Luo Yong was still very happy about Qiao Junlin's arrival. He even invited the group to have a meal and expressed his welcome.

This has never happened in the past. But these people who are learning arithmetic here have invited Luo Yong to eat a lot. Since Luo Yong started teaching, he has been ordering dishes at the Xu family's hotel and has less time to pay for the bill himself.

There are also many students who give him things. Those things are expensive and cheap, but they are generally very practical. The most common one is pork and mutton. Sometimes the Luo family can't finish it, so they will distribute it to his disciples. Sometimes they will also go to the cement workshop to add meals to the workers.

Dr. Chen and his party also brought gifts to Luo Yong this time, mainly some four treasures of the study. Luo Yong himself didn't seem to use it very much. Si Niang Wulang is still in the enlightenment stage now, and it was a bit luxurious to give them such good things, so he put them away.

Qiao Junlin brought two handwritten copies for Luo Yong, which were copied by himself word by word. The handwriting was clear and correct, and I don’t know how much time it took to complete it.

There is no movable type printing technology at this time. The books are all hand-copying. Either copy them yourself or spend money to buy others to copy them. Whether in terms of time and energy or price, books at this time are rare.

It took half a year to see each other, and Qiao Junlin looked much more stable than when she met in Chang'an City last summer.

Every time he met, Luo Yong could see the growth of this young man. He grew up too fast, and time seemed to speed up on him. Qiao Junlin is no longer the soft and stubborn boy who came to Luo Yong to learn to make tofu.

All growth must be accompanied by pain.

The perseverance and tolerance in the eyes of young people are always heartbreaking. Luo Yong can't help but wonder whether this person will grow up quickly with such acceleration and then grow old quickly...

"...A few days ago, we learned how to use symbols instead of unknown numbers. Now there are many new people coming. I am afraid that they will not be able to keep up with our learning progress. If we start class again, it will take a lot of time for you guys who have arrived earlier. So I thought about it and decided to share with you the application of arithmetic in geometric structures."

When Luo Yong said this, Qiao Junlin sat upright behind a kang table not far from him, with a pair of black and white eyes open and listening very seriously.

Perhaps because in the past two years, he has mostly locked himself in the house to study hard, Qiao Junlin now looks much whiter. His facial features are gentle, his eyes are serious and persistent, but they are a bit innocent. When he looked at Luo Yong quietly, his focused expression seemed to be looking at the whole world.

And in the days that followed, what Luo Yong showed him was indeed a brand new world.

Regarding the teaching of geometric knowledge, Luo Yong started from the simplest plane geometry. At the beginning, he just calculated the circumference and area, and placed the pace very slowly, mainly to allow the newcomers to have enough time to adapt to Arabic numerals and calculation methods.

This time, the students brought by Dr. Chen were generally well qualified, and naturally had a good background. They were not ignorant. They had a foundation in arithmetic before and did not believe in the legend about Luo Sanlang. After all, they were just a country boy, so how could they get in touch with those truly sophisticated arithmetic methods? As a result, after a few classes, their ideas completely changed.

After teaching the algorithm of circumference, Luo Yong began to teach them the algorithm of area. He first taught squares and rectangles, which is not very difficult for many scholars. They often involve this content in their daily lives. The more typical one is the calculation of land acres.

After the square, Luo Yong began to teach the area calculation method of triangles. First, he taught right-angle triangles. This is not difficult, but the same algorithm as the square, which is to divide it from two. When a non-right triangle has some foundations that are not deep enough, he will start to get into difficulties.

In fact, in the 21st century, the area calculation of triangles was just the content of the senior grades of primary school mathematics. At this time, they would come into contact with an important theorem, that is, the Pythagorean theorem.

Primary school students just learned it, not knowing how important this theorem is in life, nor knowing that this theorem was more than a thousand years ago, it was still a profound knowledge that only a small number of people could access.

When Luo used a small piece of gypsum in the hall of the Xu family's guest house, he drew a triangle shape on a small blackboard with tung oil, and then used a dotted line to draw his height, and told these readers of the seventh century AD that many people were shocked.

Some people were surprised at the ingenuity of this calculation method, while others were surprised at the young man who was born in a small mountain village and nicknamed the coffin board, which seemed to have read the book "Zhou Ren".

However, this is just the beginning. After learning triangles, they are trapezoids. After trapezoids, they are circles. In the calculation of circles, pi is often designed.

Pi also existed at this time, and it was mentioned in the Nine Chapters of Arithmetic. It is usually called "Zuyuan Rate", which is calculated through the Circle-cutting Technique.

However, when Luo used a simple number and a simple formula to calculate the circumference and area of ​​a circle, and did not seem to think that this was a great thing. When he was teaching everyone in this guesthouse, many people really discovered that the arithmetic problems that were originally very complicated and difficult to understand in their impression could also be presented in such a simple way.

Just as Luo Sanlang had told everyone before, he only taught some simple algorithms, and even if he was not a very smart person, he could apply what he learned.

In the eyes of many people, this is the most amazing wisdom. It explains originally complex things in an surprisingly simple way. This wisdom of simplifying complexity is originally very rare in this world.

Dr. Chen originally came to Xipo Village with a broad vision. He never thought that after just a few days, he devoted himself to his learning state.

When he has time, Dr. Chen often advises his students to study harder. An opportunity like today is unlikely to be encountered in the future. For a person who truly desires knowledge, being able to wander in a sea of ​​knowledge that he has never reached before is definitely the luckiest thing in his life.

In addition to this old man who has been busy and sleeping, among his students, Qiao Junlin is the most serious in studying.

Qiao Junlin does not have much talent in poetry and calculation. Although the cultural courses are not bad, because he has a deep learning and has mastered all subjects quite solidly, what really makes him stand out is his martial arts. After he goes back this time, he will have to add another arithmetic.

Among the people who were originally studying in the Xu family's hotel, Si Niang was young, but she learned faster than many adults. In addition to her talent, there is also the reason why she, as Luo Yong's sister, is very convenient for asking for advice.

After Qiao Junlin and the others came, they first became an old man who was eager to study, and soon, Qiao Junlin, who had never known 1234, ran to her front. The girl Si Niang finally felt a little nervous and no longer felt that she was very smart and learned very quickly.

Luo Yong seemed to have become more steady after seeing his sister being hit, so he was naturally happy to see her success. Although he is a well-known child, he has absolutely no intention of growing them into greenhouse flowers. He should always let them experience the ups and downs that should be experienced by themselves.

Looking back at the time when he just woke up, Luo Yong didn't even know how to support such a large group of children in his family. At the beginning, he just wanted to live a low-key life, but before he knew it, he pushed himself to the forefront.

Looking back at the time when he was a student in the 21st century, he once learned an idiom he could understand but did not understand: "Sacrifice one's life for righteousness."

In that long river of history, in those countless peaceful or war-torn eras, there were always some people who put life and death aside for their family, country, and people in the world, and even accompany their families and children. This was a difficult thing to understand at that time.

How could that ignorant and ordinary boy at that time think so hard that one day I will take the same path as those people?

Perhaps what he did today can allow those heroes who should have died in tragedy to have a relatively peaceful and peaceful life.

The progress of the times has never been taken for granted. The development process of human civilization is actually a process of the efforts and sacrifices of countless ancestors.

However, Luo Yong was fortunate to learn about the crystallization of wisdom for the next thousand years in advance in the seventh century AD. Although he repeatedly reminded himself to be low-key and cautious, when he looked back, he realized that he had already walked so far. In fact, he had never slowed down his pace of progress and was heading towards the uncertain direction of life and death, as if he was destined.

When spring came, Luo Yong and his disciples sowed many seeds of Eucommia tree on the hillside.

After two years, after these Eucommia saplings grow roughly, they can start making Eucommia ulmoide wheels.

Because Eucommia ulmoides are hard glue, not soft glue, it is very suitable as an outer tire, but there is no way to use the inner tube. In this case, they can only make solid core wheels, and the entire wheel is made of Eucommia ulmoides, or other materials are filled in it.

However, Luo Yong didn't know that just when he was considering upgrading Yan'erfei's wheels, in an ordinary house in Lishi County, a couple was working on the thousand-layer bottom of Yan'erfei's inner tubes against the kang table. Unlike others, they did not rely entirely on their hands to complete them, but made two tools that looked simple but were actually quite labor-saving.

This tool is mainly composed of a wooden structure, a thousand-layer bottom inner tube, and an iron needle. Several gears are used. As long as they turn a handle on the wooden frame, under the driving of the gears and tracks, the iron needle will be laid down by itself, driving the lines through several thick layers of linen cloth. The iron needle will be laid up and down, and the iron needle will be laid in rows of neat needle holes on the linen cloth.

Then the couple took the needle holes on the linen and put them into a thousand-layer bottom. This method can save them a lot of effort, and the needle and thread patterns finally absorbed are also very even, so the thousand-layer bottoms they have recently made can basically be sold at a relatively good price.

If Luo Yong could see this thing, he would definitely recognize it. This is the prototype of the sewing machine.

This couple didn't both of them have Yan'erfei inner tubes. The husband originally made bamboo chains because he had some contact with Heng's car manufacturer and had seen the big and small gears used on Yan'erfei. In this winter, he felt sorry for his young wife, who always grinds his hands red and swollen when he was taking Yan'erfei inner tubes. After several attempts, he finally made such a tool. Then they found that with this tool, they could make money by making money by Yan'erfei inner tubes relatively easily, so they started this job together.
Chapter completed!