Volume 5: Fellow Traveler Chapter 800 Proof
"So... that's it... Ha, it's done!"
Although Zhang Shou had always required students to explain while answering questions on the blackboard, at this moment, even though the blond boy wrote a long list and only gave a few words of verbal explanation, none of the stunned students remembered to question him. They were all stunned by the boy's complex formulas and the string of beautiful italicized math formulas.
This kind of geometry proof problem, a foreign boy who claimed to be just an auditor could actually solve it so easily? This is simply incredible!
The blond boy who put down his pen, turned around and clapped his hands, his face also full of excitement and joy. He quickly walked to Zhang Shou, and grabbed his hand and shook it vigorously: "Amazing, Master Zhang, you are really amazing! I didn't expect you to be so proficient in geometry! You have read the original version of "Στοιχεiα", right? You also understand Latino?"
Zhang Shou had already noticed that the blond boy would mix Italian and Greek into his speech when he was excited, so he was very calm at this moment. He had to be considerate, but he didn't burst out a long string of Italian or Tuscan, which was already very good. And it was obvious that this was a naughty Florentine kid with some math skills.
Therefore, although he had seen the Third Prince and others outside the door, he did not even blink, and remained calm and composed, as if he would not change his expression even if Mount Tai collapsed in front of him. Of course, if Mount Tai did not collapse, he really did not need to change his expression, because at this moment, it was just a small matter that this boy who obviously had extraordinary talents thought he knew everything.
"This word is so hard to pronounce that my tongue is almost stuck." After making a self-deprecating remark, he shook his head and said, "Of course I can't have read the original version. I'm only seventeen years old, from the capital, and I've never even left Shuntian Prefecture in my life, let alone your distant hometown."
Although he didn't fully understand Zhang Shou's words, the blond boy still understood the core meaning, and he immediately showed a look of extreme disappointment. He had listened to Zhang Shou's class before, and at first he didn't understand those unheard-of terms, and he didn't have a textbook, so he felt quite bored. However, when Zhang Shou began to explain the questions on the blackboard, his boredom immediately turned into surprise.
Although many of the symbols and letters written by Zhang Shou were different from what he knew and pronounced, the familiarity was real. After Zhang Shou finished explaining a problem on the blackboard, he couldn't hold back. This was a similar calculation he had seen on a desk in someone's study when he followed his father to visit a scholar!
Therefore, after Zhang Shou finished explaining the problem, he could not help but raise his hand to indicate that he had another method of calculation, and then he went up to calculate it again with great fanfare. Although he felt that the length of the article was much more complicated than Zhang Shou's, the excitement of meeting a fellow traveler in a foreign country overshadowed everything.
But now, his mood fell from the peak to the bottom. The young scholar in front of him actually said that he was only seventeen years old and had never left here. Therefore, it was unlikely that he knew Greek, and it was even less likely that he had read Euclid's original "Στοιχεiα". After all, even he saw the Latin text that his father had collected here.
Perhaps, this scholar Zhang just read a lot of books, or had a very knowledgeable teacher, so he knew "Στοιχεiα" and knew Caesar and Octavian... Alas, he thought the journey to the East was too simple.
Just when he was feeling dejected, he heard a faint voice in his ear: "Also, please let go. Remember, here in the capital of the Ming Dynasty, if you grab the hand of someone who is higher than you, you may be considered an assassin. I think you wouldn't be so reckless in front of those officials and nobles in your hometown, right?"
The blond boy hurriedly let go of his hand and took a step back, then hesitated to apologize, and at this moment, he glanced around uneasily and finally saw the people outside the door. At first glance, those people were not too old, most of them were about the same age as the students sitting there, but the child in the middle was obviously younger than him, and his clothes were different from the others.
Being very observant, he vaguely felt that these people seemed unusual, and because of this, he forgot to apologize. His rude gaze immediately angered a certain tutor behind the Third Prince. He stood up and scolded without hesitation: "How dare a foreigner like you be so rude in front of His Royal Highness the Crown Prince!"
This is the prince of this great Eastern country? So small? No, no, this incredibly large country in the East will be inherited and ruled by this prince? How many times bigger is this country than Florence? How many times more powerful is this prince than the patriarch of the Medici family?
With this question turning in his mind, the blond boy finally bowed his head and saluted, then raised his head calmly: "I don't know His Royal Highness, so I'm sorry. I've also heard people teach about the difference between Chinese and barbarians... Sorry, this word is difficult for me to read, but since we are Chinese, shouldn't we be more tolerant of the barbarians?"
Lu Sanlang, who arrived last, just happened to hear the last words of the blond boy. He couldn't help but burst out laughing. Especially when he saw the face of the tutor who wanted to show off in front of the third prince turned red as if dripping blood, he coughed dryly and teased him.
"They don't know His Royal Highness, so what's the harm if they take a few more glances out of curiosity? Foreigners don't know etiquette. In the past, when foreign envoys came, the Honglu Temple had to send someone to teach them! Even so, during the grand court meeting, how many people couldn't help but look up at the emperor's face?"
The fat boy walked forward as he spoke, intending to hint to the Third Prince to speak up and comfort the blond boy. However, he did not expect that the Third Prince, who had been staring at him, would suddenly turn his head stiffly and say in a dry voice, "Senior Brother Lu, look at the blackboard. That is a problem he just solved."
"Huh?"
This time, Lu Sanlang finally put away his joking heart. He walked directly into Jiuzhang Hall, came to the blackboard in full view of everyone, and concentrated on reading the problem-solving process on the blackboard. For him, who was already in the "second grade" and had a very fast self-study speed, he had almost finished learning plane geometry, so it was no problem for him to understand this fairly basic equal angle problem.
But because he was very familiar with it, when he saw the densely packed solution, even though he had realized that the solution was very complicated and some steps were even unnecessary, he still couldn't help but have some doubts.
This foreign boy is not the third prince... His Royal Highness the Crown Prince has a talent for mathematics and is willing to work hard. Most importantly, he has "Ge's New Mathematics" as a reference textbook and has been tutored by the emperor himself. And this boy is just from a small Western country, and it is said that he is the son of a concubine. How could he understand this problem so easily? This is unscientific!
However, this also proves another thing. Under the recommendation of Zhang Shou, the founder Ge Yong gradually began to use Arabic numerals and a whole set of symbol systems from the West. Much of the knowledge in Ge's New Compilation of Mathematics is more intuitive and concise than the Nine Chapters of Arithmetic, or it can be said that it is simpler and easier to understand... So, what they are learning in the Nine Chapters Hall is indeed partly from foreign countries?
Did Zhang Shou's teacher, or teachers, who always kept a low profile, really travel overseas?
Thinking this in his heart, Lu Sanlang, who had already seen the entire problem-solving process, slowly turned around and gave the blond boy a thumbs up with a smile on his face: "Not bad, not bad. I heard from Eunuch Chen before that there would be such a person to help translate those mathematical classics, but after hearing about his age, I thought he was just making up the numbers. I didn't expect that you actually have some real talent."
Although the blond boy could only understand about half of what Lu Sanlang said, he could at least hear that he was being praised. Therefore, the boy showed a bit of excitement and pride on his face, and he almost didn't say that he had only learned a little bit from a certain Florentine scholar when he had the opportunity to read the manuscripts posted on the wooden board several times when he visited him.
He straightened his chest and said with great confidence: "I have been studying on my own, of course I can do this kind of questions!"
Seeing the Third Prince's eyes flickering, and he seemed to be very interested in the blond boy, Zhang Shou couldn't help but smile to himself, thinking that the Crown Prince, who seemed calm but actually had a flamboyant heart, should not take him to the East Palace on a whim, so he said casually, "Since you have solved this problem, then try these two questions."
Zhang Shou casually called two students to come up and wipe the blackboard. After they wiped the blackboard clean with great effort, he picked up a pen and started writing on the blackboard.
In a moment, two questions with accompanying diagrams appeared under his pen. At this time, he clapped his hands and nodded slightly at the blond boy with a smile .
This time, Lu Sanlang, who saw the whole process of Zhang Shou setting questions, couldn't help but laugh.
For him, who has already memorized all the axioms, theorems and various corollaries of plane geometry, these two questions are just a little complicated in the proof process, but as long as he grasps the key ideas, the problems can be easily solved.
However, based on the proof process that he had just seen from the blond boy, he thought that the key idea might be found by someone else with intuition and sensitivity, but the two theorems and a corollary that were most important for solving the problem might not be known to the other party. As for why he knew this... it was very simple, just look at the tedious problem-solving process that the boy had just done and you would understand.
Therefore, Lu Sanlang calmly pulled the Third Prince who wanted to speak, and calmly looked at the blond boy standing in front of the blackboard with a serious face. After a long time, he only wrote three lines and stopped, and then fell into deep thought, without even trying to solve another problem next to him, he glanced at the other attendants who accompanied him.
At this time, he discovered that several people from Jiuzhang Hall were whispering. The topic of discussion was not about someone overestimating his own ability, but the difficulty and thinking of the two questions. The two tutors from Banshan Hall were chatting about which small country the person was from. On the contrary, the two people from the Imperial College were actually mocking him in private.
Especially the one who had criticized the blond boy righteously before, sneered indignantly: "A kid from a small foreign country actually thinks he is a math genius like His Royal Highness the Crown Prince?"
Another person quickly echoed: "Why don't you look in the mirror? How can he easily get involved in such a profound field as mathematics?"
Tsk tsk tsk tsk… Even though Lu Sanlang has put away a lot of his sarcastic side now, especially in front of the tutors in Ciqing Palace, he still couldn't help but raise his eyebrows when he heard these two people say such things in unison: "Oh, when did mathematics become a profound field? I remember that you didn't seem to say that when you were struggling with mathematics class."
"Your Highness, as the crown prince, you should not spend too much time on such strange instruments and tricks. No matter how good your mathematical talent is, it will not be helpful in governing the country. What's the point of learning these? I think that's what they say, right?"
Don't hit people in the face, and don't expose their weaknesses. For the two tutors who came from the Imperial College and always agreed with this saying, their private words were so ruthlessly exposed in front of them, and in front of the Third Prince at that. They were really embarrassed.
The student who had just righteously rebuked others for not looking directly at His Royal Highness the Crown Prince, now reacted almost instinctively: "Lu Sanlang, what do you mean? When did we ever say this? Don't make up stories!"
If you still insist, then show me the evidence!
Seeing that the man's expression of shock and anger, but with a weak heart, seemed to reveal this meaning, Lu Sanlang immediately smiled and said, "Ah, so you didn't tell me? Tsk, it was the person who snitched behind my back who was really too much. Well, I wrongly accused him. I apologize to you... But remember to hand in your math homework later."
"After all, the gifted Crown Prince has worked hard to learn. The arithmetic you all say is so profound must be worth your hard work, right? Don't let yourself be outdone by that foreign kid you all say!"
Although Lu Sanlang bowed his hands in a proper manner to apologize, the two students' faces turned pale. After a long while, one of them finally said, "Of course, but the other courses..."
"As the tutor of the Eastern Palace, since you are serving the Crown Prince in Ciqing Palace, you should not neglect other courses."
Zhang Shou interrupted before anyone finished. He glanced at Lu Sanlang unhappily. Seeing him laughing and rubbing his nose, he wanted to say that you killed one thousand enemies but lost eight hundred of your own, as if you were very hardworking in other courses. The next moment, he suddenly realized something. When he turned around, he saw that the blond boy was writing something in the corner of the blackboard.
When he looked again, he found that the man was trying to prove that equal sides have equal angles, and then applied it to the problem. After a slight pause, he knew that the man had never read Euclid's Elements. He walked up to him and gently pressed down the boy's hand that was trying to write down the proof process: "Okay, that's enough. Now I roughly know how good your math skills are. Don't worry, I won't send you to mine!"
