According to historical research, glass craftsmanship was already mastered in China during the Warring States Period. Unfortunately, this technology was not available in the Shang Dynasty. Although there were some precious crystals paid tribute by princes in the palace, they were all natural crystals and not artificial glass.
In fact, before the Leyden bottle was conceived, Zhang Zixing had considered the production of glass. The raw materials for glass are sand, limestone, sodium carbonate and mixtures. Sodium carbonate is soda, which has been widely used in later generations, the most common ones being soap, papermaking, and detergents.
Wait, but it was a problem in the Shang Dynasty, so I had to put it on hold for the time being. It is said that it was good luck. This time when conquering Dongyi, Zhang Zixing obtained the secret map of the mineral veins presented by Zou Qie. When he went to investigate, he also discovered other kinds of rich minerals.
Mineral deposits, including trona ore that can extract sodium carbonate, made Zhang Zixing extremely happy, secretly thinking that the reincarnation of Chi You was indeed not in vain.
Zhang Zixing passed the glass-making method developed by Super Brain to the conditions of the Shang Dynasty to several main craftsmen in the workshop, and told them to test repeatedly and not worry about failure. If there are any results, report them immediately. The craftsmen got this secret
Zhang Zixing repeatedly performed miracles and proposed ideas that were all unheard of, but they were all implemented into reality, even if he was not the supreme leader.
The Son of Heaven 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 had almost forgotten. He immediately ordered the driver to go back first, changed into civilian clothes, and sneaked out of the palace.
Zhang Zixing came to a bookstore in the market, picked up a copy of "Tian Suan" and flipped through it, and asked the store owner: "Excuse me, store owner, do you know where Tanwei Thatched Cottage is?"
"Turn left at this street intersection, and you can see the Prime Minister's Mansion. Enter the third alley next to the Prime Minister's Mansion." The shop owner looked at the "Tian Suan" in his hand and showed a clear look: "The guest is going to the thatched cottage to learn arithmetic.
Yes, please go quickly, the show should not be over yet."
"Next to the Prime Minister's Mansion?" Zhang Zixing thought for a moment and then asked: "The store's guess is good. I just came here because of his reputation. Who is the teacher? How much is the tuition fee?"
"The teacher is a young woman. Her face is covered with a veil and her face cannot be seen. However, her knowledge is extremely extensive. Especially in arithmetic, she is almost invincible. Several people have come to compare with her, and they all came back convinced.
.This woman lectures in public, and many people listen to her lectures, but she does not accept any academic fees. Everyone respects her as a 'female teacher'."
"Female teacher? Interesting..." Zhang Zixing muttered, thanked the shopkeeper, and walked straight in the direction of Tanwei Cottage.
The so-called "Tanwei Cottage" refers to a simple little house. The yard outside the house seems very spacious, but it is already crowded with people. These people are both men and women, all wearing civilian clothes, and they are listening attentively.
The female teacher in front was giving lectures. The female teacher was indeed the masked woman who had a relationship with Zhang Zixing, but the beautiful girl who was suspected to be Deng Chanyu was nowhere to be seen at this time. There were only a few sturdy men standing beside the masked woman.
Behind him, there seemed to be a guard.
Zhang Zixing wanted to see the masked woman's teaching skills, so she did not go forward to say hello, but stood in the corner and listened. After listening for a while, Zhang Zixing's face showed a look of surprise. This woman deserves the name of a female teacher.
, can combine the practical knowledge from the shallower to the deeper, and describe the corresponding mathematical knowledge, so that people can easily understand it. Many ingenious examples have not even been mentioned in "Tian Suan". From this, it can be seen that women are not only interested in mathematics.
She has considerable understanding and strong verbal expression skills. Although the knowledge explained is relatively simple, it is already quite rare.
At this time, the masked woman's lecture was coming to an end: "That's the end of today's lecture. Everyone, please leave and come back to the thatched cottage in three days to listen to the lecture."
After hearing the words, everyone dispersed one after another. Zhang Zixing walked forward quickly and wanted to say hello to the masked woman. Unexpectedly, a guard thought that he had evil intentions, scolded him angrily, and arrested him. Zhang Zixing was no longer the same person as before.
The rookie who was attacked by someone in the market gave way to the guard's claws. With a slight push, the guard was thrown out like a kite with broken strings and fell solidly.
The remaining guards didn't expect the intruder to be so powerful, and were about to rush forward when they suddenly heard the masked woman shout: "Stop!"
"Mr. Zixing is finally here. He has not been seen since we were separated a few months ago. He thought he had forgotten about our little girl's appointment..." What surprised the guards was that their young lady actually saluted the man.
, "This servant does not know your identity, so I have offended you. Please forgive me."
Zhang Zixing returned the gift: "It's okay, but I've been busy with a lot of worldly affairs recently. Although I care about Miss, I haven't been able to get around to see you. Besides, I was rude just now. I hope Miss will not blame you."
He deliberately made his words very coquettish, but the woman was also generous and said with a chuckle: "Sir, he has great talent, how can he be so useless? Just now I saw that he has extraordinary skills. It turns out that he is a versatile man in both civil and military affairs, but this little girl made a mistake.
"
Zhang Zixing did not expect the woman to be so generous, but he was too embarrassed to tease her again, and said: "Young lady, I have given you the award. May I ask your name?"
"The name is just a title. Since Mr. Zixing is named Zixing, let's call the little girl Qing'er." The meaning of Qing'er is very obvious. Everyone uses pseudonyms anyway, so you can call her whatever you want! Zhang Zixing secretly called Qu - this
The loss is huge, I am really called "Purple Star"...
Although Qing'er was generous, she was an unmarried woman after all, and it was not easy to talk to Zhang Zixing all the time. After inviting him to sit in the thatched cottage, she went straight to the topic: "Mr. Zixing is a wizard in arithmetic. Last time I heard that Mr. Zixing cleverly solved the problem of chickens and rabbits in the same cage.
Qing'er has benefited a lot from this difficult problem. Recently, Qing'er has also been thinking hard about the second solution mentioned by the teacher, but he still can't find the solution. Only then did he know that the distance between him and the teacher is not measured by miles. Fortunately, the teacher is here again today. Please also give me some advice.
Don’t hesitate to give me advice.”
When the guards heard what the young lady said, they all expressed surprise, and their eyes changed when they looked at Zhang Zixing. In their opinion, this young lady was talented in latitude and longitude, and knew everything about astronomy and geography, especially arithmetic.
It is even more admirable, but it is a pity that he is not a man, otherwise he would have already become famous in the court. Today I heard the young lady call the man named Zixing an "arithmetic wizard" and considered herself far inferior. It seems that this
A man must have real talent and learning.
Zhang Zixing looked at Qing'er who looked sincere and knew that she must have thought hard for her second solution to the "chicken and rabbit in the same cage". He secretly praised her research spirit. He did not immediately tell the solution, but asked a question.
: "I think Miss is very fond of arithmetic, and she must have studied the book "Tian Suan" very carefully. But she doesn't know that the essence of "Tian Suan" is not only the method of arithmetic, but also the way of arithmetic!
"
The essence of "Tian Suan"! This was the first time Qing'er heard this theory. He stood up with a solemn gaze and bowed respectfully: "Sir, what is the method of arithmetic? What is the way of arithmetic?"
"The 'methods of calculations' are theorems, formulas, calculation methods, etc. of calculations, which are all recorded in the book "Tian Suan", but the "way of calculations" is not stated in "Tian Suan", that is,
My personal understanding of arithmetic. One way to understand arithmetic is to understand everything. Miss Qing'er may remember that I once said that "arithmetic arithmetic requires strange thinking"? This is also my understanding of arithmetic. Miss Qing'er is extremely intelligent and proficient in arithmetic.
I know the method of arithmetic, but my way of thinking is still too rigid. If I can make a breakthrough in this aspect, my arithmetic cultivation will surely reach a higher level."
Qing'er was extremely smart and vaguely understood what he meant. She felt as if these few words had brought her to a wonderful world that she had never thought of before. Once she understood something, she would achieve a qualitative change.
"Take the question of 'chicken and rabbit in the same cage' as an example. On the surface, it seems that the conditions are too few and difficult to calculate, but from another perspective, you can also create these conditions yourself." Qing'er heard this, his eyes lit up, and he seemed to
After capturing something key, Zhang Zixing continued: "Although I don't know the number of rabbits, I can assume that it is known and call it the 'unknown number'..."
Since Qing'er is considered an expert in mathematics, Zhang Zixing proposed to her a knowledge category that was not included in "Tiansuan" - unknown numbers and equations. First, let's assume that the number of rabbits (that is, the number of heads) is x, because "chicken head + rabbit"
Head = 35", so "Chicken head = 35-x". It can be seen from this 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. It is now known that the total number of chicken and rabbit feet is 94. The relationship can be listed: 4x+2×(35-x)=94. Therefore, the number of rabbits can be easily calculated x=12, and the number of chickens
Just counting is 35-12=23.
Of course, in order for Qing'er to understand it better, Zhang Zixing changed the name of the unknown number
, immediately took out paper and pen and ink and started calculating on the table. This was the first time for Zhang Zixing to see such a studious woman. He couldn't help but want to become a "mentor" and explained it in detail.
Qing'er was extremely intelligent and perceptive. He soon understood and mastered the use of unknown numbers and linear equations of one variable. He even came up with ideas for setting up more unknown numbers, which made Zhang Zixing full of praise.
"Before, I only thought that my husband was extraordinary, but I didn't know that he was so extraordinary!" Qing'er was so impressed by Zhang Zixing's ability that she said: "Sir, he is an extraordinary master. Qing'er is really lucky to have his guidance. The little girl is willing to worship him.
As a teacher, I hope you will be successful!"
"Miss Qing'er is too modest. Although I like arithmetic, I only have a superficial understanding of arithmetic. There is no need to become a disciple. As the saying goes, a thousand cups are too little when drinking with a close friend. Zi Xing is very happy to be able to meet such a good person as Miss Qing'er.
Infinitely, if I have free time in the future, I will definitely come to the thatched cottage to study arithmetic with the lady."
When Qing'er heard his rejection, there was a look of regret in his eyes. When he heard the last sentence, he looked happy again: "That's good. I just heard Mr. explain the essence of "Tian Suan", which is amazing. From Qing'er's point of view, Mr.
What I have learned in my mind seems to be still above "Tian Suan". I wonder who Mr. Sir is? What is his current position?"