Chapter Thirty-Eight Reunion with a Beauty

  According to historical research, China had already mastered the technique of glassmaking during the Warring States period. Unfortunately, this technology was not available in the Shang Dynasty. Although there were some precious crystals presented by vassals in the imperial palace, they were all natural quartz and not man-made glass.

  Actually, before the Leiden jar was conceived, Zhang Zixing had considered glass production. The raw materials for glass are sand, limestone, sodium carbonate and mixed substances. Sodium carbonate is soda ash, which has been widely used in later generations, most commonly seen in soap, papermaking, detergents, etc., but it was a problem during the Shang Dynasty, so it could only be temporarily shelved. As it turns out, this time conquering the Eastern Yi, Zhang Zixing obtained the mining secret map presented by Zou Qi, and when he went to inspect it, he also discovered other rich mineral deposits, including natural alkali mines that can extract sodium carbonate, which made Zhang Zixing overjoyed, secretly thinking that this life of Chi You was not in vain.

  Zhang Zixing imparted the most suitable glass-making method for the Shang Dynasty to several main craftsmen in the workshop, and instructed them to repeatedly experiment without worrying about failure. If there were results, they would report immediately. The craftsmen who received this secret technique could actually "turn sandstone into crystal", and were shocked with their eyes wide open, but not a single person showed any signs of doubt. Zhang Zixing had created many miracles, and every idea he put forward was unprecedented, yet all became reality. Even if he wasn't the supreme ruler, in the hearts of these craftsmen, he was still a god-like existence.

  After leaving the imperial workshop, Zhang Zixing suddenly remembered something that was almost forgotten. He ordered the carriage to drive back and changed into a set of ordinary clothes, sneaking out of the palace quietly.

  Zhang Zixing walked into a bookstore in the market, picked up a copy of "Tian Suan" and flipped through it, asking the store owner: "Excuse me, do you know where Tan Weicao's studio is?"

  "Turn left at this intersection, and you'll see the Prime Minister's residence. The third alley to the side of the Chancellor's mansion is where you want to go." The shop owner looked at the "Tian Suan" in his hand and showed a knowing expression: "You're here to study divination at Cao Tang, aren't you? Please hurry along, they shouldn't have dispersed yet."

  "Is this the Prime Minister's residence?" Zhang Zixing thought for a moment, then asked again: "The shopkeeper guessed correctly, I am indeed here to pay respects. May I ask who is the teacher lecturing and how much is the tuition fee?"

  "That teacher was a young woman, her face veiled, so that her features could not be seen, but her learning was vast and unmatched, especially in the field of mathematics, where she had few equals. Several people who were famous for their knowledge came to compete with her, but all returned convinced of her superiority. This woman gave public lectures, which were attended by large crowds, yet she refused to accept even a small tuition fee; everyone respected her as 'Female Master'."

  "Female teacher? How interesting..." Zhang Zixing muttered a sentence, thanked the shopkeeper and walked straight towards Tanweicao Hall.

  The so-called "Exploring the Subtleties of the Grass Hut" refers to a simple and crude little house. The yard outside is quite spacious, but at this moment it was crowded with people. These people were both men and women, all dressed in plain clothes, intently listening to the lecture by the female teacher in front. The female teacher was indeed the masked woman who had met Zhang Zixing before. However, the beautiful young girl suspected of being Deng Ciyu was nowhere to be seen at this time, only a few burly men stood behind the masked woman, seemingly as guards.

  Zhang Zixing secretly wanted to see the masked woman's teaching skills, so he didn't go forward to greet her, but instead stood in the corner and listened. Having only heard for a while, Zhang Zixing's face showed a look of surprise. This woman was indeed worthy of being called a female master, able to combine theory with practice from shallow to deep, explaining corresponding mathematical knowledge in a way that made it easy for people to understand. Many clever examples were even not mentioned in "Tian Suan". From this, it can be seen that the woman not only had a good understanding of mathematics but also possessed strong oral expression skills. Although the knowledge she explained was relatively simple, it was already quite rare.

  At this point, the masked woman's lecture was nearing its end: "Today's lecture ends here, everyone please disperse and come back to the grass hall in three days to listen again."

  The crowd dispersed after hearing the words, and Zhang Zixing quickly walked forward, wanting to greet the masked woman. But a guard thought he had ulterior motives and shouted angrily, grabbing at him. Zhang Zixing was no longer the rookie who was ambushed in the market, and with a light push, the guard flew out like a broken kite, crashing heavily.

  The rest of the guards did not expect the newcomer to be so formidable and were about to rush forward, when they suddenly heard the masked woman shout: "Halt!"

  "Master Zixing has finally arrived. It's been months since we last parted, and I thought you had forgotten about the appointment with the young lady...". What surprised the guards was that their own mistress actually curtsied to the man, "The servant doesn't know your identity, please forgive any offense."

  Zhang Zixing returned a courtesy: "No need to apologize, but I've been busy with mundane affairs lately. Although my heart is tied to Miss, I couldn't find time to come and see her. Moreover, just now there were many impolite words, I hope Miss won't be offended."

  He deliberately made the conversation ambiguous, but the woman was also calm and composed, smiling lightly: "Sir, you have a broad mind and great talent, how can you be so despicable? Just now I saw that your martial arts skills are extraordinary, it turns out that you are a man of both literary and military talents, it seems that this humble woman has misjudged you."

  Zhang Zixing did not expect the woman to be so generous and didn't dare to tease her again, saying: "Miss is overpraising me, may I ask for your name?"

  "A name is just a label, if you're called Mr. Purple Star, then that little girl can be called Green Girl." This Green Girl's meaning was very clear, anyway everyone uses fake names, so just call her whatever! Zhang Purple Star secretly cursed - this time I'm in big trouble, I really am "Purple Star" ah...

  Although Qing'er was open-minded, she was still an unmarried woman and it wasn't proper for her to be too familiar with Zhang Zixing. After inviting him into the grass hut and offering him a seat of honor, she got straight to the point: "Mr. Zixing is a master of extraordinary talent in the art of calculation. Last time I heard that you cleverly solved the difficult problem of the chicken and rabbit in the same cage, which benefited me greatly. Recently, Qing'er has also been thinking deeply about the second solution you mentioned, but no matter how hard she tried, she couldn't understand it. Only then did she realize that her distance from you was not measured by miles. Today, I'm fortunate to have you visit again, so please don't hesitate to instruct me."

  Those guards heard the young lady's words and were shocked, looking at Zhang Zixing with changed eyes. In their opinion, this young lady had a talent for strategy, geography, and astronomy, and was especially skilled in calculations, which made people admire her. Unfortunately, she was not a man, otherwise she would have already been famous in the imperial court. Today, hearing the young lady call this man named Zixing "a genius of calculation" and acknowledging that she was far inferior to him, it seemed that this man must have real talent and learning.

  Zhang Zixing looked at Qing'er, whose eyes shone with sincerity, and knew that she must have thought deeply about the second solution to "chicken and rabbit in the same cage". He secretly admired her spirit of diligence. Instead of immediately revealing the solution, he asked a question: "Miss Guan is fond of arithmetic, I suppose you have studied 'Tian Suan' thoroughly. But Miss, you don't know that the essence of 'Tian Suan' lies not only in the method of arithmetic, but also in the way of arithmetic!"

  "The essence of Tian Suan!" Qing Er heard this theory for the first time, and with a serious expression, he stood up and bowed respectfully: "May I ask, sir, what is the method of technique calculation? What is the way of technique calculation?"

  "The method of calculation is the theorem, formula, and operation of calculation, which are all recorded in the book 'Tian Suan'. However, the 'way of calculation' is not explicitly stated in 'Tian Suan', but rather it is a personal understanding of calculation. Once you understand this way, everything else becomes clear. Miss Qing Er may recall that I once said 'calculation requires creative thinking'? This is also part of my own understanding of the way of calculation. You are intelligent and proficient in the methods of calculation, but your thinking is still too rigid. If you can break through this limitation, your mastery of calculation will reach a higher level."

  Qing'er was extremely intelligent and had a vague understanding of his meaning. These few short sentences seemed to transport her to a strange and wondrous world she had never thought of before, and once she grasped it, she could gain a qualitative change.

  "Take 'chicken and rabbit in the same cage' as an example, on the surface it seems that there is not enough information to calculate, but looking at it from a different angle, this condition can also be created by itself." Qing Er's eyes lit up when he heard this, as if he had caught onto something crucial. Zhang Zixing continued, "Although I don't know the number of rabbits, I can assume it is already known and call it an 'unknown number'..."

  Because Qing Er is a math expert, Zhang Zixing asked her about the knowledge category that was not in "Tian Suan" - unknown numbers and equations. Let's assume the number of rabbits (i.e., heads) is x, since "chicken head + rabbit head = 35", so "chicken head = 35 - x". From this, it can be known that there are x rabbits, which should have 4x rabbit feet, and the number of chicken feet is (35 - x), so there should be 2 × (35 - x) chicken feet. Now that we know the total number of chicken and rabbit feet is 94, we can list the equation: 4x + 2 × (35 - x) = 94, thus it's easy to calculate the number of rabbits x = 12, and the number of chickens is 35 - 12 = 23.

  Of course, in order to make Qing'er understand better, Zhang Zixing changed the name of the unknown number X to "Jin" in the five elements. Qing'er had never heard of such a novel solution before, and her body trembled slightly with excitement and agitation. She couldn't help but be rude, immediately taking out paper and ink on the table to calculate. Zhang Zixing was seeing such a studious woman for the first time, and he couldn't help but have the idea of being a "mentor", so he explained it in detail.

  Qing'er's intelligence surpassed others, and his comprehension was exceptionally high. Before long, he grasped the usage of unknown numbers and linear equations, even proposing ideas for setting up more unknowns, leaving Zhang Zixing in endless praise.

  "Previously, I only knew that Master was extraordinary, but I didn't know he was so extraordinary!" Qing'er admired Zhang Zixing's ability and said: "Master is a rare talent in the world, I am lucky to have received Master's guidance. I am willing to become Master's apprentice, please accept me!"

  "Miss Qing is too modest. Although I'm fond of arithmetic, I only have a superficial understanding of it. There's no need to become a disciple. As the saying goes, 'a thousand cups are not enough when meeting a kindred spirit', I'm delighted to make the acquaintance of Miss Zi Xing, who shares similar interests. If I have some free time in the future, I'll definitely come to the thatched cottage to study arithmetic together with you."

  Qing'er heard his refusal, a hint of disappointment flashed in her eyes. When she heard the last sentence, she showed joy: "So it's good, just now I heard Mr. explain the essence of 'Tian Suan', which made me admire. In Qing'er's opinion, what Mr. has learned seems to be above 'Tian Suan'. I wonder where Mr. is from and what his current position is?

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