According to historical research, glass technology has been mastered in China's Warring States Period, but unfortunately there is no such technology in the Shang Dynasty, although there are some treasures in the palace that the princes paid tribute to, but they are all natural crystals, not artificially made glass.

In fact, before the Leiden bottle was conceived, Zhang Zixing considered the production of glass, which is made of sand, limestone, sodium carbonate and mixture. Sodium carbonate, that is, soda, was widely used in later generations, the most common such as soap, papermaking, detergent, etc., but it was a problem in the Shang Dynasty, so it had to be temporarily stranded. It is also good luck, this time to conquer Dongyi, Zhang Zixing obtained the secret map of the ore veins presented by Zou Xuan, and when he went to investigate, he also found other kinds of rich mineral deposits, including trona ore that can extract sodium carbonate, which made Zhang Zixing overjoyed, and secretly said that this reincarnation of Chiyou was really not in vain.

Zhang Zixing passed on the glass-making method that best met the conditions of the Shang Dynasty to several major craftsmen in the workshop, and instructed him to try and test, not to worry about failure, and to report immediately if there was a result. When the craftsmen learned that this secret technique could "turn sand and stone into crystal", they were immediately stunned, but no one showed any doubts. Zhang Zixing has repeatedly created miracles, and all the ideas he put forward are unheard of, but they are all put into practice, even if he is not the supreme Son of Heaven, he is still a god-like existence in the minds of these craftsmen.

After coming out of the royal workshop, Zhang Zixing suddenly remembered something that he almost forgot, and immediately ordered the car to drive back first, changed into a set of civilian clothes, and sneaked out of the palace.

Zhang Zixing came to a bookstore in the market, picked up a copy of "Heavenly Calculation" and flipped through it, and asked the shopkeeper: "May I ask the shopkeeper, do you know where the Tanwei Caotang is?"

Turn left at this street entrance, and you can see the Prime Minister's Mansion, and enter the third lane next to the Prime Minister's Mansion. The shopkeeper looked at the "Heavenly Calculation" in his hand, and showed a clear expression: "The guest is going to the grass hall to learn arithmetic, please go quickly, it should not be over at this time." ”

"Next to the Prime Minister's Mansion?" Zhang Zixing thought for a while, and then asked: "The shopkeeper guessed well, I just came here, may I ask who is the teacher who is lecturing?

"The teacher was a young woman, covered with a veil, and could not see her appearance, but her knowledge was incomparably broad, especially in arithmetic, almost invincible, and several people had admired her to compare with her, and all of them were convinced. This woman gave a lecture in public, and there were many people who listened to the lecture, but she did not receive any academic qualifications, and everyone respected her as a 'female teacher'. ”

"Female teacher, interesting ......" Zhang Zixing muttered, thanked the shopkeeper, and walked straight in the direction of Tanwei Caotang.

The so-called "Tanwei Caotang" refers to a simple hut, and the courtyard outside the house seems to be very spacious, but at this moment it is already crowded with people, these people are men and women, all of them are civilians, and they are listening attentively to the lecture of the female teacher in front of them. The female teacher is indeed a masked woman who has a relationship with Zhang Zixing, but the beautiful girl who is suspected of being Deng Chanyu is nowhere to be seen at this time, only a few big men stand behind the masked woman, as if they are guards.

Zhang Zixing wanted to see the masked woman's ability to teach, so he didn't come forward to say hello, but stood in the corner and listened. After hearing it for a while, Zhang Zixing's face showed a look of surprise. This woman deserves the name of a female teacher, and can combine the corresponding mathematical knowledge from shallow to deep, so that people can easily understand, and many ingenious examples are not even mentioned in "Heavenly Calculation". It can be seen that the woman not only has a considerable understanding of mathematics, but also has strong oral communication skills, although the knowledge explained is relatively shallow, but it is already quite rare.

At this time, the masked woman's lecture was nearing the end: "This is the end of today's lecture, please disperse and come to the grass hall to listen to the lecture in three days." ”

When everyone heard this, they dispersed, and Zhang Zixing walked forward quickly, wanting to say hello to the masked woman. One of the guards thought he had bad intentions, and he screamed angrily and grabbed him. Zhang Zixing was no longer the rookie who was attacked in the market at this time, so he let the guards claw and gently pushed, and the guards were thrown out like a kite with broken strings, and fell firmly.

The rest of the guards were so powerful that they were about to rush up, when they heard the masked woman shouting, "Stop!"

"Mr. Zixing is finally here, since a few months ago, he has never seen the big car coming, and when Mr. has forgotten the little girl's covenant......" To the surprise of the guards, his own lady actually gave a salute to the man, "The next person does not know the identity of Mr., I have offended, please forgive me." ”

Zhang Zixing returned the salute: "It's okay, but there have been a lot of mundane things recently, although I have a heart for Miss, I haven't been able to come to see her, and there are many rudenesses, I hope Miss won't blame." ”

He deliberately said it very ambiguously, but the woman was also generous, and chuckled: "Mr. has a great talent, how can he be so tired? ”

Zhang Zixing didn't expect the woman to be so generous, but she was embarrassed to make any more teasing words, and said, "Miss has won the award, may I ask Miss Fang's name?"

"The name is just a title, Mr. Zixing's name is Zixing, so the little woman is called Qing'er. "This Qing'er's meaning is obvious, anyway, everyone uses a pseudonym, you can call it whatever you want! Zhang Zixing secretly called Qu - this time I lost a lot, I really called "Zixing"......

Although Qing'er is generous, after all, she is an unmarried woman, and it is not easy to talk to Zhang Zixing all the time, and after inviting him into the grass hall to take a seat, she went straight to the topic: "Mr. Zixing is a wizard of arithmetic, and the last time I heard that Mr. solved the problem of chickens and rabbits in the same cage, which benefited Qing'er a lot. Today, I am fortunate to have Mr. again, and please give me advice. ”

When the guards heard the young lady's words, they all showed surprise, and their eyes changed when they looked at Zhang Zixing. In their opinion, this young lady has a talent for latitude and longitude, astronomy and geography, knowing everything, especially arithmetic, which is even more admirable, but unfortunately it is not a man's body, otherwise he would have already been famous in the court. Today, I heard the young lady call this man named Zixing a "wizard of arithmetic", and he thinks that he is far inferior, it seems that this man must have real talent and learning.

Zhang Zixing looked at Qing'er with sincere eyes, knowing that she must have thought hard about the second solution of "chickens and rabbits in the same cage", and secretly praised her research spirit, he did not immediately say the solution, but asked rhetorically: "Miss Guan is very fond of arithmetic, and must have studied the book "Heavenly Calculation" quite intensively. But the young lady didn't know that the essence of "Heavenly Calculation" is not only the method of arithmetic, but also the way of arithmetic!"

The essence of "Heavenly Calculation"! Qing'er heard this theory for the first time, stood up with a solemn gaze, and said respectfully: "Mr. Ask for advice, what is the method of arithmetic? What is the way of arithmetic?"

"The 'method of arithmetic' is the theorem, formula, and method of arithmetic, which are all recorded in the book "Heavenly Calculation", but the "way of arithmetic" is the way that is not stated in "Heavenly Arithmetic", that is, the individual's understanding of arithmetic. One way, all the way. Miss Qing'er may remember that she once said that 'arithmetic requires whimsy', and this is also the way of arithmetic that she has learned. The young lady is very intelligent and proficient in arithmetic, but her way of thinking is still too rigid, if she can make a breakthrough in this area, her arithmetic cultivation will definitely go to the next level. ”

Qing'er is extremely smart, and vaguely understands what he means, feeling that these few words seem to bring him to a wonderful world that he has never thought of before, and once he understands it, he can obtain a qualitative mutation.

"Take the question of 'chickens and rabbits in the same cage' as an example, on the surface, it seems that the conditions are too few to calculate, but from another point of view, this condition can also be created by itself," Qing'er heard this, her eyes lit up, and she seemed to have captured something crucial, only to hear Zhang Zixing continue: "Although I don't know the number of rabbits, I can assume that they are known, and call them 'unknowns'......"

Since Qing'er is a mathematics expert, Zhang Zixing proposed to her the knowledge categories that are not in "Heavenly Calculation" - unknowns and equations. First set the number of rabbits (that is, the number of heads) is x, because "chicken head + rabbit head = 35", so "chicken head = 35-x". From this, it can be seen that if there are x rabbits, there should be 4x rabbit feet, and the number of chickens is (35-x), so there should be 2 × (35-x) chicken feet. Now that we know that there are a total of 94 chickens and rabbits, we can list the relation: 4x+2×(35-x)=94, so it is easy to calculate the number of rabbits x=12 and the number of chickens 35-12=23.

Of course, in order to make Qing'er better understand, Zhang Zixing changed the name of the unknown number x to the "gold" in the five elements, Qing'er had never heard such a novel solution, her body trembled slightly because of excitement and excitement, she couldn't care about the rudeness, and immediately took out the paper and pen and ink on the table to calculate, Zhang Zixing was the first time to see such a studious woman, and couldn't help but be moved by the idea of being a "mentor" and explained in detail.

Qing'er is very wise, and his surname is very high, and he soon understood and mastered the use of unknowns and unary equations, and even put forward the idea of setting more unknowns, which made Zhang Zixing full of praise.

"I only said that Mr. was extraordinary, but I didn't know that Mr. was so extraordinary!" Qing'er admired Zhang Zixing's ability so much that she threw herself to the ground: "Mr. is not a master of the world, Qing'er can be taught by Mr., it is really a blessing in three lives." The little girl is willing to worship her husband as a teacher, and she hopes to be fulfilled!"

"Miss Qing'er is too humble, although she likes arithmetic, she is only a little superficial, and there is no need to apprentice. The so-called wine is less than a thousand cups of confidants, Zixing can get to know Miss who is equivalent to a good person, and his heart is also infinitely happy. ”

Qing'er heard him refuse, her eyes showed regret, and when she heard the last sentence, she showed joy again: "That's okay, I just heard Mr. explain the essence of "Heavenly Calculation", which is convincing. In Qing'er's opinion, it seems that what Mr. has learned in his chest is still above "Heavenly Calculation", I don't know who Mr. is?

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