33 cang's calculations
"The water in this pond is living water, which is brought from the upper reaches of Weishui, and the main canal is clean river water, which flows into each house through the branch canal, and the wastewater from each family flows into the drainage culvert to be led downstream to irrigate the farmland, which was designed by Zheng Guo, an old water worker!" Zhang Cang introduced.
"I chose this one! What about the rest, please bother more! Montenegro said, then turned to the servants beside him and said, "How many of you are in this mansion now, are you the leader?" β
"I would like to tell you, there are now three men and three women on our side, a total of six people. My name is Huang Si, and I am their head. What do you command? "The male servant next to me was about thirty years old and looked very capable.
Montenegro took out ten taels of gold, handed it to Huang Si, and said, "You guys did a good job, everywhere is clean, everyone else has one tael, and the rest is yours." β
"Thank you, sir! What do you do, just command! Huang Si said.
"Master Zhang and I will go to the pavilion and sit down for a while, and I'll make us a pot of tea." Black Mountain commanded, and Zhang Cang came to the pavilion and sat down, the sun in the east was shining on him, warm.
Montenegro asked, "I don't know what other procedures to go through?" The situation in the north is tense, and I was trying to go north sooner. β
"I'll go back and fill out the paperwork later, let the prime minister use the seal, and send it to Xianyang Ling, and Xianyang Ling will let you go through the land deed and house deed!" Zhang Cang said, "You can write to your family and ask them to prepare to move to Xianyang as soon as possible, and the Prime Minister's Mansion will send a document to Tongbai County soon." Zhang Cang said.
"Thanks for the reminder! I was on the road just now, and I noticed you talking to yourself, can you talk to me? Montenegro asked.
"I'm at the teacher's place, and I studied Ji Ran Xue, and I often deal with numbers in the Prime Minister's Mansion. A few days ago, Shaofu was building a Fang Palace, because the exact ratio between the circle and the diameter could not be found, there was often a size deviation between the rafters and the hole, which was too big to fit in, too small and not stable enough. A few days ago, Shaofu Ling came to me to find a way! I drew a circle all night last night, and I calculated it until morning, and when I was with you, my mind was still thinking about pi! I'm really embarrassed to talk to myself! Zhang Cang said.
"I wonder how many you counted?" Montenegro asked.
"Zhou Math has been calculated to the third place, and I have already calculated to the fourth place, but some projects must be accurate to the fifth place." Zhang Cang said.
"I know that the circumference of a circle is three and four hundred and five nine and six times its diameter." Isn't it pi, and later generations of elementary school students will memorize dozens of them. Montenegro said casually.
When Zhang Cang heard this, he immediately took out a large handful of small wooden branches of the same size from his body, dipped them in water and let Black Mountain write them on the smooth stone table. Montenegro immediately wrote down a few Arabic numerals 3.1415926 on the table. "What is this word, why can't I understand it?" Zhang Cang asked.
Montenegro only remembered this era, and there were no Arabic numerals. He explained: "Some time ago, I learned these words from a Hu merchant in Shangjun, and he said that he came from Apabo, which was farther away than the Western Regions, and I learned it very conveniently when I looked at the records!" I'll teach you too! Montenegro asked the servant to send pen and ink and a wooden calf, and carefully wrote down the ten numbers from 0 to 9, as well as addition, subtraction, multiplication and division of various symbols and combinations!
Zhang Cang is smart and well-read. Montenegro simply taught Zhang Cang in the pavilion, and the servants also sent lunch to the pavilion, and the two talked about it until it was dark, and finally taught Zhang Cang the combination of various numbers, the application of symbols, and some calculation methods, such as the most basic vertical addition, subtraction, multiplication and division of the multi-digit sequence.
Zhang Cang is like a treasure. said: "I am writing a math book called "Nine Chapters of Arithmetic", with the Arabic numerals and symbols you taught me, it will greatly speed up the calculation in the future!" I want to include it in the book "Nine Chapters of Arithmetic", and write to King Qin, please give credit to you! β
Montenegro knew that there was a book of "Nine Chapters of Arithmetic" in history, and a famous minister of the Han Dynasty named Zhang Cang, but he did not know that Zhang Cang was the author of "Nine Chapters of Arithmetic". I admired Zhang Cang even more, and said: "I am also from Zhang Nanyang County, I will call you Brother Zhang in the future, there is no need to ask for credit, after your book is completed, show me first, I will be satisfied!" β
"What are you doing with so many little sticks?" Montenegro asked curiously.
"This is Ji Ranxue's calculation chip, according to legend, it was created by Tao Zhugong, with the formula, used to calculate, fast and accurate." Zhang Cang said.
"Oh! It's so magical, from one plus two plus three, to a hundred, how much is it? You can show me how fast. "Montenegro is full of curiosity about ancient calculations, he has long known that the answer is five thousand and fifty, and he just wants to find out.
With Zhang Cang's cleverness, he will definitely not add numbers one by one, he quickly calculated that there are 50 100 plus 1 50 equal to five thousand and fifty.
Montenegro saw the trick at a glance, Zhang Cangnian's mantra was roughly the same as the abacus formula table in later generations, but the reading method was different. The abacus is a scattered abacus, the top one horizontal represents five, the lower vertical represents one, such as nine is the top one horizontal, the lower four vertical.
Montenegro said: "It has been more than 200 years since Tao Zhugong invented arithmetic, and you have not used your brains to improve the speed and accuracy of calculations with simpler tools?" β
"I never wanted to be more proficient in the methods taught by the teacher, and I haven't thought about improving the calculation tool, where can a new calculation tool be so easy to come up with?" Zhang Cang said.
"Brother Zhang, people used axes to cut trees for thousands of years, and later Lu Ban was inspired by the small sawtooth on the blades of grass to invent the saw, which made people cut wood many times faster. Last year, when I was cutting rice, I was inspired by a saw to make a scythe that people have used for thousands of years into a zigzag shape, which makes the harvesting several times faster. I love to think about things, and you write down the mantra for me. Before I go back to Shangjun, I'm sure I've come up with a new calculation tool to make calculations faster and more accurate! Montenegro said.
The most basic knowledge that future generations will learn in school will bring a huge sensation in this era. If Zhang Cang could include the abacus and abacus formulas, Arabic numerals, calculation symbols, and calculation methods in the world's earliest mathematical masterpiece "Nine Chapters of Arithmetic", then the development of mathematics would be greatly accelerated.
Although Zhang Cang didn't believe that Montenegro could make any new tools in a few days, he still wrote the mantra on the wooden slip and handed it to Montenegro. The two discussed until midnight before leaving.
Back at the post house, Montenegro didn't look at Zhang Cang's calculation formula at all. After dawn, he found a private carpenter's workshop to draw the abacus of later generations and let the carpenter follow it. Montenegro called several carpenters for a tael of gold to work at the same time. In the evening, the first delicate nanmu abacus is ready! Montenegro took the abacus and the mantra and came directly to Zhang Cang's mansion.
Zhang Cang is now only a 400-stone official in the Prime Minister's Mansion, and his residence is only a small courtyard with two entrances.
"I Zhang Cang has two major hobbies in my life, women and books, except for a few wives in the house, there are all kinds of books piled up everywhere." Zhang Cang said.
Montenegro looked at Zhang Cang, who had a fat head, big ears and a big belly, and jokingly teased: "With your figure, I'm really worried that your women will be crushed by you!" β
Zhang Cang laughed and welcomed Montenegro into the living room to serve tea.
Montenegro handed the abacus and the "Abacus Formula" to Zhang Cang, and said: "This is the new type of abacus I asked the carpenter to make, and this "Abacus Formula" that I pondered overnight, I will tell you how to use it now, you can judge it." β
Zhang Cang has a strong learning ability, and he memorizes the mantra after reading it a few times, and he can master the abacus at a glance. Although he has just learned to use the abacus, he has already calculated faster and more accurately than the abacus, and praised: "Brother, this abacus and mantra are really all you came up with in one day and one night?" β
"The mantra is similar to what you copied me, you can see it at a glance. I spent a tael of gold to hire five or six carpenters from a private carpentry workshop to work for a day at the same time! You can go and ask them to do more tomorrow. Montenegro replied.
Zhang Cang looked surprised and said: "I have used the calculation chip for more than ten years, and I have never acquiesced to the rules, and I didn't think about changing it. β
"Thinking differently, you always want to be proficient in arithmetic. I'm thinking about how to improve my calculations to make them faster. So much for. Montenegro replied with a smile.
Zhang Cang was already immersed in the abacus, quickly calculating all kinds of addition, subtraction, multiplication and division.
"Brother Zhang, you study slowly, I'll leave first." Seeing that Zhang Cang was already fascinated by the abacus, Montenegro took his leave.
When he came out of Zhang Cang's mansion, Montenegro was in a good mood, before the advent of modern calculators, the abacus was the most advanced calculation tool, and today the abacus and abacus formulas that only had in the Eastern Han Dynasty were passed to Zhang Cang three hundred years in advance, which is also considered to be a contribution to this era!
Two days later, Montenegro completed the formalities and had his own mansion in Xianyang. He wrote three letters, the first of which was a letter to his family, asking his two brothers and mother to prepare for the family to move to Xianyang as soon as possible. The second letter was to the teacher in Tongbai County, telling him about his current situation, hoping that he could also come to Xianyang to live together, and also sent the Meng Tian pen sent by Meng Tian to the teacher. The third letter was written to Nanjun Shou Teng Yue, mainly telling him some corn planting skills.
When Montenegro turned over and left Xianyang to go north, Montenegro was still worried about Alina, since escorting Alina into Xianyang City, he never saw him again, but he only knew that in the past few days, the most talked about by Xianyang people was Alina's beautiful appearance. A few days ago, if someone said that they had seen a blonde, blue-eyed and white-skinned girl, no one would believe it.
When King Qin asked Montenegro to escort the Alina brothers and sisters into Xianyang, the summons were written on Prince Andre and Princess Alina, so the ceremonial officials could only greet the Alina brothers and sisters in the same way as receiving the prince and princess. arranged for them to live in the annex of Zhangtai Palace. The country of Yilie is only the size of a medium-sized county in the Qin country, and the Alina brothers and sisters were impressed by this magnificent palace as soon as they arrived at the Zhangtai Palace, and when she learned that the Zhangtai Palace was only one of the several palaces in the Great Qin, and the Afang Palace under construction was more than ten times larger than the Zhangtai Palace, they were so surprised that they were speechless! In the past few days, the ceremonial officials have taught them the etiquette when they were summoned by the King of Qin over and over again, especially Prince Andre, since he was rescued by Daqin, his body and mentality have gradually recovered, no matter who he sees, the eunuchs, palace maids, and ceremonial officials are all a warm hug, and they also kiss each other's faces. Once, when a concubine of King Qin of Zhangtai Palace came to see strangers curiously, she was also hugged tightly by Andre and kissed her on the face. The frightened faces of the people present turned pale, and no palace maids and concubines came to the other garden to watch the excitement! The ceremonial officer knew that he was guilty of dereliction of duty, and he did not dare to punish Prince Andrei. can only report level by level, and finally report to Prime Minister Wang Juan, and at the same time, Captain Li Si also got the news from Zhao Gao.
The ceremonial officials are all Confucians who read poetry, books, etiquette and music, and this incident can be big or small, the key is to look at the mood of King Qin! Wang Juan looked at the trembling official and said, "You go directly to ask for guilt now, with the character of King Qin, he will definitely hand it over directly to the court lieutenant to discuss the guilt." If you don't go to ask for guilt, let Li Si play first, just. There is absolutely no way to live! No, I'm going to enter the palace to see the king now, and if it's too late, it's too late. β
After Wang Juan finished speaking, he immediately walked out of the Prime Minister's Mansion and walked towards the palace gate, and several guards immediately followed. The Prime Minister's Mansion was close to the Xianyang Palace, and he arrived at the palace gate in a quarter of an hour, and several Lang Wei who guarded the palace gate saw the prime minister enter the palace and hurriedly saluted and let him go.
Wang Juan asked casually: "Is King Qin in the palace?" Are you available now? β
When Lang Wei saw the prime minister's question, he replied: "King Qin is in the side hall, and Tingwei has just entered, and he is probably talking about things." β
When Wang Juan heard this, he secretly screamed in his heart, and his feet sped up, and the eunuchs, palace maids, and guards saw that the usually steady prime minister was suddenly in a hurry, and they all flashed to the side of the road to give way. When King Yingzheng of Qin had just returned to Xianyang from Handan as the grandson of the king, Wang Juan was the teacher recommended by LΓΌ Buwei to Yingzheng. For decades, he has won the trust and respect of Yingzheng, and among all the ministers, he is the only one who can directly meet the king of Qin without a report. But the old and steady Wang Juan has always asked the eunuch at the door to tell him before entering the hall, but today he is unusual, and he actually walked into the side hall. As soon as he entered the temple, he heard Lees say in a loud voice:
"Your Majesty, the minister has come to tell the king about ......"
"Hahaha, what happened today is so interesting!" As soon as Wang Juan entered the hall, he laughed to interrupt Li Si's report.
"What happened to the prime minister today? Tell the widow about it. King Qin's attention was immediately attracted by the later Wang Juan, and Li Si was so angry that he gritted his teeth, but he was also an old traitor who had been in the officialdom for a long time, and the anger on his face flashed, so he had to stand by and listen to Wang Juan.
"It's really a custom, Prince Andrei of the Illegite country, no matter who he sees, men, women and children, eunuchs and palace maids, he must hug someone and kiss each other on the face to show respect for each other! We Confucians are familiar with the etiquette of all vassal states, and we have never heard of such a blatant indecency as the highest etiquette. Li Tingwei, are you ridiculous? Wang Juan said with a smile, and deliberately asked Li Si.
Li Si was embarrassed, and his answer was not ridiculous, King Qin would definitely blame him for not publicly arguing with the prime minister. The answer is ridiculous, which is equivalent to admitting Wang Juan's statement, and what he wants to play later cannot be played anymore.
When Li Si was thinking about how to answer, King Qin spoke first: "The customs of this Yilie people are really special, and this way of greeting is incompatible with my Chinese etiquette. The prime minister came to see me in a hurry today, and if there is anything else, just tell me directly! β
Wang Juan said: "This morning, when the celebrant official taught Prince and Princess Ilie the etiquette of Daqin in the other garden, because of the language barrier, they could only reluctantly convey it through Princess Alina. When many palace maids and concubines in Zhangtai Palace heard that the other garden was inhabited by foreigners, they came to see the freshness. Prince Andrei, in order to express his warm and joyful welcome to the people who came to see the excitement, went to hug the concubine and kissed her on the cheek. This matter can be punished by death in my Daqin, and the celebrant officials are also guilty of dereliction of duty, and the following people report to me, I dare not make my own decisions, and ask my king to decide. β
When King Qin heard this, he also laughed, until now, he is a workaholic, immersed in government affairs every day. I haven't loved that concubine yet, every time I am interested in the harem, I just catch a palace maid and solve it on the spot, and the palace maid who has been fortunate to him will immediately crown the palace maid as a beauty, and give birth to a prince or princess and then be named a lady. Except for the mother of the eldest son Fusu, he almost didn't know the names of the other concubines, and Zhao Gao would occasionally bring a newborn baby and let him marry his prince and princess, and only then would he ask about the situation of his biological mother! Molerating with King Qin's concubine, this crime is too big. He said to Wang Juan: "Since the prince of Eli does not know the etiquette of the Great Qin, he uses the great gifts of his own country to welcome people, he does not mean to molest, and he cannot be considered a crime of molesting. Forget about this matter, I have heard how strange strangers are these days, and tomorrow I will summon their brother and sister. That's it! β
"No! The old minister will do it. Wang Juan breathed a sigh of relief in his heart and took his leave.
"Tingwei, what are you going to play just now, let's play!" King Qin said to Li Si.
Li Si originally wanted to use Prince Yilie to tease the princess of Qin, but the ceremonial official was derelict in his duty to play a copy, but he was preempted by Wang Juan, an old fox, and it will definitely not work if he continues to talk about it. I had to say: "What the prime minister just played, the minister also listened to the next person, and just wanted to play the king, since the king and the prime minister have reached a conclusion, the minister retired!" β
After Wang Juan and Li Si withdrew, King Qin was immersed in the mountain of music again, and Zhao Gao, who was beside him, saw all this in his eyes, and a strange smile appeared on the corner of his mouth.
Prince Eli of the other garden didn't know that because of one of his ordinary actions, someone actually went to the ghost gate and walked around.
The next morning, at the court meeting of Xianyang Palace, King Qin sat in the center of the main hall in a crown and a balance crown. The hundred officials were also wearing court clothes, holding jade gui, looking very solemn. Although I had heard about the beauty of Princess Ille for a long time, when Prince and Princess Ile walked into the main hall to meet King Qin, many people were still stunned! With blonde hair and blue eyes, snow-white skin, and a tall figure, she is simply a legendary fairy.
After the court salute, Alina said in a stiff Chinese language: "The Huns are ferocious, sweeping dozens of countries in the Western Regions, and after the city of Iliel is broken, more than 100,000 people were killed and only a few thousand slaves remained, scattered in various Xiongnu tribes. If His Majesty the King of Qin can send troops to defeat the Xiongnu and help Yile restore the country, our brothers and sisters are willing to be subjects of the Qin State for generations. β
"What do you think of Princess Alina's words? Let's discuss! "King Qin wants to hear what the audience has to say.
The court suddenly became lively, and most of the ministers thought that the country of Illes was too far away, and it was not cost-effective to spend manpower and material resources to support a country five or six thousand miles away. Some people even suggested that King Qin should take Princess Alina as a concubine. In short, no one agreed to help the country recover.
At this time, the national lieutenant Wei Yu stood up and said: "Your Majesty, when I met my king in Zuo Gengshan the day before yesterday, I once said that there are vegetables and fruits in the west that are not available in China, as well as corn and cotton, as well as a little tiger that specializes in catching mice. If it can be introduced into China, there will be no more people in China who are hungry. I also ate a bowl of polenta that day, and I still miss the sweet and delicious taste! β
"The words of the national lieutenant are the strategy of prosperity and strength! The order was sent to fight with the Xiongnu, not to kill slaves, and to bring them all back to Shangjun and Beidi County for settlement. Prince Andrei was named the Marquis of Ile, and Princess Alina returned to Ile Township, Mizhi County, Shangjun County to gather and appease the remnants of Ile, waiting for the opportunity. Other things will be discussed after the Huns are broken. King Qin said.