Dress to be a celebrity

In the preface of Liu Hui's "Nine Chapters of Arithmetic", there is a saying that "counting is included in the six arts, the ancients use guests to promote talents and teach the sons of the country", and arithmetic is a must-learn skill for noble children.Since the Spring and Autumn Period, all Confucianism, Mohism, and calendars have been proficient in arithmetic.Since the Wei and Jin Dynasties, both official and private schools have listed mathematics as a supplement to Confucian classics. In the Song Dynasty, it was more common for masters of mathematics to open private schools and teach them to their disciples.

When Huan Ling was young, he followed his father's colleagues, and now he has been released to Jiangxi. .

Song Shi firmly refused that day, which made him secretly regret it for a long time, but fortunately Song Shi was honest with him after all, even told him about his own background, and taught him mathematics, chemistry, physics for later generations...

It is a pleasure to teach a lover to read, and it is another pleasure to read with a lover.For him, the unknown knowledge learned from Song Shi behind closed doors is very tempting to him.If he hadn't been the censor of the capital, he had the responsibility of patrolling the nine borders, and he didn't dare to be distracted by his personal affairs. I really wish he could just follow Song Shi to read and discuss Taoism every day, gather a few monographs, and then open the door to welcome the Quartet to study scholars.

Now it is God's will that gave him this opportunity to show what he has learned in his chest and to teach others——

He slowly swept across his colleagues, put down the lesson plans, and asked with a smile: "I am a teacher for the first time, and I am willing to teach according to my aptitude, and provide different courses for each of you. I don't know where you have learned in mathematics ?Da Yanshu, Tianyuanshu, Observation Technique, Dongyuan Jiurong..."

So what if I only learned "Nine Numbers" and "Straight Techniques"?Dayan technique is a technique of internal calculation, and they are not the five sense organs of Qin Tianjian, so how can they deduce astronomy and calendar?

Mr. He from the household department thought they were here to learn how to farm, and they had nothing to do with mathematics, so they stood up and resisted: "The next day before yesterday, I heard Qian Xian talk about the secret method of planting Jiahe. Tiller number method, but the method only counts the number of leaves, I am afraid that it is not necessary to study mathematics deeply?"

Um?Not necessarily in-depth research?

"The "Book of Changes" says: Only by being deep, can you understand the aspirations of the world; only by having a few things, can you accomplish the affairs of the world. If you don't have the ambition to study deeply, what can you do?"

Mathematics is the foundation of physics and chemistry they want to learn, how can they not study it in depth?To truly understand these knowledge related to the subtleties of heavenly principles, it is not just a matter of memorizing numbers like craftsmen and peasants, and copying them. You need to understand mathematics and derivation in order to truly understand the essence.

Even if you don't mention the two knowledges of later generations that you haven't learned yet, in order for them to grow Jiahe in the same way, you have to calculate the ratio of fertilizers, calculate the optimal number of transplanted seedlings per mu of field, calculate the earthwork for digging ditches, and calculate the height of seed premixing. The amount of potassium manganate...doesn't everything have to be calculated?Also, the Ministry of Industry builds chemical fertilizer and pesticide workshops, makes equipment, and hires craftsmen to manage things. Why doesn’t it need to calculate the money and food of the people in advance, and do it according to material resources?

So they have to learn arithmetic in the first lesson of school, and learn the mathematical calculation methods of later generations.Starting with addition, subtraction, multiplication and division, first memorize algebraic symbols, including positive and negative, fractions, decimals, four arithmetic operations, square root, and then learn algebraic equations when you are familiar with the calculations...

He opened the handout, picked up a piece of chalk made of lime and plaster, turned around and wrote two large characters on the blackboard: "Algebra".

"In the art of algebra, all known and unknown numbers are replaced by words, and multiplication, division, addition and subtraction have signs to distinguish them...It is based on the algebraic numbers entered, and the desired number comes out."

He also fooled these ten colleagues by saying that Song Dynasty did not trust and rely on him enough: "This is the overseas arithmetic that Song Zhuangyuan accidentally got when he was studying with his father in Fujian. It is related to the study of China. It's completely different. When I was in the Tingzhou government office in the past, I was taught this sutra by Song Xiandi, and I learned something after studying it for several years. Today, I will teach you from the beginning."

He also did not radically deny the mathematics of the dynasty immediately. He introduced Arabic numerals and English letters, and replaced them with words. He only introduced the 〇 in Suzhou codes to explain the concept of 0 in mathematics, and then introduced addition, subtraction, multiplication, division, positive and negative, fractions, Symbols such as decimal points start teaching from the four arithmetic operations.

——Although modern mathematics is good, the numbers, symbols, and formulas it uses are incompatible with the old Chinese methods. You have to abandon the old knowledge and start from scratch.If he hadn't been extremely interested in arithmetic, he might have been scared off before he learned it.

Fortunately, he has been studying books such as "Nine Chapters of Arithmetic" and "Siyuan Yujian" with his teacher since he was a child. There are methods for solving multivariate equations. Using this traditional arithmetic method to verify the modern equation solution method can naturally explain the mathematical knowledge of later generations. The depth is simple, clear and transparent.

The people sitting in the hall are all bright-minded pillars of the imperial court. They all have a certain foundation in mathematics, and they are good at drawing inferences from one another. After a short time, they sorted out the basic symbols and four arithmetic operations, and started to do oral calculations that Mr. Huan wrote on the blackboard. .

It's just addition, subtraction, multiplication and division, carry and abdication, mother and child approximation...

Although no abacus is given, you can only do mental calculations; although there are some newly learned symbols, the order of calculation of different symbols is different; although there are indivisible decimals, you must pay attention to the position of the decimal point...

But they are also people who can memorize the ninety-nine multiplication tables when they read the Three Character Classic. These simple calculations can answer the results easily, and there are almost no mistakes.

The officials who came to study were originally worried that what Huan Ling taught was the calculation of Yishu and the astronomical calendar. The techniques are so complicated that not everyone can learn them.But now after listening to him in one class and doing a few questions, everyone felt at ease, and the two commoners relied on their talents, so they got up and asked him to teach more.

"After the long Lantern Festival holiday, the two gentlemen will naturally return to the office and take up their own duties. Even if you are willing to squeeze out time to give lectures after official duties, I can't bear it. I would like to ask Mr. Huan to speak more during this holiday, even if Some things that are difficult to understand for a while, we can discuss together in the future, analyze and solve doubts. In this way, we can lay a solid foundation faster, get married as soon as possible, and live up to the expectations of the Holy Majesty, the cabinet, and the ministers. "

Although they are already ministers of the imperial court and are ministers in the same hall as Huan Ling, they still have to pay attention to the distinction between teachers and students in this class, and they should be called "Mr."Huan Ling also accepted their respect calmly, nodded slightly, and replied: "In that case, then let's not do mental arithmetic exercises in class, but first talk about foreign algebra, and I will print a few pages of exercises for you to do when you go back." gone."

However, it is not allowed to use abacus when doing the questions. These small questions should be used to hone their familiarity with new symbols and algorithms.

The hall full of successful Jinshi officials went back to the days when they were studying with their teachers in school, no, social studies, privately, and took their homework home every night to do it.Since they passed the entrance examination, most of them no longer have the time to be given topics by their husbands, and since Chunwei ascended the throne, they have never been forced to write anything...

Except for writing tomb watches and epitaphs for people, that is for money.

There was a strange silence in the hall, but Mr. Huan on the podium didn't notice the emotional fluctuations of the students. He only thought that they were Shen Xin preparing to learn new knowledge. He turned his back and wiped the blackboard clean with an eraser, and preached: "The algorithm of algebra focuses on substituting the arbitrariness. Since you and I, Mr. Song, have translated the book into Chinese, we will not mention the foreign letters here. Generation unknown..."

Just now they have talked about the method of summing and dividing, and now they are talking about the multiplication and extraction of algebra...

Until the method of "changing the Qing Dynasty".

Unique element refers to "one whose equation is unknown and has no exponent", that is, a one-dimensional equation.

Naturally, there are binary linear equations, quadratic equations, multivariate equations...the more you push, the more the arity, the higher the exponent, it is almost endless.

This kind of equation algorithm only needs to be divided into multiple formulas, and the arity is substituted in. It is very simple and convenient at the beginning; but after more and more equations are iterated, the simplicity of a single equation is not worth the trouble caused by too many calculations.So after learning deeply, I feel that it has advantages and disadvantages with the traditional Tianyuan technique, which can be verified by comparison.

Have you all learned the Tianyuan technique?

If you haven't learned it before, you can read Zhu Shijie's "Enlightenment of Mathematical Sciences" first, or ask your classmates who have learned it. After explaining the solution of "quadratic equation", he will set up a separate class to teach Tianyuan.

He kindly left enough homework before talking about linear equations in one variable.This class was taught from morning to noon, and it was not until Mr. Song brought Zhai Fu over to deliver the meal that he announced "Class is over" with a lot of meaning, and then pulled away from the teacher's role, and greeted his colleagues as the master: "This school is here!" The border is far away from Fucheng, and the food is simple, I hope you don't mind."

do not mind!do not mind!They are here to study, not to go on patrol, so how can they pick and choose and let the local magistrate throw a banquet to welcome the wind?

Although they had heard in Beijing that Song Sanyuan's father was good at receiving guests, had a good cook at home, and was good at cooking fresh dishes, but what they were facing right now was not the legendary send-off, but his son-in-law.This Song Sanyuan's father, Xiao Buxiao, had no choice but to follow his fate when it came to the reception, it was not something they could think of.

Everyone looked eagerly at Zhai Fu behind him, but what they were waiting for was ten boxes of ordinary savings boxes.

But after opening the lid of the box, the dishes exposed inside are enough to amaze even the grown-ups: the new rice harvested last year was steamed into snow-white and crystal-clear rice, and there are more than a dozen delicate side dishes in the box: Bad fish, pickled fish, cured fish made of flower fish; fresh cucumber, rapeseed, beans, green peppers cultivated in the nursery greenhouse, or stir-fried, or fried meat, stewed meat; plus chopped bacon, ham , wind chicken, steamed meatballs...

The fresh vegetables are neatly arranged, and the bright oil is poured on the fresh vegetables, so that the leaves of the vegetables are green and dripping.It doesn't look like the Mengchun season in the north, but it looks like March in the south of the Yangtze River, when the warbler is flying and the grass is growing, and the vegetables are everywhere. The banquet should be served.

His skill in this kind of cooking seems to be comparable to his skill in growing rice!

All the officials tasted the crisp and fragrant fresh vegetables and vegetables that were cooked properly, and they forgot the exhaustion of listening to the whole morning class and the pressure of not knowing how much homework they had. They couldn't wait to ask Song Shi after swallowing the rice: " When will Mr. Song teach us how to farm?"

Just focus on sowing and harvesting, without using equations or derivations, and without going home to do homework.

Song Shizheng was picking chopped scallions in sweet-scented osmanthus cucumbers. Hearing the respectful address of "Mr. Song", his fingers trembled with excitement. Brother Nian can't wait to learn for the Holy One and the imperial court, so how can I take your wishes into consideration?"

Don't eat, bring the teaching aids he prepared!

He raised his hand, and the attendants went out to spread the word, and after a while, someone came in from the outside, carrying a handful of finely crafted hoes, sickles, rakes, picks, and shovels...

?

? ?

???

Several concubines, censors, and Yuanwailang were so surprised that they almost stood up, pointing at those agricultural tools and looking at Song Shi: "This, this is, Mr. Song's intention is not to let us learn, learn to use these... "

Yes, Mr. Song nodded to them approvingly.

To increase food production, it is necessary to vigorously develop productivity, and this production tool is also an important part.It is not yet the time for wheat to turn green and rice to raise seedlings. There is no agricultural production practice that can lead them to practice. Let's start with understanding and improving production tools.

The author has something to say: Reference:

Translation and dissemination of algebra in Chinese version in China——Li Yazhen

On Mathematics Education in Ancient Chinese Private Schools——Fu Hailun

An Attempt to Master Chinese and Western Mathematics——Taking the Compilation of "Tongwen Suanzhi" (1614) as an Example——Pan Yining

Quoting some original sentences from "Algebra", I will talk about some words without explanation tomorrow, go to bed first