in teaching counting to the children of Zhuang households.

His family is an euphemist in the village. His father participated in the trilogy before and died in battle a few months ago.The ten mu of military land allocated to the family was completely exempted from taxation, so A Niang returned the original twenty mu of land, and supported the two of them by farming the ten mu of military land and twenty mu of mulberry fields.If I help A Niang with work first, and join the army after a few years, the family will not have to worry about food and clothing.But now he ran to the school to learn counting.

Just in the school, it takes at least one hour a day, and after returning home, you have to complete the exercises assigned by the master.These two things will take a lot of time, and the time to help A Niang will naturally be less.He also learned such knowledge as counting, and many neighbors felt that he wasted his time here and was just wishful thinking.

However, Aping could not give up!He never knew that there are such interesting things in the world!The numbers and formulas taught in the school were refreshing, like a door opened suddenly, and he saw the truth of the world.This is not something you can find by staring down at the fields.

What's more, Master Zhou said that if he can finish his studies, he can work in the accounting office.The government will be responsible for all the expenses. Maybe in the future, I can be a bookkeeper like my master and receive a monthly salary!

With an extremely pious heart, A Ping walked into the school and did a good job in his own corner.Carefully took out a stack of paper-bound notebooks and a charcoal pencil wrapped in cloth strips from the sackcloth bag.This is from the school. You can use a sand table for exercises, but you need paper for notes and answers to exercises.One copy per person, record the front and back to do the questions, it can be used for a month.If the error rate in solving problems in one month is too high, I am afraid that I will be expelled from the school.

Opening the book, Ah Ping carefully checked it again, and he was relieved after confirming that it was correct.At this time, another schoolboy came into the school one after another, including him, a total of 12 people.This was left after several screenings, no one dared to make noise, and they all sat obediently in their seats, waiting for Master to give a speech on the stage.

"This scorpion!" Zhou Kan was flushed with anger at the moment.

He kindly recommended Li Xin to come to the Liang Mansion, and because of the friendship between the two teachers in the past, he also paid a special visit to the two of them.Unexpectedly, after a few trips, he was so angry that his heart, liver and lungs ached.That kid Li Xin is a complete bastard. Not only did he not regard himself as a fellow student, but he also mocked his account management work with contempt, saying that he is good at counting, so he deserves to keep the count.

No wonder the brothers at home didn't take this idiot to heart.Having this kind of thing by your side is simply life-threatening!

Walking into the school angrily, seeing the eager eyes of the young people below, Zhou Kan's anger subsided a little, and he coughed: "Put all the notebooks on the case!"

No one dared to be negligent, and everyone hurriedly put the notebook on the desk.This desk was just made, it is only three feet wide, just enough to put down the arm, and there is a sand table beside the desk, although it is crude, it is very practical.Seeing that the apprentices had put away their notebooks, Zhou Kan checked them one by one with his hands behind his back.

The numbers written on the paper are not counting chips, but weird Indian numbers.From 1 to 9, compare the chips one by one, and there is also a 0 for carry.This was given to him by the owner before, and there are also vertical operations of addition, subtraction, multiplication and division.Even Zhou Kan has to say that these things are much simpler than using calculation chips.If you are counting chips, you will not be able to figure out how to put them if you are stupid, but the vertical formula and numbers are simple and clear, and you can check the calculations against each other, so it is not easy to make mistakes.

There is also the original Jiujiu song, and the master also ordered that it be changed from 36 sentences to 81 sentences, and be written on a sheet according to the Tianzhu numbers, and posted on the wall for people to recite and study.It can be said that those who can stay here have a good memory, are quite diligent, and have some talent in logarithms, otherwise Zhou Kan would not spend time on them.

Now I heard that the two senior brothers Li Xin are also recruiting people to teach, and they still teach the method of heavy difference.Hmph, he wants to see what kind of things Li Xin can hand over with that dog temper.

After checking it from beginning to end, he nodded with satisfaction, Zhou Kan returned to the podium, opened the book and said: "From today onwards, I will start studying the chapter 'Chestnut Rice', which is the exchange of grains and grains. If you can't learn important subjects, go home and farm."

Seeing the focused and longing eyes of the apprentices below, Zhou Kan nodded slightly and began to lecture.

■

"Zile, it's time to teach those apprentices." Liu Jian called, but no one answered, so he had no choice but to push the door into the room.I saw discarded paper all over the floor in the house, black painted boards were covered with white lines in all directions, and there were strings of Tianzhu numbers.Li Xin was sitting in front of the desk, writing something furiously, as if he didn't hear him at all.

After taking another two steps, Liu Jian said again: "Zile, it's time for you to go out and teach."

"No, no, no! A bunch of idiots!" Li Xin didn't raise his head, but was still concentrating on his calculations. The paper in front of him had been drawn with charcoal so that he couldn't see its original shape.

"This is what we promised the Lord!" Liu Jian was helpless to the extreme.

He has also been with Li Xin for several years, so he naturally understands this person's temperament better than others.Although he is called a junior, Li Xin is actually a few years older than him. He has been disgusted since he came into the family.Unexpectedly, he is extremely talented in arithmetic, and I am afraid that all the knowledge of his grandfather's life, and even the work of sorting out the manuscripts, will fall on him.

He also had high hopes for it, and wanted to pass on his grandfather's commentaries to the world, so Liu Jian helped him leave Qingzhou with the manuscript, and traveled thousands of miles to Liang's mansion.However, after finally settling down, his stinking problem broke out again.It is also because the Tianzhu numbers and vertical formulas taught by the Lord Lang are so easy to use, that this person was instantly fascinated.By the way, there is also the theory of trigonometric functions, not to mention Li Xin, even he is a little obsessed with it.

But what should be done must be done!If even an assistant can't teach him, how can he explain to the master?

"What's the use of my teaching for a fool who has just memorized the ninety-nine table?" Li Xin quickly wrote a value on the paper, then turned out several sheets of paper pressed underneath, and suddenly raised his head and said, "Senior brother, look at me. Calculated another one!"

Looking at the man's shining eyes, Liu Jian sighed: "Forget it, I'll teach those people. But you can't just be obsessed with functions. The manuscript must be revised as soon as possible and sent to the bookstore for publication. This is the future textbook in the Fuchu. It must be Take grandfather's commentary as the original!"

"Is it up to you to say that?" Li Xin waved his hand in disgust, and went back to check the calculation.

Not knowing whether to laugh or cry, Liu Jian shook his head and walked out the door.Alas, I'm afraid I'll have to look at the waterwheel sent by Mufang yesterday, but if Zile can calculate a few more function values, maybe the calculation will be faster.Striding towards the study beside him, Liu Jian didn't realize it, and there was a little smile on his face.

■

Seeing the ink-smelling paper that had just been printed in his hand, Liang Feng nodded in satisfaction.This is the chapter "Fang Tian" that was first sorted out in the manuscript of Liu Hui's "Nine Chapters of Arithmetic".There are not only questions, answers, and skills, but also analysis and illustrations.This is also the concept advocated by Liu Hui, "Analyze with words, disintegrate with pictures".Such a rigorous and meticulous marking method makes "Nine Chapters of Arithmetic" one of the classic textbooks for later generations.

As for such a version, I am afraid that only woodblock printing can fully display the essence of it.If it is copied by hand, people who do not know how to count may make mistakes and omissions, and they will not be able to express the meaning of the question intuitively.

The progress in organizing the books was good, and Liang Feng was extremely satisfied with the progress on functions.A few days ago, he consciously revealed some concepts of trigonometric functions to Li Xin and the others. As a result, their comprehension ability was simply admirable, worthy of being Liu Hui's direct successor.

This was also what Liang Feng expected most.

Although there were many mathematical works and great mathematicians in ancient China, formulas and theorems were rarely formed.Of course, there are reasons for the prohibition of astronomy, and I am afraid that there are also problems caused by the habit of teaching materials.Just like in the nine chapters, there are "techniques", that is, the steps to solve the problem, but there are no steps to prove this process.The lack of inductive expressions naturally makes mathematics a top knowledge that only a few people can reach.

And Liu Hui was one of the few people who broke this inertia.He took the lead in proving the circle area formula, "Using one side to multiply the radius, the goblet cuts it, and each time it doubles. Therefore, the circle is multiplied by the radius to be the power of the circle." It is precisely because of this that it proves the inaccuracy of "three-week diameter one" in the past. Accurate, the pi is accurate to 3.14.And circumcision is the theory and algorithm of pi calculation. This achievement alone is quite amazing.

If all the contents of the mathematics category are brought into this field of inference and demonstration, then the development of this subject will inevitably take a different path.Liang Feng remembered a lot of formulas, but he is not a professional after all, and he can't remember many of the argumentation process clearly. If he taught people of this era all at once, it would only spoil the seedlings.Perfecting the process of derivation and conclusion is the real thing.Anyway, those more advanced mathematics may not be available now.Step by step, maybe you can bear some surprising fruits.

It seems that there will be a higher education system in the future. If there are good seedlings on Zhou Kan's side, they can also be sent directly to Liu Jian's side, and those who are not even solid in basic skills, let Zhou Kan take care of them first.It's a pity that he has too few talents at hand. It might be more beneficial for Li Xin to find a few companions of the same level who can communicate.

Zu Chongzhi also seems to be from before the Tang Dynasty. When was he born?He only remembered that there was such a big cow as Zuti in this era. Could it be that he belonged to the whole family?

Just dreaming of recruiting a few more math geniuses, someone outside the door reported that Wang Wen's messenger had arrived.

Wang Wen is one of his biggest reliance now, so Liang Feng will naturally not neglect and recruit people in immediately.However, when he opened the letter and read the content clearly, he couldn't help raising his eyebrows: "Go to Jinyang to participate in the Shangsi Festival?"

Shangsi can be said to be the most solemn festival in spring, so it is not surprising to invite him to go.But Wang Wen's meaning is quite clear, he wants to repair the relationship between him and Duke Dong Ying, and resolve the misunderstanding.Liang Feng was really not interested in the idiots of the Sima family, but after thinking for a moment, he nodded and said, "How dare you not go when invited by Zhongzheng? Wait for me to write back and pass it on to him."

Whether he can please Sima Teng is not important, what is important is to show his face on this occasion.Those two expeditions should not be wasted, they were just used to improve their reputation.With a reputation, it is much easier to do other things.

The author has something to say: Arabic numerals, in fact, were originally spread from India. Anyway, Liang Shao opened the Buddha's hanging, so it is not wrong to say so.In addition to the number system used for writing such as one, two, and three in ancient China, there were also counting numbers, which are mathematical symbols specially used for calculation as shown in the figure below.So learning Arabic numerals should not be a problem.

As for Zu Chongzhi, he was from the Southern and Northern Dynasties era, but one thing is true, Zu Ti should be his great-grandfather, Zu Taizhi's clan brother.