Lan Ruochan
Chapter 166 The Ancient Yelang
Chapter 166 There was Yelang eight hundred miles in ancient times, and it is known that the Han family has tens of thousands of hectares
After Gongsun Qing shook his head, everyone looked at Zu Dianzhi in unison.
Even if the holy minister didn't speak the Chinese language or understand Chinese customs, he was not slow to respond, so he naturally understood that the young man in white was not an ordinary person.
So he voluntarily left the table and chatted with Zu Dingzhi accompanied by an interpreter.
The holy minister sincerely asked Zu Dingzhi to share a relatively deep research proposition about mathematics in the Central Plains.
After hesitating for a moment, Zu Dingzhi took out the unfinished secret biography of "Zhushu".
He really wanted to sell the content of this book,
Writing a book that no one can understand is really a lonely thing.
(Narrator): Ahhhhh~ Kong has a dragon-slaying skill~.
Zu Tingzhi took out the book, showed the picture, and gestured with body language, but he still interpreted the translation as rare scratching his head and scratching his head.
In short, the book "Zishu" is divided into five chapters.
Chapter 1, cut the trunk to the branch, and cut the branch to the end.
It is an in-depth study of Liu Hui's cutting circles, cutting cones, and various cutting techniques.
According to modern mathematics point of view, it is differential calculus.
Chapter 2, accumulate the ends into branches, and accumulate branches into trunks.
This is the algorithm for reintegrating and calculating the area after the cut method.
That is the calculus of modern mathematics.
Chapter 3, remove the leaves and save the branches, remove the branches and save the trunk.
This chapter talks about how to do simplification, calculation analysis, and partial differentiation when there are multiple unknowns (fixes).
Chapter 4, numbers make trees, and trees make forests.
This is the technique of finding out the original operational relationship between them by studying the changes of different variables (fixes),
Roughly equivalent to differential equations today.
Chapter 5, there is already a picture, and the solution can be found.
This is actually the simplest chapter in the whole book, but it needs to build on the research foundation of the first four chapters.
Study functions, analytic geometry, and these algorithms based on pictures.
Now that this book is in place, just change the cover and paste the four characters of "Advanced Mathematics", then it can be directly sent to major universities as textbooks.
(Readers almost jumped up after reading this. How dare you say that? Why don’t you go to heaven? Don’t worry, don’t we have time to knock on the blackboard? Speak slowly, slowly.)
Kuizhi talked on and on for about two hours, from noon to about dinner time.
Everyone who has nothing to do with it is a bit tired of talking,
But Jizhi, Shengchen, Xin Dufang, Tao Hongjing and that poor interpreter, this small circle has not finished talking.
To be honest, if the King of Wei hadn't intended to strengthen the country's prestige, the banquet would have ended long ago.
But at this point, it's easy to save trouble, just turn over the table and change to the dinner.
The holy minister listened intently for two full hours.
When Tunzhi finished speaking, he shook his head sideways, upright, and obliquely repeatedly.
Some express their affirmation of Zu's works, thinking that they have gained something,
But more is expressing that I can't figure it out, I don't understand.
Don't say he doesn't understand, Xin Dufang and Tao Hongjing can only understand no more than [-]%.
Tao Hongjing stroked his beard and sighed,
"Pindao has heard Zu Wenyuan talk about this "Zhushu" three times.
I listened to Junzhi again today, but most of it was still in the fog.
But every time the truth is tested, the results of the ancestors and father and son's calculations are roughly the same.
Pindao has only one way to worship, not to think about it. "
At this time, the holy minister had long lost the courage to fight for victory, and he did not dare to put on a contest other than expressing his willingness to learn from Min Zhi.
With this half-day emotional exchange, at night, you can talk about some relatively formal topics.
King Wei first thanked the Tianzhu Mission for their help,
With their participation, the gold content of this uncovered event naturally increased a bit.
It's just that Wei's scouts met the mission in the territory of Shu by chance.
Since it was a beautiful coincidence, the mission here naturally had another purpose.
So the king of Wei asked the holy minister very tactfully about his intention.
The holy minister stood up respectfully and began to introduce the difficulties encountered by the Ji Duo dynasty.
To the west of Congling, there used to be Guishuang, a great country.
After the disintegration of the empire and the rise of King Chaori, he regained northern Tianzhu and unified Central Tianzhu. The Jiduo dynasty established was very prosperous.
But since the death of King Chao Ri, Ji Duo has actually been going downhill.
The White Huns in the Kubin area rebuilt the Heda Empire, quickly took control of the former land of Guishuang, and began to encroach on the territory of Tianzhu regained during the reign of King Chaori.
By the time of King Yuri, the Heda Empire had invaded the Ganges River Basin and began to squeeze the strategic hinterland of the Jido Dynasty.
King Youri didn't want to sit still, so he sent an envoy to ask Wei for help.
The King of Wei pondered for a moment, then replied seriously,
"Da Wei and Ji Duo are thousands of miles apart.
It is separated from Xiaoqi in the south, separated by mountains outside the southwest, and has to go through the vast Western Regions in the west, and then it can reach Tianzhu by zigzagging south.
The geography of the mountains outside the mountains is not suitable for large-scale marches,
And Xiao Qi would never use the excuse to let Wei's army pass, which is a taboo for military strategists in the Central Plains.
Yao Sixia, please translate the allusion for me while translating.
The route to the west is even more tortuous.
My Great Wei's control over the Western Regions is not stable.
Rouran, Gaoche, Tuyuhun, Kangju and other major powers are all sensitive to our movements, and it is not wise to use a large army rashly.
Therefore, it is more difficult for my Great Wei to directly participate in the Tianzhu war.
But since the two countries intend to become friendly states, we naturally have no reason to ignore it.
My great Wei will send military experts and smelting craftsmen to Tianzhu,
But I also hope that Tianzhu can use something in exchange. "
After listening to Yao Sixia's translation, the holy minister was a little disappointed, but after thinking about it, it was true.
What King Wei promised is the greatest help they can provide right now.
It's just that I don't know what King Wei will ask for. Is it a special product of his hometown?
Its mountains and rocks are important strategic resources. At that time, only Tianzhu had property in the world. Unfortunately, the king of Wei didn't know about it.
When the sage minister raised a question, King Wei's answer made him laugh dumbfounded,
"I need the holy yellow dye from Tianzhu.
Today's Huaxia printing and dyeing Minghuang still uses the precious mineral deposits of Huangdi Chijing (chrome yellow).
This yellow ore powder is found in Hexi, and the output is extremely low.
I intend to use the yellow robe to replace the Han-made deep clothing, to restore the appearance of the Yellow Emperor's royal presence.
However, due to the scarcity of raw materials, it is really painful to use it for printing and dyeing.
I heard that the clothes of the holy monks in Tianzhu are all dyed yellow. I think your country must have special dye resources.
My state of Wei has no way to give you direct military assistance, so I don't speak much.
A little dye, should be no problem, right? "
The holy minister agreed immediately without hesitation.
King Wei's appetite is indeed not great, and he still has these authorizations.
Just talking about the holy yellow of Tianzhu, we have to talk about the sacred bull drowning in gold.
Although modern Indian scholars have proved through "rigorous experiments" that small gold can really be extracted from the urine of their holy cow Jier cattle,
But you all understand, it’s good not to talk about it.
However, it is not a fairy tale to insist that there are gods drowning in gold.
For example, the dye of holy yellow is indeed refined by drowning cows.
In ancient times, it was exported to Europe and Asia, and it was very valuable, and it did earn a lot of real money for Tianzhu.
Tianzhu veterinarians fed mangoes to cattle, and found that the digestive system of cattle cannot decompose the yellow pigment contained in mangoes, and will excrete all the colored substances through urine.
These cows can be used as dyes after being smelted and dried.
In the final analysis, the yellow pigment in the dye comes from mango, and through the action of bovine kidney, it becomes soluble and has good color solidity.
It can be described as a very original and environmentally friendly green technology.
"""""Knock on the blackboard time"""""
The costumes of Chinese emperors began to take Ming Huang Dagon dragon robes from the Sui Dynasty, and there are well-documented records at this time.But the Sui Dynasty was ruled by the Wei Dynasty, so this trend should have already started in the Northern Wei Dynasty.Since the Han Dynasty, the Twelve Chapters of the Yellow Emperor have not been dyed bright yellow, mainly because of the scarcity of dyes.But Tianzhu is close to the tropics, and there are more natural plants with bright colors, so there has always been no shortage of yellow dyes.The ox drowned Indian yellow mentioned in this article is a real ancient craft. The finished product was once exported to the British Empire and has a history of being used in the modern textile industry.
We haven't finished talking about the past in Tianzhu in the previous section.However, the history of Tianzhu is probably not the focus of the readers. Putting it aside for a while should not affect the reading mood too much.On the contrary, if there is no reasonable explanation for the two items of calendar and calendar, the author will probably receive the blade soon.
There are many things, without horizontal comparison, we will never know how much China was ahead of the world in ancient times.This is the case in mathematics.Aye Podo, a master of mathematics in India, has the same status as Zu Chongzhi in China.Let's skip the calendar part for now (we'll talk about it in the next few sections).There are three major breakthroughs in Ayebodo's mathematics: the deduction of pi to the fifth decimal place (actually four digits in actuarial calculation); summarizing the formula for calculating the area of a triangle and proposing the concept of suspected trigonometric functions; A breakthrough in understanding.
Based on these three points alone, compared with the three generations of Zu's family who were the masters of mathematics in China at that time, we can only reply with "呵~".
We listen to Westerners commenting on Chinese mathematics. Of course, they will affirm many facts that cannot be erased, such as Zu rate, square root algorithm and so on.But in general, they still have a deep discrimination against Chinese mathematics, saying that ancient Chinese mathematics did not have the concept of irrational numbers and the concept of trigonometric function calculations, so the calculations that can be performed are very preliminary.
Bah~
As mentioned in the main text of this article, China's Suanjing focuses on calculation and has an independent system, which is completely different from the Western one in concept.Modern mathematics in the West was developed using the vocabulary definitions of ancient Greece. If you think their concepts are accurate and their words are accurate, that is because of the advantages of the native language.As the author mentioned before, is "The Elements of Geometry" the original?Completely reread ancient Greek books in a modern language.
Indeed, China has never clearly put forward the concept of "irrational number".However, the mathematical crisis of irrational numbers did not come to a conclusion until the end of the nineteenth century in the West. The person who first discovered irrational numbers was thrown into the sea as a heretic and fed to the fish!If it is believed that the West took the lead in mastering irrational numbers because of the discovery of a small group of scholars who have been abandoned by the world, then can it be said that China's "Xuan Ye Theory" proves that China has mastered the truth of the universe?Can "Youyang Zazu" prove that China took the lead in landing on the moon?But China has indeed mastered the algorithm of square extraction, and there is a whole chapter of square extraction examples in "Nine Chapters of Arithmetic".Not only the square, but also the cube can be opened.This article only cites an example:
"Nine Chapters of Arithmetic Shaoguang" has another five steps of 39.Ask for square geometry?
The answer was: 25 and [-] steps.
The method of prescribing said: ... the specific algorithm of prescribing.
Square root is one of the basic algorithms in Chapter Nine Arithmetic.The calculation of square root and cube was quite mature in Zu Chongzhi's period. "Nine Chapters of Arithmetic" is equivalent to a junior high school textbook for one of the ancient six art numbers (this will be discussed later).Therefore, discussing issues similar to square root [-] is too naive in China, too naive!
About trigonometric functions, let's say this.Chinese mathematics does not use scales to record angles, and has always used trigonometric functions to record angles.That is, the Pythagorean Mystical Angle Method.Neither does India.We don't talk about those ambiguous statements, but only look at the essence. Isn't the essence of Pythagorean Xuan the triangular operation?
As early as in the "Zhoubi Suanjing" of the Zhou Dynasty, there was a saying that "Pythagorean shares are multiplied separately, and the formula is used to divide them".
"Nine Chapters of Arithmetic" says: The Pythagorean technique says: Pythagorean shares are multiplied separately, combined, and the square is divided, that is, the string.And the stock is multiplied by itself, and the string is multiplied by itself, and the rest is divided by the square, that is, the hook.Also hook the self-multiply, use the reduced string to multiply the self-multiply, and divide the rest by the square, that is, the stock.
This is China's own definition of trigonometric functions, sine = hook/string, cosine = strand/string...and so on.All trigonometric functions can be expressed by Pythagorean, and the values of these trigonometric functions can be used to mark the sizes of all angles.We have our own definitions, formulas and calculation methods, why should we copy the West?You said that China has not mastered the application of analytic geometry other than right triangle?Please, Descartes, the originator of analytic geometry, was a mathematician in the seventeenth century. Isn't it a bit unfair to compare with Zhang Cang and Geng Shouchang in the first century AD?
Chinese applications of triangles shine in surveying.American mathematician Frank J. Swetz said when he read "Sea Island Mathematical Classics" by Liu Hui, "China's achievements in mathematical measurement surpassed that of the West by about 1000 years." Master trigonometric complex calculations.When trigonometry was introduced to China, Chinese and Western scholars generally believed that Tang Ruowang and Xu Guangqi's "Da Chou" did not surpass the content of "Sea Island Suan Jing".Let’s take an example question about island arithmetic:
Today, it is hoped that there will be a white stone under Qingyuan.On the bank of Yanju, the hook is three feet high.Looking obliquely at the water's edge, the penetrating thigh is four feet five inches.Looking at Baishi, the next stock is two feet and four inches.Also set a heavy moment on the top, and the distance between them is four feet.Looking obliquely at the water bank from the end of the hook, it is four feet into the upper thigh.Looking at Baishi, the stock is two feet and two inches.What is the depth of the water?The answer is: one foot and two feet.
The technique said: Subtract the upper and lower shares of Wangshui, and multiply the upper shares of Wangshi as the upper rate.The upper and lower shares of Wangshi are subtracted from each other, and the lower rate is calculated by multiplying the upper shares of Wangshi.Subtract the two rates, and the remainder is the real moment; the multiplication of the two differences is the law.If the truth is the same as the law, you will get the depth of the water.
This sample question can be understood, high school ancient Chinese, trigonometry, geometry, all graduated.Since there is no way to explain this question without drawing a picture, you can only Baidu for the specific algorithm of this question.
What level does this "Sea Island Mathematical Classic" belong to in ancient mathematics textbooks?Like Nine Chapters of Arithmetic, it is also a junior high school textbook.This section is already a bit long. We will talk about the ancient mathematics textbooks, ancient counting methods and the magical "Zhushu" in the next chapter.
(End of this chapter)
After Gongsun Qing shook his head, everyone looked at Zu Dianzhi in unison.
Even if the holy minister didn't speak the Chinese language or understand Chinese customs, he was not slow to respond, so he naturally understood that the young man in white was not an ordinary person.
So he voluntarily left the table and chatted with Zu Dingzhi accompanied by an interpreter.
The holy minister sincerely asked Zu Dingzhi to share a relatively deep research proposition about mathematics in the Central Plains.
After hesitating for a moment, Zu Dingzhi took out the unfinished secret biography of "Zhushu".
He really wanted to sell the content of this book,
Writing a book that no one can understand is really a lonely thing.
(Narrator): Ahhhhh~ Kong has a dragon-slaying skill~.
Zu Tingzhi took out the book, showed the picture, and gestured with body language, but he still interpreted the translation as rare scratching his head and scratching his head.
In short, the book "Zishu" is divided into five chapters.
Chapter 1, cut the trunk to the branch, and cut the branch to the end.
It is an in-depth study of Liu Hui's cutting circles, cutting cones, and various cutting techniques.
According to modern mathematics point of view, it is differential calculus.
Chapter 2, accumulate the ends into branches, and accumulate branches into trunks.
This is the algorithm for reintegrating and calculating the area after the cut method.
That is the calculus of modern mathematics.
Chapter 3, remove the leaves and save the branches, remove the branches and save the trunk.
This chapter talks about how to do simplification, calculation analysis, and partial differentiation when there are multiple unknowns (fixes).
Chapter 4, numbers make trees, and trees make forests.
This is the technique of finding out the original operational relationship between them by studying the changes of different variables (fixes),
Roughly equivalent to differential equations today.
Chapter 5, there is already a picture, and the solution can be found.
This is actually the simplest chapter in the whole book, but it needs to build on the research foundation of the first four chapters.
Study functions, analytic geometry, and these algorithms based on pictures.
Now that this book is in place, just change the cover and paste the four characters of "Advanced Mathematics", then it can be directly sent to major universities as textbooks.
(Readers almost jumped up after reading this. How dare you say that? Why don’t you go to heaven? Don’t worry, don’t we have time to knock on the blackboard? Speak slowly, slowly.)
Kuizhi talked on and on for about two hours, from noon to about dinner time.
Everyone who has nothing to do with it is a bit tired of talking,
But Jizhi, Shengchen, Xin Dufang, Tao Hongjing and that poor interpreter, this small circle has not finished talking.
To be honest, if the King of Wei hadn't intended to strengthen the country's prestige, the banquet would have ended long ago.
But at this point, it's easy to save trouble, just turn over the table and change to the dinner.
The holy minister listened intently for two full hours.
When Tunzhi finished speaking, he shook his head sideways, upright, and obliquely repeatedly.
Some express their affirmation of Zu's works, thinking that they have gained something,
But more is expressing that I can't figure it out, I don't understand.
Don't say he doesn't understand, Xin Dufang and Tao Hongjing can only understand no more than [-]%.
Tao Hongjing stroked his beard and sighed,
"Pindao has heard Zu Wenyuan talk about this "Zhushu" three times.
I listened to Junzhi again today, but most of it was still in the fog.
But every time the truth is tested, the results of the ancestors and father and son's calculations are roughly the same.
Pindao has only one way to worship, not to think about it. "
At this time, the holy minister had long lost the courage to fight for victory, and he did not dare to put on a contest other than expressing his willingness to learn from Min Zhi.
With this half-day emotional exchange, at night, you can talk about some relatively formal topics.
King Wei first thanked the Tianzhu Mission for their help,
With their participation, the gold content of this uncovered event naturally increased a bit.
It's just that Wei's scouts met the mission in the territory of Shu by chance.
Since it was a beautiful coincidence, the mission here naturally had another purpose.
So the king of Wei asked the holy minister very tactfully about his intention.
The holy minister stood up respectfully and began to introduce the difficulties encountered by the Ji Duo dynasty.
To the west of Congling, there used to be Guishuang, a great country.
After the disintegration of the empire and the rise of King Chaori, he regained northern Tianzhu and unified Central Tianzhu. The Jiduo dynasty established was very prosperous.
But since the death of King Chao Ri, Ji Duo has actually been going downhill.
The White Huns in the Kubin area rebuilt the Heda Empire, quickly took control of the former land of Guishuang, and began to encroach on the territory of Tianzhu regained during the reign of King Chaori.
By the time of King Yuri, the Heda Empire had invaded the Ganges River Basin and began to squeeze the strategic hinterland of the Jido Dynasty.
King Youri didn't want to sit still, so he sent an envoy to ask Wei for help.
The King of Wei pondered for a moment, then replied seriously,
"Da Wei and Ji Duo are thousands of miles apart.
It is separated from Xiaoqi in the south, separated by mountains outside the southwest, and has to go through the vast Western Regions in the west, and then it can reach Tianzhu by zigzagging south.
The geography of the mountains outside the mountains is not suitable for large-scale marches,
And Xiao Qi would never use the excuse to let Wei's army pass, which is a taboo for military strategists in the Central Plains.
Yao Sixia, please translate the allusion for me while translating.
The route to the west is even more tortuous.
My Great Wei's control over the Western Regions is not stable.
Rouran, Gaoche, Tuyuhun, Kangju and other major powers are all sensitive to our movements, and it is not wise to use a large army rashly.
Therefore, it is more difficult for my Great Wei to directly participate in the Tianzhu war.
But since the two countries intend to become friendly states, we naturally have no reason to ignore it.
My great Wei will send military experts and smelting craftsmen to Tianzhu,
But I also hope that Tianzhu can use something in exchange. "
After listening to Yao Sixia's translation, the holy minister was a little disappointed, but after thinking about it, it was true.
What King Wei promised is the greatest help they can provide right now.
It's just that I don't know what King Wei will ask for. Is it a special product of his hometown?
Its mountains and rocks are important strategic resources. At that time, only Tianzhu had property in the world. Unfortunately, the king of Wei didn't know about it.
When the sage minister raised a question, King Wei's answer made him laugh dumbfounded,
"I need the holy yellow dye from Tianzhu.
Today's Huaxia printing and dyeing Minghuang still uses the precious mineral deposits of Huangdi Chijing (chrome yellow).
This yellow ore powder is found in Hexi, and the output is extremely low.
I intend to use the yellow robe to replace the Han-made deep clothing, to restore the appearance of the Yellow Emperor's royal presence.
However, due to the scarcity of raw materials, it is really painful to use it for printing and dyeing.
I heard that the clothes of the holy monks in Tianzhu are all dyed yellow. I think your country must have special dye resources.
My state of Wei has no way to give you direct military assistance, so I don't speak much.
A little dye, should be no problem, right? "
The holy minister agreed immediately without hesitation.
King Wei's appetite is indeed not great, and he still has these authorizations.
Just talking about the holy yellow of Tianzhu, we have to talk about the sacred bull drowning in gold.
Although modern Indian scholars have proved through "rigorous experiments" that small gold can really be extracted from the urine of their holy cow Jier cattle,
But you all understand, it’s good not to talk about it.
However, it is not a fairy tale to insist that there are gods drowning in gold.
For example, the dye of holy yellow is indeed refined by drowning cows.
In ancient times, it was exported to Europe and Asia, and it was very valuable, and it did earn a lot of real money for Tianzhu.
Tianzhu veterinarians fed mangoes to cattle, and found that the digestive system of cattle cannot decompose the yellow pigment contained in mangoes, and will excrete all the colored substances through urine.
These cows can be used as dyes after being smelted and dried.
In the final analysis, the yellow pigment in the dye comes from mango, and through the action of bovine kidney, it becomes soluble and has good color solidity.
It can be described as a very original and environmentally friendly green technology.
"""""Knock on the blackboard time"""""
The costumes of Chinese emperors began to take Ming Huang Dagon dragon robes from the Sui Dynasty, and there are well-documented records at this time.But the Sui Dynasty was ruled by the Wei Dynasty, so this trend should have already started in the Northern Wei Dynasty.Since the Han Dynasty, the Twelve Chapters of the Yellow Emperor have not been dyed bright yellow, mainly because of the scarcity of dyes.But Tianzhu is close to the tropics, and there are more natural plants with bright colors, so there has always been no shortage of yellow dyes.The ox drowned Indian yellow mentioned in this article is a real ancient craft. The finished product was once exported to the British Empire and has a history of being used in the modern textile industry.
We haven't finished talking about the past in Tianzhu in the previous section.However, the history of Tianzhu is probably not the focus of the readers. Putting it aside for a while should not affect the reading mood too much.On the contrary, if there is no reasonable explanation for the two items of calendar and calendar, the author will probably receive the blade soon.
There are many things, without horizontal comparison, we will never know how much China was ahead of the world in ancient times.This is the case in mathematics.Aye Podo, a master of mathematics in India, has the same status as Zu Chongzhi in China.Let's skip the calendar part for now (we'll talk about it in the next few sections).There are three major breakthroughs in Ayebodo's mathematics: the deduction of pi to the fifth decimal place (actually four digits in actuarial calculation); summarizing the formula for calculating the area of a triangle and proposing the concept of suspected trigonometric functions; A breakthrough in understanding.
Based on these three points alone, compared with the three generations of Zu's family who were the masters of mathematics in China at that time, we can only reply with "呵~".
We listen to Westerners commenting on Chinese mathematics. Of course, they will affirm many facts that cannot be erased, such as Zu rate, square root algorithm and so on.But in general, they still have a deep discrimination against Chinese mathematics, saying that ancient Chinese mathematics did not have the concept of irrational numbers and the concept of trigonometric function calculations, so the calculations that can be performed are very preliminary.
Bah~
As mentioned in the main text of this article, China's Suanjing focuses on calculation and has an independent system, which is completely different from the Western one in concept.Modern mathematics in the West was developed using the vocabulary definitions of ancient Greece. If you think their concepts are accurate and their words are accurate, that is because of the advantages of the native language.As the author mentioned before, is "The Elements of Geometry" the original?Completely reread ancient Greek books in a modern language.
Indeed, China has never clearly put forward the concept of "irrational number".However, the mathematical crisis of irrational numbers did not come to a conclusion until the end of the nineteenth century in the West. The person who first discovered irrational numbers was thrown into the sea as a heretic and fed to the fish!If it is believed that the West took the lead in mastering irrational numbers because of the discovery of a small group of scholars who have been abandoned by the world, then can it be said that China's "Xuan Ye Theory" proves that China has mastered the truth of the universe?Can "Youyang Zazu" prove that China took the lead in landing on the moon?But China has indeed mastered the algorithm of square extraction, and there is a whole chapter of square extraction examples in "Nine Chapters of Arithmetic".Not only the square, but also the cube can be opened.This article only cites an example:
"Nine Chapters of Arithmetic Shaoguang" has another five steps of 39.Ask for square geometry?
The answer was: 25 and [-] steps.
The method of prescribing said: ... the specific algorithm of prescribing.
Square root is one of the basic algorithms in Chapter Nine Arithmetic.The calculation of square root and cube was quite mature in Zu Chongzhi's period. "Nine Chapters of Arithmetic" is equivalent to a junior high school textbook for one of the ancient six art numbers (this will be discussed later).Therefore, discussing issues similar to square root [-] is too naive in China, too naive!
About trigonometric functions, let's say this.Chinese mathematics does not use scales to record angles, and has always used trigonometric functions to record angles.That is, the Pythagorean Mystical Angle Method.Neither does India.We don't talk about those ambiguous statements, but only look at the essence. Isn't the essence of Pythagorean Xuan the triangular operation?
As early as in the "Zhoubi Suanjing" of the Zhou Dynasty, there was a saying that "Pythagorean shares are multiplied separately, and the formula is used to divide them".
"Nine Chapters of Arithmetic" says: The Pythagorean technique says: Pythagorean shares are multiplied separately, combined, and the square is divided, that is, the string.And the stock is multiplied by itself, and the string is multiplied by itself, and the rest is divided by the square, that is, the hook.Also hook the self-multiply, use the reduced string to multiply the self-multiply, and divide the rest by the square, that is, the stock.
This is China's own definition of trigonometric functions, sine = hook/string, cosine = strand/string...and so on.All trigonometric functions can be expressed by Pythagorean, and the values of these trigonometric functions can be used to mark the sizes of all angles.We have our own definitions, formulas and calculation methods, why should we copy the West?You said that China has not mastered the application of analytic geometry other than right triangle?Please, Descartes, the originator of analytic geometry, was a mathematician in the seventeenth century. Isn't it a bit unfair to compare with Zhang Cang and Geng Shouchang in the first century AD?
Chinese applications of triangles shine in surveying.American mathematician Frank J. Swetz said when he read "Sea Island Mathematical Classics" by Liu Hui, "China's achievements in mathematical measurement surpassed that of the West by about 1000 years." Master trigonometric complex calculations.When trigonometry was introduced to China, Chinese and Western scholars generally believed that Tang Ruowang and Xu Guangqi's "Da Chou" did not surpass the content of "Sea Island Suan Jing".Let’s take an example question about island arithmetic:
Today, it is hoped that there will be a white stone under Qingyuan.On the bank of Yanju, the hook is three feet high.Looking obliquely at the water's edge, the penetrating thigh is four feet five inches.Looking at Baishi, the next stock is two feet and four inches.Also set a heavy moment on the top, and the distance between them is four feet.Looking obliquely at the water bank from the end of the hook, it is four feet into the upper thigh.Looking at Baishi, the stock is two feet and two inches.What is the depth of the water?The answer is: one foot and two feet.
The technique said: Subtract the upper and lower shares of Wangshui, and multiply the upper shares of Wangshi as the upper rate.The upper and lower shares of Wangshi are subtracted from each other, and the lower rate is calculated by multiplying the upper shares of Wangshi.Subtract the two rates, and the remainder is the real moment; the multiplication of the two differences is the law.If the truth is the same as the law, you will get the depth of the water.
This sample question can be understood, high school ancient Chinese, trigonometry, geometry, all graduated.Since there is no way to explain this question without drawing a picture, you can only Baidu for the specific algorithm of this question.
What level does this "Sea Island Mathematical Classic" belong to in ancient mathematics textbooks?Like Nine Chapters of Arithmetic, it is also a junior high school textbook.This section is already a bit long. We will talk about the ancient mathematics textbooks, ancient counting methods and the magical "Zhushu" in the next chapter.
(End of this chapter)
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The savior of American comics? I am the evil god of the subspace!
Chapter 328 3 hours ago -
Ultimate Torment! The Yandere Movie Queen Is Madly in Love with Me
Chapter 289 5 hours ago -
Xuantian Immortal Cultivation Record
Chapter 840 5 hours ago -
Orderly tyrant
Chapter 225 5 hours ago -
Douluo: Qianyue was reborn, I am her own brother
Chapter 603 5 hours ago -
I created the Bureau of Anomaly Control
Chapter 752 13 hours ago -
Twenty Years of Cheating in the Royal Ancestral Land: I Am Invincible in the World
Chapter 619 16 hours ago -
The anime has gradually become perverted since the beginning of the game
Chapter 182 16 hours ago -
I have a wizarding world
Chapter 385 16 hours ago