Chapter 122: The Shoelace Theorem. Those who
rushed to Changningwei to buy an article were none other than Chen Moqun, the mountain chief of Yanping Academy, and his friend Mr. Tuohu He Liangjun.
After the two entered Changning Guard, they found out that Su Ze was farming at the edge of the Jian River at the entrance of the village. He Liangjun, who was impatient, directly pulled Chen Moqun out of Changning Guard and went to look for Su Ze at the edge of the Jian River.
At this time, Lin Liangjun, the little carrot head, was instructing other children to measure the acres of fields. These were new fields created with the excavated mud after the creek was built.
The mud on the river bottom is rich in nutrients, so floodplains have been the cradle of human civilization since ancient times. The Nile River that often flooded fed the ancient Egyptians. River flooding brought destruction and rebirth to civilization.
These fields are close to rivers, and as long as they are leveled, they will be prime paddy fields.
Su Ze asked the little carrot heads to clear the fields and survey and draw detailed maps. Another purpose was to plan and design irrigation water conservancy facilities.
For children of Xiaoluotou's age, being able to take classes outdoors is the happiest thing.
Since awakening his mathematics skills, Su Ze has added mathematics courses in addition to the original introductory learning courses.
Calculating the area of acres is naturally not something these children can do, but it is no problem to let them measure and draw maps. Lin Liangjun directed the children to pull the ruler and record while measuring.
He Liangjun had not seen such a childlike scene for a long time. He recalled his hometown, Songjiang Prefecture before the Japanese turmoil. In early summer, the fields were full of children running.
Regarding the current situation, He Liangjun could no longer complain. The imperial court had been suppressing the Japanese for so many years, and the more they suppressed the Japanese, the more serious it became. Even the dignified Songjiang Mansion was poisoned by the Japanese pirates.
I didn’t expect to see such a paradise on the coast of Fujian.
He Liangjun stepped forward and watched an impressive child instructing other children to measure the length. He was writing and drawing on the paper with a charcoal pen, and marked the measured length on the paper.
Seeing the charcoal in the little carrot's hand, He Liangjun asked with interest: "Little baby, what is this?"
The little carrot looked at Chen Moqun and He Liangjun, and saw the students and guards following them.
Although Little Carrot Head is naughty and mischievous, he is also the son of a hundred households in the guard house. He also has some knowledge and knows that these two people have a good background.
At any rate, he held back his temper and said, "Two elders, this is charcoal."
Charcoal is actually a pencil, and the Ming Dynasty had already begun to use graphite to make ink.
Some working people discovered that graphite could be used to leave marks on many objects. The first people to use charcoal were carpenters and masons.
However, the charcoal pencil in Little Luobotou's hand was modified by Su Ze. He ground the graphite into a cylindrical shape, then put a thin reed rod on it, and then wrapped it with rag strips and tied it tightly. It was almost like a modern pencil.
He Liangjun looked at the symbols and Arabic numerals on the paper and asked: "What word is this?"
The little carrot head said: "This is a number."
He Liangjun stroked his beard and said: "Numbers? Interesting, this is similar to the Suzhou code. They are very similar, but more suitable for writing horizontally."
He Liangjun discovered that the numbers written by Little Carrot Head were all written horizontally. He probably also understood the usage of these numbers. The Arabic numerals written horizontally were indeed better than the Suzhou code written vertically. More convenient to read.
Mathematicians before the Song Dynasty in China used calculations, and when recording numbers, they also used a symbol called Suzhou code.
The writing method of Suzhou code and Arabic numerals are simplified numerical symbols, and it is very convenient to use with calculations. He Liangjun also has property in his family, and the numbers in the ledger are also recorded in Suzhou code.
After the emergence of the abacus, calculations gradually disappeared from the stage of history, and writing horizontally with a pen made it easier to perform calculations. So by the late Qing Dynasty, Arabic numerals completely replaced the Suzhou code and became the popular "number" across the country.
When Su Ze checked Yu Zongyuan's accounts, the number used in the account book was "Suzhou Code".
Su Ze studied modern mathematics, and the mathematical formulas he memorized were all modern formulas. For mathematics, numbers are just symbols, so what he taught the little carrot heads were Arabic numerals.
He Liangjun looked at the little carrot head writing and drawing on the paper, and saw that he was in the Qingzhang field. He was also very surprised. The children in Changningwei also knew how to do math?
Chen Moqun is the headmaster of Yanping Academy. He looked at the picture drawn by Little Luobotou and the dimensions were clearly marked.
Chen Moqun said to He Liangjun: "I heard that Su Rulin set up a health school in Changningwei. These children should be his disciples." He Liangjun stroked his beard and
said: "There is a scholarly atmosphere in Jiaohua Township."
Chen Moqun He also nodded. Although he didn't like Su Ze very much, Su Ze teaching children to read in the countryside was still very suitable for him and was in line with the political correctness of literati and doctors.
Chen Moqun became interested and casually asked a few elementary school questions. Little Carrot Head and other children could answer them fluently. Now he was even more satisfied with Su Ze.
He Liangjun couldn't help but sigh, this Su Ze was indeed no ordinary scholar.
After receiving the news, Su Ze saw the two men's huge team of followers and knew that a big shot from the county had arrived.
When he found He and Chen, He Liangjun was asking Lin Liangjun for advice on arithmetic.
"You don't even understand the coordinates? Using Tianyuan as the center and the longitude and latitude to determine the point, you can naturally calculate the area of the field using this method." The little carrot head found that He Liangjun was approachable and soon forgot his awe for the scholar
. , began to yell at He Liangjun, showing off the analytic geometry knowledge taught by Professor Su Ze a while ago.
In fact, Little Luobotou had only scratched the surface, but He Liangjun was attracted by this calculation method.
He was a famous dramatist and a bibliophile who loved books. Scholars in the Ming Dynasty all aspired to be polymaths.
He Liangjun is very interested in analytic geometry. Using this method to calculate land is definitely much more convenient and accurate than the segmentation and summation method.
Land sales are also very frequent in southern Jiangsu, and the most important thing in land sales is the area of the land.
Therefore, in private transactions, scholars who are proficient in arithmetic are often asked to calculate the area of acres. Such people are called "counting scholars" in the Jiangnan area, and they can also be regarded as a kind of employment direction for scholars who cannot enter the imperial examination.
A scholar who can quickly and accurately calculate the area of acres will have a very high income.
In addition to liking opera, He Liangjun also likes to study mathematics when he has nothing to do. He has bought and sold land before, and He Liangjun always measured and calculated the land himself, but the method he used did not seem to be as good as the one mentioned by Little Luobotou.
However, Little Luobotou only knew how to establish a coordinate system, and the answers were all calculated by rigid formulas.
The two discussed it for a long time, but He Liangjun couldn't figure out how to calculate the area.
Su Ze knew Chen Moqun. He stepped forward to greet him and said, "I've met Mr. Chen."
Su Ze didn't understand why Mr. Chen from Yanping Academy wanted to find him, but since he came over, Su Ze treated him with courtesy. Waiting.
After Chen Moqun responded to the salute, he pulled He Liangjun and said to Su Ze: "Su Rulin, this is my good friend He Yuanlang, Mr. Tuohu. He has something to ask you today."
He Liangjun is about the same age as Chen Moqun. He has a gray beard and a Confucian scholar's crown. He looks like a celebrity at first glance.
However, He Liangjun didn't look like a gentleman at all at this time. His hands were full of toner, and his beard was tangled up from thinking about Zhang Tian's calculations.
It turned out to be Mr. Tuohu who was recruiting opera writers in Yanping Mansion. Su Ze also saluted He Liangjun. He Liangjun pulled Su Ze and said, "Su Rulin, is this child your disciple?" "
I am a health teacher, and I only teach these children." "Did you teach
this child the farming methods? Can you teach me? Could you help me clear up my doubts?"
Su Ze looked at He Liangjun doubtfully, aren't you a famous opera artist? Why are you interested in mathematics?
He Liangjun couldn't wait to say: "The child said that after establishing the coordinate system, the area of the field can be calculated through the formula. What is the principle?" Su Ze taught the little carrot head the calculation
formula of the shoelace theorem. Using this formula can roughly Calculate the area of the polygon, but the little luobotou only knows the formula and does not know the specific calculation principle.
He Liangjun also used the segmentation and sum method to check the calculation, and the answer was similar to the result calculated by the little carrot headband formula.
Moreover, Su Ze's method is faster and more convenient. Children can calculate it as long as they know the formula.
Gaussian shoelace formula, also called Gaussian area formula, is a mathematical algorithm that can find the area of a simple polygon in a certain area.
This is what I was asking. The principle of Gaussian shoelace formula is actually very simple. It is to divide a polygon into multiple triangles and then calculate the areas of these triangles respectively.
Gauss further formulated this method and gave a formula that can roughly calculate the area as long as the coordinates of the vertex are known.
In fact, in the late Ming Dynasty, folk also invented a method based on the same principle, which was called the Pushing Steps and Juding technique in arithmetic books.
After hearing the principles of Su Ze's formula, He Liangjun verified it with charcoal and said with admiration: "Wonderful! So wonderful! Su Rulin can invent this algorithm, he is really a mathematical genius!" Chen Moqun knew that he
was He was a good friend with arithmetic skills. He couldn't understand the algorithm explained by Su Ze and He Liangjun just now. He just nodded along mechanically. He Liangjun said he was a genius, so he must be a genius.
Su Ze was wondering, did these two old men come all the way from the county town just to discuss arithmetic with him?
He Liangjun finally remembered the business, and he said to Su Ze: "Rulin, you wrote the article "Du Shiniang sank in the treasure chest in anger" in "The Surprise", right?" It turned out that he came here
for this article, Su Ze Ze smiled and said: "Mr. Hui Tuohu, it was Wansheng's work."
He Liangjun said: "Well, I want to change "Du Shiniang's Furious Sinking of the Treasure Box" into a play and let the theater troupe rehearse it. What do you think of Ru Lin? ?"
Su Ze frowned and said, "I am late in life and I don't understand rhythm and phonology, so I'm afraid I won't be able to catch Mr. Tuohu's eyes."
He Liangjun said quickly, "I'll do the adaptation myself, and I'll also do the rehearsals."
Seeing that Su Ze didn't agree immediately , , He Liangjun said again: "Rulin, don't worry, this play is still signed by you. I am only responsible for the adaptation and arrangement. In addition, you will be ranked first in this essay competition. This one hundred taels of silver will be considered as your writing fee." , how about it?"
One hundred taels of silver!
Su Ze's eyes lit up! Otherwise, it would be easy for scholars to make money! One article is one hundred taels of silver!
In order to authorize an adaptation, these two old men came to Changning Guard. Were there not many piracy and plagiarism incidents in the Ming Dynasty?
Su Ze quickly figured out that Du Shiniang's angry dumping of the treasure chest was published in a tabloid. Now everyone in Nanping City knows that the article was written by Su Ze.
If He Liangjun secretly adapted the play without Su Ze's authorization, he would definitely be cast aside by all the scholars in the city.
Su Ze now understood the importance of controlling public opinion. Although "The Surprise" is still a tabloid sold in Nanping, it has already made wealthy gentry like Chen Moqun and He Liangjun afraid of snatching Su Ze's articles at will. , but also respectfully spend money to buy Su Ze’s adaptation authorization.
No wonder Donglin Academy was so popular in the late Ming Dynasty. If you control public opinion, you control everything!
Su Ze became more determined in his idea of running a newspaper. He not only wanted to run "Surprise", but also wanted to run it into a provincial and national newspaper!
Su Ze agreed, and He Liangjun also relaxed. He was very confident in the story of "Du Shiniang's Furious Sinking of Treasure Chest". It was like a famous director who found the best script. He was confident of producing a movie that would go down in history. The drama comes out!
"It's hot in the fields, so you two gentlemen should go and sit at Changning Guard."
Someone came up to give money, so Su Ze naturally showed his hospitality and invited the two of them to sit at Changning Guard.
The sun was getting hotter, and Chen He was a little tired, so he followed Su Ze towards Changning Guard.
Looking at the young men who were building ditches in the field and the children who were measuring the fields, Chen Moqun asked: "Why does Rulin want to lease the fields? Is this newly opened land?" Su Ze nodded and said: "The Changning Guards were cleaning up the land a few days ago
. River, some new land has been opened, and the health office is making records."
Chen Moqun looked at Jianxi in surprise. They came to Changningwei along the Jianxi River all the way east. The middle reaches of Jianxi River were turbid, but it was clear at the lower reaches. Chen and He thought that this stream was so magical, but they didn't expect that it was because of the recent water conservancy construction.
Su Ze explained the method of water flushing sand again, and now Chen Moqun also understood the principle.
The principles of physics are often simple and easy to understand. In later generations, physics questions in the college entrance examination are still discussed every year, but no one cares about mathematics questions.
Unexpectedly, Su Ze could also build water conservancy. He Liangjun had a higher evaluation of him. Even Chen Moqun thought Su Ze was a talent.
Organizing the family, governing the country and bringing peace to the world, and benefiting the village are originally the political correctness of scholars.
After arriving at Changningwei, Su Ze took the two of them to visit the School of Health. Chen Shanchang generously donated some books and the Four Treasures of the Study to Changningwei.
For these two angel investors who had just invested money, Su Ze ordered Lin Cainiang to kill chickens and pick vegetables, and entertained them warmly. Naturally, the guests and hosts were enjoying themselves for a while.
At the same time, Nanping County.
Huang Shixing stood in front of He Liangjun's door with great expectation, and finally got the news from the door.
"What, Mr. Tuohu went on a trip?"
"Where did he go? Changning Guard?"
ps1: The algorithm of the Ming Dynasty under the microscope
of push-step gathering technique
, and the algorithm of Shuai Jiamo Zhang Tian.
This drama is quite interesting. I recommend
ps2:
Suzhou code, 〡〢〣〤〥〦〧〨〩十, this symbol is still used in some areas today.
I checked the information and found that the mathematics of the Ming Dynasty was indeed not bad, which is a pity.
(End of chapter)