In the Mathematics of the Tang Dynasty, I can only do 1 way to gamble!

Author:High Energy Institute of the C Time:2022.06.21

The following article comes from the WeChat public account, the author cleaner

Today's settings are like this: You hate mathematics too much, so you can cross the imperial examination in ancient times, and you want to memorize the reputation. It seems okay.

Indeed, most of the imperial examinations of the dynasties do not take a little more difficult mathematical problem.

But you cross the Tang Dynasty, alas.

The worst major in the Tang Dynasty

There is a central education institution called "Jiàn) in the Tang Dynasty. It is both a government agency and the highest institution.

There are 6 main parts of Guozijian. The relationship is roughly as shown in the figure below.

In fact, the specific situation is different in different periods. This is just an example based on the system of "New Tang Book · Election Book".

Theoretically, there are 4 "majors" that are open to civilian children: "Four Division Studies" are infinitely future, "law learning" is dim, and "book studies" and "counting learning" are only a miserable look. And when you go back and go back, you have become a "study major".

Entry school!

Come here, let's take a brief understanding of the learning system and see how many years can be in the early years.

The study system of calculation is 7 years. Entry conditions are also okay: tuition is a silk (not expensive at the time, because your breaking major is not promising), just pass the two rounds of exams (this breaking major is not volume).

After entering school, you have two classes to choose.

Learning content 丨 Drawing: Cleaner; Source: "New Tang Book · Election Chronicle" for example

Learn 10 books in the first class, and only 4 books in the second class. I advise you to choose the first class, because the concentrated coffee is strong, the concentrated uranium will explode, and the mathematical problem is concentrated? Who looks at who is big. Don't believe it.

Figure 丨 Author soul hand -painted

Go to school!

After the selection, the seven -year cold window is about to start.

During this period, a small test for ten days, a big test every year, and no winter and summer vacations. Fortunately, if you listen to me and choose the first class, most questions are really not difficult, and we will see them later.

The exam is an official!

Time is like an arrow. You pass the seventh -year -end exam in 9 years and finally ushered in the graduation exam. If your graduation test is also over, then ... there is another exam- "Ming Calculation" imperial examination.

The imperial examinations held by the Tang Dynasty were also divided into six types, and the pattern was a bit similar to the six "majors" of Guozi Supervisor. Needless to ask, the "Ming Calculation Department" you want to take is the worst.

Six types of exams 丨 Drawing: cleaner; Source: "New Tang Book · Election Jobs"

Let me briefly introduce how miserable you are.

The first is very low.

In the late period of the Tang Dynasty, "Books, Calculated in Jiupin Line" -Chopathic exams, you will have the opportunity to get the official position of the "from the nine products".

How low is this level? We usually say that official positions are small, and we use the saying of "Jiupin Sesame Officer".

Then the promotion was slow.

If there are no special circumstances, officials of the Tang Dynasty can generally be promoted every 4 years.

Your start is the lowest level "from the nine grades", which is separated from level 8 of the middle official position (county level) of Qipin, and the senior officials (state level) of the five grades are separated by level 16. In other words, you have finished your job in 7 years, and then you can take the exam of the Ming Dynasty immediately. If you do n’t retire for 64 years, you can be a big official.

Your long promotion road 丨 drawing: cleaner

However, according to the practice of the Tang Dynasty, a small official like you, at the age of seventy, the boss will urge you to "glory home" anyway. Anyway, I personally haven't seen any big official in historical materials.

However, there are always people like you to take the test. After all, you have been admitted to the preparation of civil servants!

Calculating students' homework

The students of mathematics in the Tang Dynasty are basically application questions. The theme is something that the ancients would come into contact in the daily life of the ancients. Like what kind of field weaving, digging dykes, selling rice staining food, dinner, stealing money to catch thieves ...

Judging from today's mathematical knowledge, most of the applications are quite simple, and basically do not require mathematical knowledge above junior high school. I will bring you a few questions today.

Question 1: So simple

"Today there are fifteen steps in Tianguang, from sixteen steps, ask for field geometry?"

- "Nine Chapters Arithmetic · Fang Tian"

translate:

The step is an ancient length unit, and 240 square meters are one acre. There is a fifteen -step and sixteen step -wide rectangular field. How big is its area?

Two questions: Chasing the problem!

There are 50 steps for those who are late today, and 70 steps for the disease. Those who are late are first, and the diseasedrs will post it in the future. Ask the delay to send the geometry first?

—— "Zhang Qiu Jian Couple Scriptures" Volume

translate:

The two exercise at a constant speed. Each unit can run 50 steps in each unit ("step" or that length unit); A Kuai can run 70 steps for so long.

A slowly ran, A Kuai chased again, and persistently ran 87 miles and 150 steps (300 steps = 1 mile) to go up. How far did A slow run the first time?

Figure 丨 Author soul hand -painted

Third question: still chase

Today, someone stole a horse and took it. For thirty -seven miles, the owner of the horse is aware of it, chasing 145 miles, less than twenty -three miles, and not chasing it today, asking for geometry.

—— "Zhang Qiu Jian Couple Scriptures" Volume

translate:

The thief stole the horse, and when he ran 37 miles, the owner began to chase. The owner chased 145 miles (about 77 kilometers) and did not run away. At this time, there was still 23 miles away from the thief. If the owner is perseverance, how far can you run to catch up?

Figure 丨 Author soul hand -painted

Fourth question: The encounter is five feet thick today, and the two rats are worn. The rats are one foot a day, and the mouse is one foot. The rats are self -doubling, and the mouse is half from half. Ask the geometry meeting? Wear geometry?

- "Nine Chapters of Arithmetic · Insufficient"

translate:

One wall, five feet thick (about 1.2 meters), each side has a mouse on each side. They are digging the holes, and they exercise at a constant speed every day.

On the first day, the two mouse dug a foot each. After that, the larger mouse was digging and more motivated, and decided to speed up 100%per day; the small mouse refused the inner roll, and digged 50%per day.

How long did the two mouse dug when you dig through this wall and how far he dug it.

Figure 丨 Author soul hand -painted

Question 5: Starting hard to start

Today, there are doctors, no more, 褭夫, Shangming, and princes. Want to make Gao Jue less, and get more time, ask each geometry?

- "Nine Chapters of Arithmetic · Destry"

translate:

When eating, every time the title increases N, the money is 1/(n+1). For example, if the minimum "prince" costs 6 yuan, it will only cost 3 yuan for "not more", "簪簪" spend 2 yuan, and "upper" will only spend 1.5 yuan ...

So, the five people adjacent to the juncture cost a total of a hundred dollars. How much does everyone pay for each person?

Jazz 丨 Map: Moisturizer

Question 6: annoying geometry

There are also around the field, three steps and four steps on Steel, one hundred and three steps, one of the two steps, one of the two steps, twelve steps and two steps. Ask for the field geometry?

- "Nine Chapters Arithmetic · Fang Tian"

translate:

There is a ring -shaped field, but it may not be a whole circle. Its inner arc is 62.75 steps, the outer arc is 113.5 steps, and the spacing of the two arcs is 12+2/3 steps. How big is this field?

Figure 丨 Author soul hand -painted

Question 7: The last big question!

Finally, let's take a look at the most difficult question, it comes from the "Ancient Ancient Classics".

There are only twenty questions in the book "The Calm Calculation", but in the Tang Dynasty's academic system, it has to be studied for four years, and the average of five a year is learned. The content in this book is quite difficult to be ordinary people today, especially when the calculator is not allowed.

Let's look at the most famous three questions.

The dyke of the fake order is six feet, eight feet and two inches in the west, and the upper and lower east are six feet and two inches. The east is less than three feet high in the west, and the east is four feet and nine inches high in the east. There are 6,724 people in the county, 16,777 in B County, 13,488 people in B County, and 12,781 in Ding County. Four counties wearing nine stone nine -nine buckets and two liters each day. Each person often accumulates 11 feet four inches and thirteen inch a day. Wear a foot with a foot to get eight fighting. The ancients negative to the soil, two buckets, four liters of eight -lit, and 192 steps, 62 a day. Today, crossing the mountains and soil, the flat road is only one step, the mountains are thirty steps high, the water width is one twelve steps, the mountains are three four, the downhill is six, the water line is one or two, the flat road is ten plus one plus one , Load 14 steps. Reduce one person's work. Four counties are created together, and one -day service. From the east and A today, followed by B, C, and Ding. Question: Give it to oblique, Zhengtong and high, and each person.

- "Ancient Ancient Classics" Third question

I drew Zhang Tu to help you understand, although you are likely to be difficult to understand.

Figure 丨 Author soul hand -painted

translate:

It is known that AB = CD, EF = GH, AC = EG, AE = CG, AC∥BD∥FH, AB∥EF, CD∥GH, AC⊥AE, CI⊥BD, JG⊥FH, BD is 682 inches longer than AC AC than AC , FH is 62 inches longer than EG, CI is 310 inches longer than GJ, EG is 49 inches longer than GJ, CG is 4769 inches longer than GJ, and the entire hexagonal area is 275924800 cubic inch (this number is not set to the question, but is in the question. The other data is calculated, but the algorithm is very complicated, and the three words are unclear, you are fine by default). Find the length of AC, BD, AE, FH, CI, GJ.

Guokr

In the end, you have to talk about it in ancient times and finally finished mathematics and after the test, but if the time is not appropriate, the fifth generation will be abolished: in the fifth generation period, the status of Ming Calculation has continued to decline, and from "unimportant" to change to change to change to change, from "unimportant" to change to change to change to "does not exist". Until modern times, the relatively complicated mathematical knowledge returned to the ranking of regular education examinations.

references

[1] "New Tang Book", China Book Company 1975.

[2] "Datang Sixth Code", Sanqin Publishing House in 1996 Yingchi Guangchi.

[3] "Han Book", China Book Company 1962.

[4] "Nine Chapters of Arithmetic Fine Articles", "Island Film Sutra", "Sun Tzu's Classics", "Five Cao Cao Classics", "Digital Records", "Xia Houyang's Classics" Volume 1041 photo book, Shanghai Ancient Books Publishing House 2002.

[5] "Zhou Ying Calcus", "Five Classic Arithmetic", "Zhang Qiu Jian Calcus", "Anti -Ancient Classics (Fine Grass)", "New Book Integration" Volume 40, 41 Essence

[6] Qiu Guangming's "Balance of Termidity of China", Science Press 1992.

[7] "Old Tang Book", China Book Company 1975.

Author: cleaners

Edit: Li Xiaogui

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