Luo Yong was very happy for Qiao Junlin's arrival.
He even treated the group to a meal to express his welcome.
This has never happened in the past, but these people who learn arithmetic here have treated Luo Yong to dinner many times.
Since Luo Yong started teaching, he rarely paid for the food he ordered at the Xu Family Guest House. .
In addition, there were many students who gave him things.
Those things may be expensive or cheap, but generally they are very practical.
The most common ones are pork and mutton.
Sometimes the Luo family can't finish it themselves, so they give it to his disciples. , and sometimes take it to the cement workshop to give extra 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 didn't seem to use them very much.
Si Niang and Wu Lang were still in the enlightenment stage.
It was a bit luxurious to give them such good things, so They all were put away.
Qiao Junlin brought two manuscripts to Luo Yong, both of which he copied word for word.
The handwriting was clear and regular.
He didn't know how much time it took to complete.
At this time, there was no movable type printing technology, and all books were copied by hand.
You either copied them yourself or paid to buy them copied by others.
Books at this time were very rare, both in terms of time, energy and price.
After not seeing each other for half a year, Qiao Junlin looked much more stable than when we met in Chang'an City last summer.
Every time they met, Luo Yong could see the growth in this young man.
He grew up so fast that time seemed to speed up on him.
The current Qiao Junlin was no longer the one who came to Luo Yong to learn how to make tofu.
A cute and stubborn boy.
All growth must be accompanied by pain.
The perseverance and forbearance in the eyes of young people always make people feel heartbroken.
Luo Yong sometimes couldn't help but wonder whether this person would grow up rapidly in such an acceleration and then grow old quickly.
"Some time ago, we learned the calculation method of using symbols to replace unknown numbers.
Now many new people have come.
I am afraid that they cannot keep up with our learning progress.
If we start the class again, it will take up a lot of time for all the gentlemen who came before. , so I thought about it and decided to share with you the application of arithmetic in geometric structures.”
When Luo Yong said these words, Qiao Junlin was sitting behind a Kang table not far from him, with his black and white eyes open, listening very seriously.
Perhaps it was because he had locked himself in his room and studied hard in the past two years.
Qiao Junlin looked much fairer now.
His handsome facial features were soft, and his eyes were serious and persistent, but also revealing.
With a bit of innocence, when he looked at Luo Yong calmly, 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 geometry knowledge, Luo Yong started from the simplest plane geometry.
At first, he just calculated the perimeter and area, and the pace was very slow, mainly to allow the newcomers to have enough time.
Adapt to Arabic numerals and calculation methods.
The several students brought by Dr.
Chen this time are generally quite qualified, and their backgrounds are naturally good, and they are not ignorant people.
They have arithmetic foundation before.
For those legends about Luo Sanlang , and they didn’t quite believe it.
After all, they were just a country boy, so how could they be exposed to those truly profound arithmetic methods?
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However, after taking a few classes, their ideas completely changed.
After teaching the perimeter algorithm, Luo Yong began to teach them the area algorithm, first teaching squares and rectangles.
This is not difficult for many scholars, and they often involve this aspect in their daily lives. , one of the more typical ones is the calculation of acres.
After the square, Luo Yong began to teach the area calculation method of the triangle.
First, he taught the right triangle.
This is not difficult.
It is still the same algorithm as the square, which is to divide by two.
When he got to the non-right triangle, some foundations were not deep enough.
Yes, it started to be difficult.
In fact, in the 21st century, the calculation of the area of a triangle is only a matter for the upper grades of primary school mathematics.
It is at this time that they will come into contact with an important theorem, which is the Pythagorean theorem.
The primary school students are just learning it, not knowing how important this theorem is in life, let alone that more than a thousand years ago, this theorem was a profound knowledge that only a small number of people had access to.
When Luo Yong used a small piece of plaster to draw a triangular shape on a small blackboard smeared with tung oil in the hall of the Xu family's guest house, and then used a dotted line to draw his height, he gave these people in the seventh century AD When readers talk about the Pythagorean Theorem, many people are shocked in their hearts.
Some people were surprised by the sophistication and simplicity of this calculation method, while others were surprised that this young man who was born in a small mountain village and was nicknamed "Coffin Board" actually seemed to have read Zhou Bi's book.
However, this is just the beginning.
After learning the triangle, it is the trapezoid, and after the trapezoid, it is the circle.
Among the various calculations of the circle, pi is often included in the design.
Pi also existed at this time, and was mentioned in the Nine Chapters on Arithmetic.
It is usually called the "ancestral ratio" and is calculated by cutting a circle.
However, when Luo used a simple number and a simple calculation formula, he was able to calculate the circumference and area of a circle, and he didn't seem to think that this was anything extraordinary.
He easily found it in this guest house.
When taught to everyone, many people really discovered that arithmetic problems that were originally very complicated and difficult to understand in their minds could actually be presented in such a simple way.
Just like what Luo Sanlang said to everyone before, he only teaches some simple arithmetic methods, and even people who are not very smart can learn and apply them.
In the eyes of many people, this is the most amazing wisdom.
It explains originally complex things in a surprisingly simple way.
This kind of wisdom that reduces complexity to simplicity is originally very rare in this world.
Dr.
Chen originally came to Xipo Village with an attitude of broadening his horizons, but he never thought that after just a few days, he would devote himself wholeheartedly to learning.
When he has free time, Dr.
Chen often advises several of his students to study harder.
Opportunities like today will probably be rare in the future.
For a person who truly desires knowledge, he can Wandering like this in an ocean of knowledge that he has never reached before is definitely the luckiest thing in his life.
Apart from this old gentleman who was forgetting to eat and sleep, among his students, the one who studied most seriously was Qiao Junlin.
Qiao Junlin doesn't have much talent in poetry and divination.
Although the cultural courses are not bad, because he has learned Kegu, he has mastered all the subjects quite solidly.
But what really makes him stand out is his martial arts.
Wait until this time After going back, there will be one more calculation.
Among those who originally studied in the Xu family guest house, Siniang, although she is young, learns faster than many adults.
In addition to her talent, there is also the reason why she is Luo Yong's younger sister, so it is very convenient for her to ask for advice. .
When Qiao Junlin and the others arrived, first an old gentleman who was eager to learn, and then soon Qiao Junlin, who didn't even know 1234, ran in front of her.
The girl Siniang finally felt a little nervous, and then I don’t think I am very smart and learn quickly.
Luo Yong saw that his elder sister seemed to have become more stable after suffering some blows, and he was naturally happy to see this happen.
Although he was famous for spoiling children, he had absolutely no intention of raising them into greenhouse flowers. , the ups and downs they should experience should always be experienced by themselves.
Looking back on when he first woke up, Luo Yong didn't even know how to support such a large group of children at home.
At the beginning, he just wanted to live a low-key life, but unknowingly, he still pushed himself to On the cusp of the storm.
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Recalling that when he was a student in the 21st century, he once learned an idiom that he understood but did not understand: "Sacrifice one's life for righteousness."
In the long history, in countless eras of peace or war, there are always some people who risk life and death for the sake of their family, country, clan, and the people of the world, and even accompany their families and children.
Regardless, this was something difficult to understand for Luo Yong at the time.
How could that ignorant and ordinary young man at that time imagine that one day he would embark on the same path as those people?
Perhaps the things he did today can allow those heroes who should have died in misery to have a relatively comfortable 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 dedication and sacrifice of countless ancestors.
However, Luo Yong was fortunate enough to know in advance the crystallization of wisdom for more than a thousand years 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 come so far.
In fact, he had never slowed down his progress, heading in the direction of uncertainty about life and death, as if it was fate.
When spring arrived, Luo Yong and his disciples sowed many seeds of Eucommia trees on the hillside.
In another two years, when these eucommia saplings are roughly grown, they can start making eucommia rubber wheels.
Because Eucommia gum is a hard rubber, not a soft rubber, it is very suitable for outer tires, but there is no other way for inner tubes.
Under the current situation, they can only make solid wheels, and the entire wheel is made of Eucommia gum, or filled inside.
Other materials.
However, Luo Yong didn't know that just when he was thinking about upgrading Yanerfei's wheels, in an ordinary house in Lishi County, a couple was facing the kang table, and the Qian who was processing Yanerfei's inner tubes was sitting there.
At the bottom level, unlike others, the two of them did not rely solely on their hands to complete the work.
Instead, they made two tools that looked simple but were actually quite convenient and labor-saving.
This tool is mainly composed of a wooden structure, a thousand-layer inner tube, and an iron needle.
Several gears are also used in it.
As long as they turn a handle on the wooden frame, driven by the gears and tracks, the needle The iron needle will pierce down on its own, driving the lines through several layers of thick linen.
As the iron needle moves up and down, it will soon pierce rows of neat needle holes in the linen.
Then the couple put fine linen thread through the needle holes on the linen cloth and made it into a thousand-layer bottom.
This method could save them a lot of effort, and the final stitching pattern was also very uniform, so they The mille-feuille bottoms that my family has recently made can basically be sold at a relatively good price.
If Luo Yong could see this thing, he would definitely recognize it as the prototype of the sewing machine.
This couple did not originally make Yanerfei inner tubes.
The husband originally made bamboo chains.
Because he had some contact with Heng's car-making shop, he had also seen the large and small gears used on Yanerfei.
In this winter, because he felt sorry for his young wife, he was always there When Na Yaner flew inner tubes, his hands were red and swollen.
After several attempts, he finally made such a tool.
Then they found that with this tool, they could relatively easily make money by making Yan'er flying inner tubes. , so they started this job together.
These two people were very happy to have a useful tool.
They worked hard to earn money every day, but they had no idea how much convenience this seemingly inconspicuous tool would bring to the society in the future.
Little did he know that he had unknowingly become the world's earliest sewing worker. gd1806102: