Volume 4: Gathering of Sages Chapter 587: A Teacher
"Among all of you present today, apart from these four uninvited guests, Gao Yuan and I, and... the students of Jiuzhang Hall, there must be a few who have rich collections of books at home, so you may have come across the Nine Chapters on the Mathematical Art and other mathematical classics."
Zhang Shou almost pointed out the emperor directly, but fortunately he stopped in time and used the students of Jiuzhang Hall to cover it up. At this time, he saw that among the crowd, there were quite a few people with wandering eyes, including Lu Sanlang's two brothers, and he couldn't help but laugh.
Obviously, because of the emperor's praise for Lu Sanlang's turnaround and transformation into a genius, the eldest and second sons of the Lu family were not convinced and also went to read the arithmetic classics.
Even if, as the middle-aged man just said, it is difficult to find the Nine Chapters on the Mathematical Art among the common people these days, the Lu family must have it, otherwise where would the little fat man have read it? As for what the two brothers gained after reading it, just by looking at the fact that they deliberately avoided his sight at this time, it can be known that there are nine kinds of dragons, each with a different terrible talent for mathematics.
He smiled and continued calmly, "But after reading it, I think most people would throw the book aside in confusion. Why is it that they have the opportunity to learn, but cannot go deeper? Is it because they do not know how to appreciate the blessings they have, so they do not know how to cherish them, or is it because the author does not care whether others can understand it, so most people simply cannot understand it?"
After hearing this, the middle-aged man who had angrily accused Zhang Shou before was stunned, and then he was furious: "What nonsense! Zhang Shou, you are judging others by your own mean heart! How can you misinterpret and slander the outstanding works left by those mathematical masters who worked so hard?"
Zhang Shou was not angered by the accusation. He glanced at Ye Mengqiu and saw that he had stopped solving the problem. He didn't know whether he was distracted by the tense atmosphere or he was just not up to the task. He just laughed and said, "Those works are indeed outstanding. I would like to ask you, can you understand all of the "Ji Gu Suan Jing" that Young Master Ye mentioned just now?"
The middle-aged man who was just filled with righteous indignation suddenly choked and blushed. After a long while, he said awkwardly: "That's because I am not qualified enough, so I can't fully grasp the essence of the predecessors!"
"You can admit that you have little talent, but you are unwilling to slander the predecessors. You are indeed a person of good character." Zhang Shou praised him calmly, and then said calmly, "Well, even if you can't understand everything, you don't have to belittle yourself. Because even if the Imperial Academy in the Tang Dynasty offered a mathematics course, the students there were not really able to study all ten mathematical classics."
"Of the ten books on mathematics, Sun Tzu and Wu Cao take one year to study together, Jiu Zhang and Hai Dao take three years to study together, while Zhang Qiu Jian and Xia Hou Yang only take one year each, Zhou Bi and Wu Jing Suan also take one year together, and Ji Yi and San Deng Shu are just studies that can be completed in conjunction with the other eight classics. However, there are two classics that are different."
"One is the 'Ji Gu Suan Jing' that Young Master Ye just mentioned. This book alone takes three years to study. As for the other more difficult book, it is the 'Zhui Shu' that Gao Yuan just mentioned. This book has been lost. In the Tang Dynasty, it took four years to study the mathematics department of the Imperial Academy."
"From the time spent studying these ten mathematical classics, it takes a total of fourteen years. Some people may say that scholars studied hard for ten or even dozens of years to pass the imperial examinations, which is not the same? But you have to know that this is the Imperial Academy. In which dynasty or generation of the Imperial Academy, besides mathematics, what other subjects would allow people to study for fourteen years, and they might not even be admitted after fourteen years?"
As Zhang Shou spoke, he stood up from his seat, walked to the middle-aged man, bent down to pick up the book that the middle-aged man had just thrown on the ground, then gently brushed off the dust on it with his hand, and then turned around to look at everyone.
"You just asked why we didn't pursue the mathematical classics that our ancestors once thought were lost, but instead introduced symbols from foreign countries. I can answer you now. Let's take the second question in the Ji Gu Mathematical Classics, assuming that the historian built the Yangguan Terrace as an example."
Zhang Shou casually snapped his fingers, which was a common action in Jiuzhang Hall. Whenever this happened, he would write furiously, showing people his extraordinary blackboard writing skills. Today, the students of Jiuzhang Hall came the most to support Lu Sanlang, the first head of the hall. When they heard this sound, I don't know how many people felt a chill on their backs and tingling on their scalps.
Sure enough, the next moment, Ah Liu came in with a blackboard in one hand. He placed the two heavy objects in front of Zhang Shou and handed him a white pen. He then quietly left. But not long after, he returned and brought back two more blackboards...
When he copied the same pattern again and again, and filled up the huge space with ten blackboards, even the emperor couldn't help but cover his forehead. He just thought that Lu Sanlang had stolen the limelight by taking advantage of the assessment, but now Zhang Shou, the teacher, has rolled up his sleeves and joined the battle himself!
However, the emperor was indeed very curious. You know, the "Ji Gu Suanjing" was indeed as complicated as Zhang Shou just said. Anyway, he did read it at that time but didn't understand it... and after reading the step-by-step "Ge's New Edition of Mathematics", he was even less interested in reading the difficult and complicated questions and answers in the "Ji Gu Suanjing".
"From the title, we can see that this observation platform is in the shape of a straw boy. If you are not familiar with the Nine Chapters on the Mathematical Art, but have read the New Edition of Ge's Mathematics, then we can use another term, this is a rectangular four-sided platform. In other words , the top and bottom are parallel rectangles."
After repeating the question first, Zhang Shou began to explain. However, his explanation was actually redundant. Those who could understand his explanation at this time would definitely not be laymen in mathematics. Ordinary people would not understand the term "Chu Tong", but those people definitely understood it.
However, he deliberately used the technical terms in "New Edition of Ge's Mathematics" to replace "Chu Tong", and after a brief explanation, he began to write on the blank blackboard.
"If the width of the top rectangle of the four-sided pyramid is x zhang, then the length is x+3 zhang, the length of the bottom rectangle is x+7 zhang, the width is x+2 zhang, and the height of the observatory is x+11 zhang. In this way, the volume of the four-sided pyramid is..."
Zhang Shou didn't even bother to look at the others' expressions, and continued to speak flamboyantly:
"V＝{[2(x+7)+x+3](x+2)+x[x+7+2(x+3)]}(x+11)/6＝[(3x+17) (x+2)+x(3x+13)](x+11)/6+17400…”
"Finally, we get the volume equation..."
Zhang Shou directly used the cubic style to mark and came up with a cubic equation. He looked up at everyone and saw that the students of Jiuzhang Hall were thinking about something. Lu Sanlang beside him was already beaming with joy. The emperor was also tapping the table with one hand. As for the four people including Ye Mengqiu who had just barged in, some of them frowned in confusion, while others seemed to be thinking about something. He smiled slightly and continued to write.
Solving a cubic equation was naturally extremely difficult for the ancients, especially in the era when there was no symbolic system. They had to spread out the counting sticks on the ground and spend a lot of time to finally calculate the result.
But for Zhang Shou, he didn't think twice and directly used the general root-finding formula of Cardan's formula.
When he used a bunch of formulas and wrote on two blackboards, and finally came up with the result x=7 (the other two complex roots were directly discarded by him), he heard a scream behind him.
"Is this the solution to the Tianyuan Technique? It's so simple and intuitive..." Although Ye Mengqiu only shouted out one sentence and the voice stopped abruptly, when he saw his three senior brothers suddenly looking at him, he still showed an annoyed but unwilling expression.
Zhang Shou glanced at him and saw that the pile of blackboards that Ah Liu had brought in were still empty. He chuckled and solved the remaining equations one by one. Then he solved the third problem of the Ji Gu Suan Jing, which also involved three cubic equations. This time he used four blackboards. When it came to the fourth problem, he simply skipped the steps and solved the three cubic equations.
Only then did he throw down his pen, then turned around and clapped his hands gently, looking calmly at the four uninvited guests who had initially come with great momentum but now looked dejected, and smiled faintly, "Do you understand now?"
"Children learn classics and history books, such as the Three Character Classic and the Thousand Character Classic. But what about mathematics? Can the Nine-Nine Songs be considered a basic mathematics book? There have been so many mathematics masters throughout history, and their works are all for people who have at least a basic understanding of mathematics. But where does the so-called basic understanding come from? Children can learn the Three Character Classic and the Thousand Character Classic, but can they learn the Nine Chapters on the Mathematical Art? Obviously, they can't."
"However, if there are these simple and intuitive symbols, as long as children can recognize them all, they can start learning from the simplest addition, subtraction, multiplication and division, from various simple graphics, and from the simple application of numbers."
Zhang Shou didn't know whether the four people who came today had read "New Edition of Ge's Mathematics", so he listed the table of contents and explained the step-by-step content and the knowledge points of the mathematical classics involved. This was also something he had sorted out in his spare time over the past year or so. Of course, most of it was the credit of Ge Yong, Chu Ying and Qi Jingshan, in order to lay the most solid foundation for the so-called Ge's Mathematics.
Sure enough, after his explanation, among the four people in front of him, the round-faced boy Ye Mengqiu lowered his head deeply, and the remaining three looked at each other, feeling quite embarrassed, as if they wanted to find a crack in the ground to crawl into but there was no place to crawl into.
Seeing this, Zhang Shou couldn't help but glance at the real protagonist of the day, the little fat man: "Gao Yuan, today is your coming-of-age ceremony. You have friends coming from afar, you must be responsible for entertaining them well. You should also give these guests a bowl of the fine wine from the banquet!"
"That's right!" As long as he had the upper hand, Lu Sanlang didn't mind being humble. Seeing him enthusiastically entertaining the four uninvited guests, ordering the servants to add more seats and tableware, and forcing them to sit down, Zhang Chen, who had just managed to hold back his sleepiness, breathed a sigh of relief.
He whispered to Zhu Er, who was also looking pale, "I now feel that when Fatty Lu and you were hanging out with us, you were really good at hiding your true intentions. You and I will at best be outstanding nobles in this life, but he is different. He might be like Wang Xiaotong, whom he just looked down upon, and write books and articles. Maybe he will be called a master of mathematics in the future!"
Zhu Er didn't know how to face Zhu Ying last night, so he stayed at Lu's house for a night. At that time, he had already witnessed the different life of the former Fatty Lu. Just the piles of textbooks and exercises in the study made his scalp tingle when he flipped through them.
Hearing Zhang Chen's words, he snorted and said, "If Fatty Lu ever gets that day, it's what he deserves. This kid has really put a lot of effort into studying mathematics, otherwise he wouldn't be able to become the head of the Jiuzhang Hall, let alone the tutor of the Eastern Palace... But by the time Fatty Lu becomes a master of mathematics, my brother-in-law should have already become a master of mathematics!"
At this moment, the huge place was a bit noisy, and not many people heard what Zhu Er said, but the emperor had sharp ears and eyes, and he heard it keenly.
He found that Zhu Er was not jealous of his former friends because they were now powerful. At most, he would use Zhang Shou to suppress Zhang Chen. After a little thought, he waved to Zhu Ying, who was looking around boredly. Seeing that the girl stood up and sat next to him without hesitation , he smiled and said, "Yingying, go tell your second brother that I want to give him a task."
Zhu Ying suddenly became curious: "What mission? He is very sensitive now. He even shouted at me before, saying that as long as he is willing to put in the effort, he will be no worse than Lu Sanlang!"
"That's right." The emperor smiled and then said calmly, "There is not only one path in this world, but most scholars can only take the path of studying, taking the imperial examinations, becoming an official, cultivating oneself, managing the family, governing the country and pacifying the world. But your second brother already has wealth and glory. If he is really willing to work hard, he may really be remembered in history one day!"
If "leave a name in history" is changed to "bring honor to the family", Zhu Ying still feels that Zhu Er does have a great chance. However, even the famous ministers in past dynasties may not be able to leave a name in history - although Zhang Shou is in the limelight now, but in a hundred, five hundred or even a thousand years, no one may remember his name. How could his second brother have such a great opportunity?
Zhu Ying was full of doubts, but when the emperor whispered something to her, she was stunned.
After staring at the emperor for a long time, she couldn't help but said sullenly, "Uncle, are you sure this isn't a hollow dumpling? If my second brother really listened to you and put his head down to work, it wouldn't take a year or two, three years or five years, or even ten years to accomplish it! Even though he used to be slow to do things, he's different now!"
"I just thought he was different from usual, so I asked him to do it. If it was your second brother's behavior in the past, I wouldn't even mention it."
The emperor chuckled, and then saw that Zhang Shou had returned to his seat and was chatting and laughing with the elders around him who could at least be his father or even grandfather. He sighed and said, "I used to think that those who keep company with vermilion will become red, and those who keep company with ink will become black. This saying was a bit exaggerated, but now I believe it."
"The closer people are to Zhang Shou, the more they are affected. Whether it's your second brother, Zhang Chen and Lu Zhu, Zhang Wu and Zhang Lu, or San Lang and Si Lang... everyone is changing for the better. Not to mention the students in Jiu Zhang Hall. That kind of positive and progressive style of study has not been seen in the Imperial College for a long time."
"From this point of view, Zhang Shou is indeed a very good teacher."
